Magnetic and transport properties of ferromagneticinfo.ifpan.edu.pl/ON-1/on13_pliki/phd_iza.pdf ·...

Magnetic and transport properties of ferromagneticsemiconductor multinary alloys

Pb1−x−y−zMnxEuySnzTe and Ga1−xMnxAs

Izabela Kudelska

PhD Dissertation

Institute of PhysicsPolish Academy of Sciences

Thesis Supervisor doc. dr. hab. W. Dobrowolski

Warsaw 2004

Mojemu kochanemu Synkowi Olesiowi,który towarzyszył mi

przez cały okres pisania pracy

3

PODZIEKOWANIAPragne serdecznie podziekowac mojemu Promotorowi doc. dr hab. W. Dobrowol-

skiemu za stała, wszechstronna pomoc i opieke nad praca, pouczajace rozmowy izycz-liwosc w trakcie wykonywania pracy.Prof. dr J. Furdynie bardzo dziekuje za inspirujace dyskusje i wprowadzenie w tematykebadan ferromagnetycznych kryształów Ga1−xMnxAs.Prof. dr M. Dobrowolskiej dziekuje bardzo za opieke i pomoc w badaniach.Dr M. Arciszewskiej serdecznie dziekuje za pomoc przy wykonywaniu pracy izyczliwezainteresowanie wynikami badan.Doc. dr hab. T. Wojtowiczowi dziekuje bardzo za wyhodowanie kryształów Ga1−xMnxAsuzytych do badan i pomoc przy powstawaniu pracy.Pragne podziekowac dr X. Liu za pomiary namagnesowania oraz wyhodowanie krysz-tałów Ga1−xMnxAs, W. Lim za pomoc w badaniach transportowych oraz dr Y. Sasaki zawyhodowanie kryształów Ga1−xMnxAs badanych w pracy.Współpraca z pracownikami Laboratorium Silnych Impulsowych Pól Magnetycznych wTuluzie była bardzo pomocna. W szczególnosci pragne podziekowac dr O. Portugall zapomoc w pomiarach magnetotransportowych, dr M. Goiran za pomoc w pomiarach mag-netooptycznego efektu Kerra, a takze dr E.Haanappel, dr J.-M. Broto, dr H. Rakoto, dr B.Raquet za pomoc w pomiarach magnetotransportowych.Pragne takze podziekowac Prof. dr V. Dugaev za cenne i inspirujace dyskusje.Prof. dr W. Walukiewiczowi oraz dr K. M. Yu dziekuje za pomiary c-PIXE oraz c-RBS.Bardzo dziekuje dr J. Domagale za pomiary dyfrakcji rentgenowskiej.Dr E. I. Slynko oraz dr V. E. Slynko dziekuje za wyhodowanie kryształówPb1−x−y−zMnxEuySnzTe uzytych do badan.Dr I. M. Fita dziekuje za pomiary namagnesowamia w cisnieniu hydrostatycznym.Pragne takze podziekowac Prof. dr hab. R. Szymczak oraz dr Baranowi za pomiary nam-agnesowania.Wszystkim pracownikom i doktorantom z Odziału Fizyki Półprzewodników Półmagne-tycznych dziekuje za stworzenie miłej izyczliwej atmosfery.Mojemu Mezowi Arkowi pragne podziekowac za nieustanne wspieranie mnie i cierpli-wosc.

CONTENTS

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2. Experimental techniques. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.2 The experimental technique of energy dispersive X-ray fluorescence

(EDXRF) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.3 The experimental setup for magnetotransort measurements . . . . . . . . 122.4 AC/DC magnetometer . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.5 The measurements in the range of high pulsed magnetic fields . . . . . . 182.6 The experimental setup for Kerr effect measurements . . . . . . . . . . . 19

3. Samples of Pb1−x−y−zMnxEuySnzTe and Ga1−xMnxAs. . . . . . . . . . . . . 213.1 Ferromagnetic bulk crystals of Pb1−x−y−zMnxEuySnzTe . . . . . . . . . 213.2 Ferromagnetic layers of Ga1−xMnxAs. . . . . . . . . . . . . . . . . . . . 21

4. Transport and magnetic investigations of Pb1−x−y−zMnxEuySnzTe . . . . . . . 274.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.2 Transport characterization of Pb1−x−y−xMnxEuySnzTe samples . . . . . . 304.3 Magnetic measurements of Pb1−x−y−zMnxEuySnzTe mixed crystals . . . 34

5. Low temperature annealing studies of Ga1−xMnxAs . . . . . . . . . . . . . . . 485.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485.2 The procedure of annealing . . . . . . . . . . . . . . . . . . . . . . . . . 515.3 The results of zero-field resistivity measurements . . . . . . . . . . . . . 515.4 The results of magnetotransport measurements . . . . . . . . . . . . . . 565.5 The results of SQUID measurements . . . . . . . . . . . . . . . . . . . . 645.6 The results of magnetooptical Kerr effect measurements . . . . . . . . . . 69

5.6.1 Introduction - magnetooptical Kerr effect . . . . . . . . . . . . . 695.6.2 The results of MOKE measurements for the as-grown and an-

nealed GaMnAs epilayers . . . . . . . . . . . . . . . . . . . . . 715.7 The channeling experiments - the results of c-RBS and c-PIXE measure-

ments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 845.8 The results of diffraction (HRXRD) measurements . . . . . . . . . . . . 90

6. Conclusions and Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . 996.1 Pb1−x−y−zMnxEuySnzTe . . . . . . . . . . . . . . . . . . . . . . . . . . 996.2 Ga1−xMnxAs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 996.3 Suggestions for further studies . . . . . . . . . . . . . . . . . . . . . . . 101

Contents 5

7. Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1037.1 Appendix 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1037.2 Appendix2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

1. INTRODUCTION

In this thesis, the results of a study of the magnetic and transport properties of III-V aswell as IV-VI based ferromagnetic semimagnetic semiconductors will be presented. Twosystems of ferromagnetic semiconductor multinary alloys: PbSnMnEuTe and GaMnAswere systematically investigated.

The common characteristic of two investigated semimagnetic materials,Ga1−xMnxAs and Pb1−x−y−zMnxEuySnzTe, is mediation of free holes in ferromag-netic interactions of Mn ions. The mechanism of exchange interactions is well exploredfor Pb1−x−yMnxSnyTe mixed crystals. The RKKY interaction is known to be responsiblefor the ferromagnetic properties of IV-VI semimagnetic semiconductors. However,the origin of ferromagnetism in Ga1−xMnxAs is still under active discussion. Theexperimental studies of physical properties are necessary to examination the origin offerromagnetism in this material.

Recently, manipulation of the spin degree of freedom in semiconductors has becomea focus of interest. The main goal of spintronics is to make use of both charge and spindegrees of freedom in semiconductors. In the context of spin electronics particularlyinteresting are ferromagnetic semimagnetic semiconductors. In the case of Mn-based IV-VI, III-V and II-VI SMSC’s the ferromagnetism can be observed provided that the holeconcentration is sufficiently high.

Understanding of the carrier mediated ferromagnetism was initiated by a study offerromagnetism in IV-VI based SMSC’s. In this class of materials deviations from stoi-chiometry result in the carrier density sufficiently high to produce strong ferromagneticinteractions between the localized spins. Ferromagnetic properties are observed for IV-VI semimagnetic materials with Mn and with the concentration of conducting holesp≥ 2-3 1020 cm−3. However, in the case of ferromagnetic IV-VI semimagnetic materials(such as PbSnMnTe), one have to admit that the ferromagnetic characteristics (magneticanisotropy, coercive field) are not superior to other magnetic materials. Thus, applica-tions related to ferromagnetic properties of these materials can be rather related to hybridsystems with IV-VI electronic devices incorporating the ferromagnetic element with con-trolled magnetic properties. An additional obstacle for these materials is the low tempera-ture of ferromagnetic phase transition. However, two important features give IV-VI semi-magnetic materials the distinguished position within the whole family of semimagneticsemiconductors. First, the variety of magnetic properties observed in Mn based IV-VISMSC’s. Second, the characteristic feature are semi-metallic electric properties with thewell developed methods of control of carrier concentration. Pb1−x−y−zMnxEuySnzTe area unique compounds in which the interplay between magnetic and electronic propertiescan be observed and studied. Particularly, the carrier induced paramagnet-ferromagnetand ferromagnet-spin glass transitions are present [1], [2].

Recently, due to the rapid progress achieved in SMSC’s technology, namely non-equilibrium growth methods, the ferromagnetic phase transition was observed in III-V

1. Introduction 7

semimagnetic materials. For the first time, by using low-temperature molecular beamepitaxy (LT-MBE;T < 3000C), a III-V based SMSC, In1−xMnxAs layers were success-fully grown in 1989 [3] and shown to exhibit hole-induced ferromagnetic ordering atlow temperatures. Development of this technique resulted in the successful epitaxy ofGa1−xMnxAs [4], [5]. The III-V based compounds are prospective materials for spinelectronics because are already in use in everyday electronics. The low temperature (LT)MBE grown Ga1−xMnxAs, has become a favorite material for spintronics when it wasshown [6] that the substitution of Mn for Ga in GaAs leads to ferromagnetism at tem-peratures as high as 110K. For a long time this was the highest Curie temperatureTC

observed in semimagnetic semiconductors. For the spintronic applications, however, thetemperature of the transition to the ferromagnetic phase has to be considerable increased.

In this thesis, the systematic measurements of magnetic AC susceptibility, magneti-zation as well as transport characterization of bulk samples of Pb1−x−y−zMnxEuySnzTemultinary alloy were performed. The as-grown as well as annealed samples with differentconcentration of Mnx as well as Euy were investigated. The paramagnet-ferromagnet aswell as ferromagnet-spin glass transitions were observed and studied. The results of mag-netic and transport studies showed that by introducing of two types of magnetic ions intoIV-VI semiconductor matrix, one can change the magnetic properties of the investigatedsemimagnetic material.

The variety of experimental techniques were used to explore the physical properties ofGa1−xMnxAs epilayers. The transport, magnetotransport, magnetic, structural as well aschannelling experiments were carried out and analyzed. The magnetooptical Kerr effectstudies allowed to explore the magnetooptical properties of the investigated samples. Theas-grown as well as annealed at various conditions samples were investigated. The mainsubject studied is the role of Mn interstitial in Ga1−xMnxAs epilayers. The magnetic,transport, structural and channeling experiments indicated that the formation of interstitialMn ions plays a crucial role in controlling the ferromagnetic transition in GaMnAs. Forthe first time it is shown that by a proper choice of annealing conditions (temperature,time, flow of the gas) the limit of the Curie temperature of Ga1−xMnxAs epilayers (TC

∼ 110K) can be shifted to much higher values (up to 127K for the sample with high Mnconcentrationx∼ 0.08) [7]. The results presented in the thesis initiated further studies oflow temperature annealing in many laboratories. At present, Curie temperature exceeding160K was reported [8]. This progress has been achieved basically though optimization ofpost-growth annealing time and temperature.

The variety of experimental techniques were used in the studies presented in the thesis.The measurements of energy dispersive X-ray fluorescence (EDXRF), magnetotransportstudies (up to 13T using superconducting magnet), AC magnetic susceptibility as wellas DC magnetization (up to 9T) by use of 7229 LakeShore Susceptometer/Magnetometersetup were performed in Division ON-1 Physics of Semiconductors of Institute of PhysicsPolish Academy of Sciences in Warsaw.

The results were obtained in collaboration with many groups. The XRD as well asRHEED measurements were carried out in Department of Physics, University of NotreDame. High resolution X-ray diffraction studies as well as the standard powder X-raymeasurements were performed in Laboratory of X-ray and Electron Microscopy Re-search, Group of Applied Crystalography, Institute of Physics Polish Academy of Sci-ences in Warsaw.

The transport as well as magnetotransport investigations in the static magnetic field

1. Introduction 8

were carried out in Department of Physics, University of Notre Dame (up to 0.5T by useof classical electromagnet; up to 5T by use of superconducting magnet). The magne-totransport measurements in high pulsed magnetic fields (up to 55T) were performed inLaboratoire National des Champs Magnetiques Pulses Toulouse.

The magnetization measurements under hydrostatic pressure were carried out in Di-vision of Physics of Magnetism, Group of Phase Transitions, Institute of Physics PolishAcademy of Sciences in Warsaw. The SQUID measurements were performed in Depart-ment of Physics, University of Notre Dame and Division of Physics of Magnetism, Groupof Phase Transitions, Institute of Physics Polish Academy of Sciences in Warsaw. Indi-rect magnetization measurements were also performed. The magnetooptical Kerr Effect(MOKE) was measured in high pulsed magnetic fields (up to 25T) in Laboratoire Nationaldes Champs Magnetiques Pulses Toulouse.

The channeling experiments i.e. channeling Rutherford backscattering (c-RBS) andchanneling particle-induced X-ray emission (c-PIXE) measurements were performed inMaterial Science Division Lawrence Berkeley National Laboratory.

The thesis is organized in the following way. Chapter 1 describes selected experimen-tal techniques used in the studies. The characterization of the samples is given in Chapter2. The results of transport and magnetic measurements of Pb1−x−y−zMnxEuySnzTe crys-tals are presented and analyzed in Chapter 3. The results of experimental studies of LTGa1−xMnxAs epilayers: the procedure of annealing, the results of zero-field resistivity,magnetotransport, magnetic, channelling as well as structural measurements are presentedand discussed in Chapter 4. The summary and outlook is given in Chapter 5.

The results presented in this thesis were partially published in the papers:

1. Kuryliszyn I., Arciszewska M., Abdel Aziz M.M., Slynko E.I., Slynko V.I., DugaevV.K., "In quest of Mn-Eu interaction in IV-VI mixed crystals", Proc. 9th Int. Conf.On Narrow Gap Semiconductors, ed. by N. Puhlman, H.-U. Müller, M. Von Orten-berg, Humboldt University Berlin, p. 96-98 (2000).

2. Yu K.M., Walukiewicz W., Wojtowicz T., Kuryliszyn I., Liu X., Sasaki Y., FurdynaJ.K.,"Effect of the location of Mn sites in ferromagnetic Ga1−xMnxAs on its Curietemperature", Phys. Rev. B, vol.65, p. 201303(R), (2002).

3. Kuryliszyn I., Wojtowicz T., Liu X., Furdyna J., Dobrowolski W., Broto J.-M., GoiranM., Portugall O., Rakoto H., Raquet B.,Transport and magnetic properties of LTannealed Ga1−xMnxAs", Acta Phys. Pol. A, vol.102, No 4-5, p.659, (2002).

4. Kuryliszyn I., Wojtowicz T., Liu X., Furdyna J.K., Dobrowolski W., Broto J.-M.,Goiran M., Portugall O., Rakoto H., Raquet B., "Low Temperature annealingstudies of Ga1−xMnxAs", Journal of Supercondactivity (Incorporating Novel Mag-netism), vol. 16, No 1, p. 63, (2003).

5. Yu K.M., Walukiewicz W., Wojtowicz T., Kuryliszyn I., Liu X., Sasaki Y., FurdynaJ.K., "Thermodynamic Limits to the maximum Curie Temperature in GaMnAs",Proceedings- 26th International Conference on the Physics of semiconductors, Ed-inburgh 2002.

1. Introduction 9

6. Racka K., Kuryliszyn I., Arciszewska M., Dobrowolski W., Broto J.-M., Goiran M.,Portugall O., Rakoto H., Raquet B., " Anomalous Hall Effect in Sn1−x−yMnxEuyTeMixed Crystals", Journal of Supercondactivity, (Incorporating Novel Magnetism),vol. 16, No 2, p. 289, (2003).

7. Furdyna J.K., Liu X., Lim W.L., Sasaki Y., Wojtowicz T., Kuryliszyn I., Lee S., YuK.M. and Walukiewicz W., "Ferromagnetic III-Mn-V Semiconductors: Manipula-tion of Magnetic Properies by Annealing, Extrinsic Doping, and Multilayer De-sign", Journal of the Korean Physical Society, vol. 42, p. S579, (2003).

8. Kuryliszyn-Kudelska I., Domagala J.Z, Wojtowicz T., Liu X., E. Łusakowska, Do-browolski W., Furdyna J.K., "The effect of Mn interstitials on the lattice parameterof Ga1−xMn1−xAs", J. Appl. Phys. 95 (2) 603 (2004).

9. Kuryliszyn-Kudelska I., Wojtowicz T., Liu X., Furdyna J.K., Dobrowolski W., Do-magala J.Z., E.Łusakowska, M.Goiran, E.Haanappel, O. Portugall,"Effect of an-nealing on magnetic and magnetotransport properties of Ga1−xMnxAs epilayers",Journal of Magnetic Materials and Magnetism 272-276, p. e1575, (2004).

10. Kacman P., Kuryliszyn-Kudelska I., "The role of Interstitial Mn in GaAs-based Di-lute Magnetic Semiconductors", Lecture Notes in Physics (in press)

2. EXPERIMENTAL TECHNIQUES

2.1 Introduction

Chapter 2 includes briefly description of the selected experimental methods which wereused by author.

The chemical composition of the investigated samples was determined by use ofdifferent techniques. The X-ray dispersive fluorescence analysis measurements (forPb1−x−y−zMnxEuySnzTe samples), X-ray diffraction (XRD) as well as high resolusion X-ray diffraction (HRXRD) studies and reflection high energy electron diffraction (RHEED)measurements (for Ga1−xMnxAs epilayers) were employed to characterize the investi-gated samples. Section 1.1 contains briefly description of Tracor X-ray Spectrace 5000 -automated EDXRF analyzer.

The structural characterization of both - Pb1−x−y−zMnxEuySnzTe as well asGa1−xMnxAs epilayers was carried out. X-ray diffraction (Ga1−xMnxAs samples), highresolution X-ray diffraction (Ga1−xMnxAs samples) and standard powder X-ray measure-ments (Pb1−x−y−zMnxEuySnzTe samples) were performed.

The transport (resistivity) as well as magnetotransport (Hall effect, anomalous Halleffect, magnetoresistance) properties of investigated ferromagnetic materials were stud-ied by use of several experimental setups. The resistivity measurements of Ga1−xMnxAssamples were performed in the temperature range between 10K and 300K by use of ahelium flow cryostat. The DC six probe technique was used for the magnetotransportmeasurements. Section 2.2 describes the experimental setup for magnetotransport mea-surements built by author in Department of Physics University of Notre Dame. The sys-tem together with the cryostat and superconducting magnet allows to perform the standardDC six probe technique measurements in magnetic field up to 5T and in the temperaturerange between 1.3 and 300K. Section 3 of this Chapter describes briefly pulsed magneticfields.

The magnetic studies (AC susceptibility and magnetization investigations) were per-formed by use of several techniques. The Pb1−x−y−zMnxEuySnzTe samples were ex-plored using AC/DC magnetometer - AC susceptibility as well as DC magnetization (upto 9T) were measured. The principle of operation and schematic figures of the 7229LakeShore Susceptometer/Magnetometer setup are shown in Section 2.4. Additionally,the magnetization measurements under hydrostatic pressure were performed using the vi-brating sample magnetometer for Pb1−x−y−zMnxEuySnzTe samples. For Ga1−xMnxAsepilayers magnetization studies were performed. First, directly magnetization investiga-tion were carried out by use of SQUID magnetometer. Second, magnetoptical Kerr effect(MOKE) were performed. The experimental setup for MOKE measurements is describedin section 2.5.

The channeling experiments - channeling particle-induced X-ray emission (c-PIXE)as well as channeling Rutherford backscattering (c-RBS) were performed for GaMnAs

2. Experimental techniques 11

samples. The principle of channeling experiments is briefly described in Section 7 ofChapter 5.

2.2 The experimental technique of energy dispersive X-ray fluorescence(EDXRF)

The chemical composition of IV-VI semimagnetic semiconductors was determined by X-ray dispersive fluorescence analysis technique. This technique allows for determination ofchemical composition of the samples with uncertainty of 10%. The experimental setup -X-ray beam geometry is shown schematically in Figure 2.1. The Tracor X-ray Spectrace5000 is an automated energy dispersive X-ray fluorescence (EDXRF) analyzer. It can beused for nondestructive elemental analysis of solids and liquids.

Fig. 2.1: The schematic view of the Tracor X-ray Spectrace 5000.

The principle of operation is very simple. The primary X-rays from X-ray tube hitthe sample and induce the emission of secondary X-rays by the elements contained in thesample.

The relative intensity of an X-ray spectral line excited by monochromatic radiationcan be computed for a given element and known spectrometer geometry using followingequation:

IL = I0ωAgLrA − 1

rA

dΩ

4π

CAµA(λpri) csc(φ)

µM(λpri) csc(φ) + µM(λL) csc(Φ)(2.1)

where:IL is the analyte line intensityI0 is the intensity of the primary beam with effective wavelengthλpri

λpri is the effective wavelength of the primary X-rayλL is the wavelength of the measured analyte linegL is the fractional value of the measured analyte line L in its series


rA is the absorption edge jump ratio of analyte ACA is the concentration of analyte AdΩ/4π is the fractional value of the fluorescent X-ray that is directed toward a detectorµA(λpri) is the mass absorption coefficient of analyte A forλpri

µM (λpri) is the mass absorption coefficient of the matrix forλpri

µM (λL) is the mass absorption coefficient of the matrix for analyte lineλL

φ is the incident angle of the primary beamΦ is the takeoff angle of fluorescent beam

The Spectrace 5000 uses a low power X-ray tube (less than 50 watts) with a rhodiumanode target. The X-ray tube generates the X-rays that are incident upon the sample soas to cause the sample to fluorescence. The X-rays emitted by the anode pass through a0.005" Beryllium window. Then the beam is collimated and filtered. The collimator andX-ray tube define the illumination beam. To minimize scattering, the detector acceptanceis 900 from the incident beam. The sample is placed at the intercept of the two beams asis shown in Figure 2.1. Liquid nitrogen inside a dewar cools the Si(Li) detector to reducenoise caused by the leakage current in the detector.

2.3 The experimental setup for magnetotransort measurements

The experimental setup for transport measurements presented in this section was builtby author in Department of Physics University of Notre Dame. Figure 2.2 and Figure2.3 show schematically the principle of operation of the system. The system was builtmaking use of Oxford Instruments optical cryostat and superconducting magnet. Themain advantage of this system is possibility of carrying out both magnetooptical as wellas magnetotransport investigations. One of the application example are magnetotransportmeasurements with simultaneous optical excitation of the sample.

The system allows to perform magnetotransport studies in magnetic field up to 5T andin the temperature range between 1.3K and 300K.

The principle of operation involves the standard DC six probe technique. The 220Keithley Current Source serve as a source of DC current steering the sample, HP DMMis used for conductivity voltage measurements and 2001 Keithley DMM for Hall voltagemeasurements (see Figure 2.2). The Hall probe mounted inside the cryostat allows fordetection of magnetic field. During the experiment the temperature is collected also.

Additionally, the configuration with 7001 Keithley Scanner and 7065 Hall Card allowsto study high resistivity samples as is shown in Figure 2.3. In this case the 2001 KeithleyDMM is used to collect both the conductivity as well as Hall signal.

In the present thesis the described experimental setup was used for magnetotransportinvestigations of GaMnAs epilayers with typical resistance of 1 kΩ. In this case theconfiguration shown in Figure 2.2 was used.

Additionally, employing the second Lake Shore power supplier connected in parallelwith Oxford Instruments power supplier (see Figure 2.4) allows for fluently reversionthe direction of magnetic field (passing through zero of magnetic field). In particular, thehysteresis loops of Hall voltage were measured using two power suppliers.


Cryostat &

Superconducting Magnet

HP DMM (Magnetic Field)

Current Source

Sample

Hall Probe

R

Temperature Controller

Oxford Instruments Power Supplier

HP DMM (Temperature)

Keithley DMM 2001

VH

Current Source Keithley 220

HP DMM

Vσ

Fig. 2.2: The experimental setup for magnetotransport measurements.

2.4 AC/DC magnetometer

The magnetic properties of IV-VI semimagnetic semiconductors were investigated by useof 7229 LakeShore Susceptometer/Magnetometer system. The experimental setup pre-sented schematically in Figure 2.5 allows to perform AC susceptibility as well as DCmagnetization measurements. The specifications of the setup are shown in Table 2.1.

The principle of operation of AC susceptometer involves subjecting the sample to asmall alternating magnetic field. The flux variation due to the sample is picked up by asensing coil surrounding the sample and the resulting voltage induced in the coil is de-tected. This voltage is directly proportional to the magnetic susceptibility of the sample.The alternating magnetic field is generated by a solenoid which serves as the primary ina transformer circuit. The solenoid is driven with an AC current source with variableamplitude and frequency. Additionally, a DC field may also be applied by supplying aDC current to the primary coil. Two identical sensing coils are positioned symmetricallyinside of the primary coil and serve as the secondary coils in the measuring circuit. Fig-ure 2.6 shows a cross-sectional view of the coil assembly. The two sensing coils areconnected in opposition in order to cancel the voltages induced by the AC field itself orvoltages induced by unwanted external sources. Assuming perfectly wound sensing coilsand perfect symmetry, no voltage will be detected by lock-in amplifier when the coil as-sembly is empty. When a sample is placed within one of the sensing coils, the voltagebalance is disturbed. The measured voltageU is proportional to the susceptibility of the


Cryostat &

Superconducting Magnet

HP DMM (Magnetic Field)

Current Source

Hall Probe

R

Temperature Controller

Oxford Instruments Power Supplier

HP DMM (Temperature)

Keithley DMM 2001

VH, Vσ

Current Source Keithley 220

Keithley 7001 Scaner

+ 7065 Hall Card

Sample

Fig. 2.3: The experimental setup for magnetotransport measurements (configuration with 7001Keithley Scanner and 7065 Hall Card).

Coil

R

Oxford Instruments Power Supplier I

Lake Shore Power Supplier II

HP DMM

Fig. 2.4: The configuration with two power suppliers (Oxford Instruments and Lake Shore powersupplier) connected in parallel. This configuration allowed to reverse fluently the direc-tion of magnetic field.


Tab. 2.1: Specifications of 7229 LakeShore Susceptometer/Magnetometer system.

Temperature Range: From 1.3 K to 325 K

Accuracy:±0.5% of T

Stability:±0.1K

AC/DC Magnetic Field (Primary Coil) Range: from 0.00125 gauss to 20 gauss

Accuracy:±1.0%

Stability:±0.05%

Frequancy: from 1Hz to 10kHz

AC Susceptibility Sensitivity to 2 · 10−8 emu

DC Moment Sensitivity 9 · 10−5 emu

Superconducting Magnet SpecificationsField range:±90000 gauss (±9 Tesla)

Accuracy:±1.0% of setting

Accuracy:±1.0% of setting

Remnant field: 30 gauss

(< 15 gauss after demagnetization cycle)

sample and depends on a number of other experimental parameters:

U = (1/α)mfBχ (2.2)

whereU is measured voltage,α is calibration coefficient,m is sample mass,f is frequencyof AC field, B is magnetic field andχ is volume susceptibility of sample.

The calibration coefficient is dependent on the sample and coil geometry and is ex-perimentally determined by use of standard materials with a known susceptibility andmass.

The sample susceptibility has the following form:

χ = αU/mfB (2.3)

The absolute accuracy of the susceptibility depends on the accuracy with which all exper-imental parameters in the equation above can be determined.

The AC susceptometer allows to measure both the real (in phase)χ’ as well as imag-inary (out of phase)χ" component of susceptibility. As shown in Figure 2.5, the lock-indetector requires a reference signal which is at the same frequency and in phase with thecurrent from AC current source. The reference signal serves two purposes. It tunes thelock-in amplifier to the frequency of the reference signal, and the lock-in amplifier pro-vides an outputEout which is sensitive to the phase differenceΦ between the input signalEin and the reference signal:

Eout = Ein cos(Φ) (2.4)


The measurement has two contributions to the phase angleΦ. One contribution arisesfrom the circuit itself. The second contribution to the phase shift arises from the signaldue to the sample. Information about the phase angleΦ can be obtained through the phaseadjust feature on the lock-in, that introduces a phase shiftΘ in the reference channel ofthe lock-in. The output is modified as follows:

Eout = Ein cos(Φ−Θ) (2.5)

"Phasing" a lock-in amplifier refers to the process of setting the phase shiftΘ equal toΦ.However, the lock-in amplifier is most accurately phased by adjusting the phase for a zerooutput and then shifting the phase setting by 900.

The proper separation ofχ’ and χ" requires that the phasing be performed with atest sample with a knownχ"=0 (paramagnetic, insulating sample). Once this phase isdetermined, the lock-in amplifier signal measured atΘ will be proportional toχ′ and thesignal measured atΘ + 900 will be proportional toχ".

In order to maintain consistency in the data acquisition and to guarantee that no in-formation is lost for future analysis, all dual phase data are measured with the lock-inamplifier phase set to 00 and 900. The phase angleΘ is then used in the data analysis toconvert the measured voltages to the equivalent in phase and out of phase voltage signal:

U ′ = U0 cos(Θ) + U90 sin(Θ) (2.6)

U” = U90 cos(Θ)− U0 sin(Θ) (2.7)

whereU0 is lock-in voltage at 00, U90 is lock-in voltage at 900, U’ is in phase voltagereading for sample (voltage at phase angleΘ), U" is out of phase voltage reading forsample (voltage at phase angleΘ + 900).

The voltageU’ is then used to determine the measured susceptibilityχ′:

χ′ = αU ′/mfB (2.8)

The imaginary component of the measured susceptibility is determined from the followingrelationship:

χ” = −αU”/mfB (2.9)

The sign difference arises from the phasing conventions used in the 7229 LakeShore Sus-ceptometer.

The measurement of the magnetic moment is performed by using what has tradition-ally been called an extraction technique. This terminology is used generally to describeany method which relies on detecting a flux change as the sample is removed (extracted)from a sensing coil. The change in flux is then related directly to the moment of thesample.

The configuration of 7229 LakeShore Susceptometer is adapted to perform such anextraction measurement by disabling the AC current source and replacing Lock-in Am-plifier with a high-speed integrating digital voltmeter (DVM) (look at the Figure 2.5).The stepping motor is then used to move the sample between the centers of the two sec-ondary coils. Since the DVM can operate on a much faster time scale than the samplemovement, the output voltage can be recorded. The integral of the voltage over time canthen be determined and directly related to the moment of the sample:

M = klv (2.10)


whereM is magnetic moment,k is DC moment calibration coefficient,lv =∫

vdt isvoltage integral over time.

The DC moment calibration coefficient (k) is closely related to the AC susceptibilitycalibration coefficient (α). Both coefficients relate the flux coupled between a magnetizedsample and a sensing coil.

k = πα (2.11)

Multiple "scans" (the single scan is defined as a moving the sample from coil 1 to coil 2and then back to coil 1 again) can be performed and averaged to yield measurements withgreater precision.

The mass magnetization or the volume magnetization cam be determined by dividingthe moment by the appropriate quantity.

Fig. 2.5: Experimental setup for AC susceptibility/DC magnetization measurements - 7229LakeShore Susceptometer/Magnetometer system.


Fig. 2.6: The cross-sectional view of the coil assembly. The two sensing coils are connected in op-position in order to cancel the voltages induced by the AC field itself or voltages inducedby unwanted external sources.

2.5 The measurements in the range of high pulsed magnetic fields

The Ga1−xMnxAs epilayers were investigated in the range of high magnetic fields. Thepulsed magnetic fields were used to perform DC magnetotransport measurements (Halleffect as well as magnetoresistance measurements) as well as magnetization measure-ments - by use of magnetooptical Kerr effect (MOKE). The high magnetic fields ex-periments were performed in LNCMP (Laboratoire National des Champs MagnetiquesPulses) in Toulouse.

Pulsed field magnetometry uses capacitive discharge to generate high magnetic fieldsin conventional resistive solenoids. In principle, this technique employs short measure-ment cycles - the duration of high magnetc field is short.

All experiments described in the thesis were performed in long pulsed magnetic fields.The Toulouse facility allows to use the pulsed magnetic fields with the pulse duration≤1 second. The magnet is a conventional compact solenoid with uniform current distribu-tion [9]. The coil performance is determined by mechanical constrains (the accumulatedstress due to the applied magnetic pressure) and is limited by heating. The use of properconductor materials (see [9]) allows to meet the necessary requirements, i.e. maximummechanical strength to guarantee the highest possible peak field and large specific heatcombined with low resistivity to permit the longest possible pulse duration. The coils aredriven by a 24 kV, 14MJ capacitor bank. The 600 capacitors are divided into 10 modulesthat can be used separetely and with different polarity. The capacitor bank is dischargedinto the coil via stacks of optically triggered thyristors. In the present thesis the MOKE


measurements were performed in magnetic fields up to 25T, the magnetotransport exper-iments up to 55T.

2.6 The experimental setup for Kerr effect measurements

The magnetooptical Kerr effect (MOKE) was measured in the high pulsed magnetic fields(up to 25T) by use of the experimental setup shown schematically in Figure 2.7. Themethod consists in detection of the intensity difference between two orthogonal compo-nents of linear polarized light−→ex and−→ey .

The principle of the measurement is as follows. The incident beam of light from thelaser (red HeNe laser:λ=632.8 nm, P=5mW or green HeNe laserλ=540.5 nm, P=0.1mW)first passes through a linear Glan-Taylor polarizator. Next, the mirror placed on the topof the sample holder sends the incident as well as reflected beam of light. The samplereflects the light that comes almost at the normal incidence. After reflection from thesample, the polarization axis turns about Kerr angleΘK . Then, the light passes throughthe retardation plate (λ

2) that works as a compensator. The Wollaston biprisme separates

the beam of the light for two spatial orthogonal linear polarizations−→ex and−→ey . Finally,the intensity difference between two components:−→ex and−→ey is measured by means of twosilicon photodiodes.

In the Jones-vector representation (see Appendinx1) the linearly polarized (incident)wave (introduced here as a−→ex) has the following form:

Ei =

(1

0

)(2.12)

After reflection from the sample, the polarization axis turns about Kerr angleΘK :

Er =

(cos(ΘK)

sin(ΘK)

)(2.13)

The action of theλ2

retardation plate with the optical axis leaned at theφ angle to thex axis can be written as:

(cos(φ) − sin(φ)

sin(φ) cos(φ)

)(1 0

0 −1

)(cos(φ) sin(φ)

− sin(φ) cos(φ)

)=

(cos(2φ) sin(2φ)

sin(2φ) − cos(2φ)

)(2.14)

The Wollaston biprisme separates beam of the polarized light for two orthogonal linearpolarizations−→ex and−→ey , thus

(Ex

Ey

)=

(cos(2φ) cos(ΘK)+sin(2φ) sin(ΘK)

sin(2φ) cos(ΘK)−cos(2φ) sin(ΘK)

)(2.15)

The two Si PIN photodiodes allow to measure the difference of intensities for twoorthogonal linear polarizations−→ex and−→ey :

∆V = C(|Ex|2 − |Ey|2) = C(cos(2ΘK) cos(4φ) + sin(2ΘK)sin(4φ)) (2.16)

The procedure of measurement is as follows. First, at zero magnetic field (i.e.ΘK=0),the λ

2plate is oriented (forφ = ±π

8, φ = ±3

8π, φ = ±5

8π...) to obtain:

∆V = 0 (2.17)


Next, after turning on the magnetic field the equation 5 has the following form:

∆V = C(sin(2ΘK)) (2.18)

Usually, (for most of compounds), the following condition is satisfiedΘK ¿1, then:

ΘK =∆V

2C(2.19)

For ΘK=0 andφ=0 (or φ = π2) ∆V has maximum value:∆V=∆Vmax=C, thus constant

C can be determined. Finally, determined Kerr rotation angleΘK has the following form:

ΘK =∆V

2∆Vmax

(2.20)

The sensitivity of the Kerr rotation is of order of 1·10−3 deg. Being a reflectivitymeasurement, the MOKE is extremely sensitive to any movement of the sample and themain difficulty is to cancel all the mechanical vibrations generated by the pulsed magnet.

λλ !" ## $% λλ&'()*' ++

,-./01230

4567895:;<=><?@ABCDEFDCGHI

JKDCB

LMHCHFGHFBN[

Fig. 2.7: The schematic view of experimental setup for magnetooptical Kerr effect measurements.

3. SAMPLES OF Pb1−x−y−zMnxEuySnzTe AND Ga1−xMnxAs.

Two types of ferromagnetic mixed crystals were studied. The bulk crystals ofPb1−x−y−zMnxEuySnzTe were grown by use of the modified Bridgman method in Cher-nivtsy Department of the Institute of Materials Science Problems Ukrainian Academyof Sciences. The thin layers of Ga1−xMnxAs were obtained using the non-equilibrumgrowth conditions of low-temperature molecular-beam epitaxy (LT-MBE) in Departmentof Physics University of Notre Dame.

3.1 Ferromagnetic bulk crystals of Pb1−x−y−zMnxEuySnzTe

The crystals of Pb1−x−y−zMnxEuySnzTe were grown by the modified Bridgman method.In the present work the samples coming from several technological processes were inves-tigated. The chemical composition of the samples was determined by X-ray dispersivefluorescence analysis technique (see section 2 of Chapter 2). This technique allows todetermine the chemical composition of the samples with uncertainty of 10%. Typically,the crystals were cut crosswise the growth axis to the 1 - 2mm thick slices. The changeof the chemical composition along such area is very slight (1-2%). The results of chem-ical analysis of all investigated Pb1−x−y−zMnxEuySnzTe samples are gathered in Table3.1. Figure 3.1 shows the typical chemical composition distribution along the growthdirection of the Pb1−x−y−zMnxEuySnzTe crystal.

The standard powder X-ray measurements revealed that investigated samples aresingle-phase and crystallize in NaCl structure, similarly as a nonmagnetic matrix andsemimagnetic semiconductor - Pb1−x−yMnxSnyTe. It was shown that introduction ofMn ions into the nonmagnetic matrix of Pb1−xSnxTe leads to the decrease of the latticeconstant of resultant Pb1−x−yMnxSnyTe [10]. The measured values of the lattice con-stant for several Pb1−x−y−zMnxEuySnzTe samples as well as the lattice constant valuesof Pb1−x−yMnxSnyTe crystals with analogous content of Mn and Sn content [11] are col-lected in Table 3.2. The careful inspection of Table 3.2 shows that introduction of Euions to Pb1−x−yMnxSnyTe lattice leads to the increase of the lattice constant of resultantcompound.

3.2 Ferromagnetic layers of Ga1−xMnxAs.

The second investigated system was III-V Mn based Semimagnetic Semiconductor -GaMnAs. The layers of Ga1−xMnxAs studied in the thesis were grown by use of lowtemperature (LT) MBE with elemental sources Ga, Mn, As, without intentional doping.Semi-insulating epiready (100) GaAs wafers were used as the substrates. Typically, abuffer of GaAs was first grown at high temperature (6000C). The substrate was thencooled to a temperatures in the range 2500C - 2850C, and a layer of low temperature (LT)

3. Samples of Pb1−x−y−zMnxEuySnzTe and Ga1−xMnxAs. 22

Tab. 3.1: The chemical composition of Pb1−x−y−zMnxEuySnzTe samples determined by meansof X-ray dispersive fluorescence analysis technique.

sample # of the sample xPb xMn xEu xSn

SnMnEuTe 841_14 - 0.116 0.011 0.873SnMnEuTe 841_18 - 0.131 0.134 0.735SnMnEuTe 842_4 - 0.063 0.0045 0.932SnMnEuTe 842_8 - 0.068 0.003 0.929SnMnEuTe 842_14 - 0.070 0.007 0.923SnMnEuTe 842_20 - 0.091 0.009 0.900SnMnEuTe 848_4 - 0.061 0.0115 0.927SnMnEuTe 848_10 - 0.064 0.012 0.924SnMnEuTe 848_16 - 0.050 0.011 0.939SnMnEuTe 848_22 - 0.065 0.018 0.917SnMnEuTe 848_24 - 0.051 0.019 0.930SnMnEuTe 848_26 - 0.074 0.023 0.903PbSnMnEuTe 809_2 0.116 0.031 0.0027 0.850PbSnMnEuTe 809_4 0.118 0.030 0.0016 0.850PbSnMnEuTe 809_10 0.187 0.030 0.0031 0.780PbSnMnEuTe 809_12 0.215 0.022 0.003 0.760PbSnMnEuTe 809_28 0.243 0.020 0.007 0.730PbSnMnEuTe 809_30 0.256 0.024 0.010 0.710PbSnMnEuTe 809_32 0.27 0.026 0.014 0.690PbSnMnEuTe 809_34 0.276 0.027 0.017 0.680PbSnMnEuTe 809_36 0.272 0.025 0.013 0.690PbMnEuTe 793_2 0.990 0.010 0.000 -PbMnEuTe 793_4 0.989 0.010 0.001 -PbMnEuTe 793_6 0.982 0.009 0.009 -PbMnEuTe 793_10 0.910 0.005 0.004 -PbMnEuTe 793_12 0.990 0.007 0.003 -

Tab. 3.2: The lattice constanta0 of Pb1−x−y−zMnxEuySnzTe samples determined by the standardpowder X-ray measurements and the values of the lattice constant of Pb1−x−yMnxSnyTea [11] with similar content of Mn and Sn as for the samples investigated in the thesis.

# of the sample xPb xMn xEu xSn a0 a ∆ a=a0-a ∆ a/a0

[Å] [Å] [Å] %809_2 0.116 0.031 0.0027 0.85 6.3130 6.2866 0.0264 0.42809_4 0.118 0.030 0.0016 0.85 6.3237 6.2876 0.0361 0.57809_12 0.215 0.022 0.003 0.76 6.3375 6.3113 0.0262 0.41809_28 0.243 0.020 0.007 0.73 6.3563 6.3309 0.0254 0.40809_36 0.272 0.025 0.013 0.69 6.3427 6.3311 0.0116 0.18


!

N

Fig. 3.1: Chemical composition distribution along the crystal growth direction for the crystal ofPbSnMnEuTe.


! "

! #

Fig. 3.2: RHEED oscillations observed during the growth of a Ga1−xMnxAs film with x = 0.062.The first 7 periods correspond to LT-GaAs. The "jump" in the signal occurs at the pointwhen the Mn shutter has been opened and the rate of oscillations increased.

GaAs was grown to a thickness in the range between 2nm -100nm. Finally, Ga1−xMnxAslayer in the same range of substrate temperatures to a thickness of the 105nm - 302nm wasgrown. No special precaution was needed at the start of Ga1−xMnxAs growth. However,the properties of grown Ga1−xMnxAs do depend on growth parameters as As overpressureandTS. The growth was monitored in situ by reflection high energy electron diffraction(RHEED).

The determination of Mn content in Ga1−xMnxAs epilayers is quite difficult task. TheMn concentrationx was determined using two different methods. First, during the growththe x values were estimated from the change in the growth rate monitored by RHEEDoscillations after the Mn shutter was opened. An example of such data is shown in Figure3.2.

Note the rate of growth measured by RHEED oscillations is in terms of atomic layersper second, and after the Mn shutter is opened it increases in proportion to precisely thatfraction of the Mn flux which is required to completion of atomic layers as the growthproceeds. It is thus assumed that RHEED oscillations provide a measure of the concen-tration of substitutional Mn cations MnGa, since only these only are required to completethe formation of atomic layers.

And second, the Mn content was obtained from X-ray diffraction measurements byassuming that the GaMnAs layer is fully strained by the GaAs substrate. The Mn concen-trationx was calculated from measured relaxed layer lattice constant (XRD measurements


Tab. 3.3: The parameters of the LT MBE growth of GaMnAs samples - substrate temperatureTS

and temperature of the Mn effusion cellTMn, thickness of the GaMnAs layersdGaMnAs

determined from RHEED oscillations and Mn composition of investigated samplesx (de-termined from RHEED oscillations, X-ray diffraction and high resolution X-ray diffrac-tion measurements

# of the sample TS TMn dGaMnAs x x x[0C] [0C] [nm] (RHEED) (XRD) (HRXRD)

GaMnAs/GaAs00811A 285 780 302 - 0.01 -

GaMnAs/GaAs00119C 275 880 269 - 0.032 -

GaMnAs/GaAs10727C 270 870 131 - 0.027 0.027

GaMnAs/GaAs10727D 270 900 149 0.062 0.061 0.056

GaMnAs/GaAs10727E 265 920 105 0.086 0.084 0.078

GaMnAs/GaAs10823C 265 920 111 0.07 0.082 -

GaMnAs/GaAs10823E 250 925 115 0.093 0.085 -

GaMnAs/GaAs10529A 275 820 300 0.014 - -

GaMnAs/GaAs11127A 275 - 220 0.048 - -

performed at the Notre Dame University) by use of the following equation [12]:aLrelax

= 5.6547 + 0.0002433*x. The presence of Mn interstitials atoms as well as antisite de-fects can be the reason for the observed expansion of the lattice constant of GaMnAs.The results of high resolution X-ray diffraction measurements (HRXRD) (performed inthe Institute of Physics Polish Academy of Sciences) and the effect of Mn interstitials onthe lattice parameter of Ga1−xMnxAs will be discussed in details in Chapter IV. In fact, amethod of determining the Mn concentrationx based on the measurements of the latticeconstanta0 in Ga1−xMnxAs is not very reliable. The Mn concentration determined fromRHEED oscillations, the results of XRD and HRXRD and details of the growth conditionsof Ga1−xMnxAs are collected in Table 3.3.

Additionally, the Mn concentration for the sample 10823C was confirmed by use ofsystematic particle-induced X-ray emission (PIXE) measurements [13]. The PIXE mea-surements revealed that sample withx determined by RHEED as 0.07 has total of Mncontent equal to 0.092. The PIXE results show the total Mn content - substitutional, in-terstitial, and in the form of random precipitates (Mn inclusions) and are higher than thevalues obtained from RHEED oscillations.

The Mn concentration specified in the next Chapters comes from the RHEED oscilla-tions measurements with the exception of three samples with the lowest Mn content for


which the change in the RHEED oscillations was too small to be reliable. In this case, i.e.00811A, 00119C, 10727C samples the Mn content was determined only by use of X-raydiffraction technique.

4. TRANSPORT AND MAGNETIC INVESTIGATIONS OFFERROMAGNETIC Pb1−x−y−zMnxEuySnzTe

4.1 Introduction

One of the purposes of the studies presented in the thesis were magnetic and transportinvestigations of ferromagnetic Pb1−x−y−zMnxEuySnzTe mixed crystals. In particular,the influence of the presence of two types of magnetic ions incorporated into semicon-ductor matrix on magnetic properties of resultant semimagnetic semiconductor is ana-lyzed. There are several reasons for which the semimagnetic semiconductors (SMSC’s)based on lead chalcogenides are ideal materials for such kind of investigations. Thevariety of magnetic properties occurring in IV-VI SMSC, e.g., the carrier concentra-tion induced paramagnet-ferromagnet and ferromagnet-spin glass transition observed inPb1−x−yMnxSnyTe [1], [2] makes this system particularly attractive for such purposes.The non-trivial advantage of IV-VI materials is also relative simplicity of crystal grow-ing and carrier concentration controlling – the latter may be achieved by means of eitherdoping or isothermal annealing. The magnetic properties of these compounds dependnot only on the concentration of manganese ions, but also on the density of free carriers[14]. This behaviour is due to the combination of an RKKY type of interaction betweenthe magnetic ions as well as the possibility to manipulate the free carrier concentration.The additional advantage is that for Pb1−x−yMnxSnyTe crystals are very well known pa-rameters of crystal and energy structure. In order to simplify theoretical description ofinvestigated magnetic system, two types of magnetic ions were choosen with spin-onlyground state: substitutional Mn2+ possessesS = 5/2, while Eu2+, the second ion in oursamples, hasS = 7/2.

Practically all IV-VI semimagnetic semiconductors crystallize in rock salt crystalstructure. The lattice parametera0 changes linearly with the content of magnetic ionsfollowing the Vegard law.

In general, all IV-VI semimagnetic semiconductors show metallic type of conductiv-ity with a very large, temperature independent, concentration of carriers. However, un-der special conditions, IV-VI based semimagnetic semiconductors can exhibit insulatingproperties – recently, the Eu composition induced metal-insulator transition was observedin epitaxial layers of Pb1−xEuxTe [15]. Carriers are generated by metal vacancies, andtheir concentration can be controlled by thermal annealing or doping. In semimagneticlead chalcogenides with Mn or with Eu the range of carrier concentration and the methodsto control it are quite similar to the case of appropriate IV-VI semiconductors. The pres-ence of even 10 at.% of Mn or Eu ions has practically no effect on carrier concentration.Mn and Eu ions are electrically inactive in semimagnetic lead chalcogenides.

IV-VI materials are narrow gap semiconductors. Qualitatively, the electron band struc-ture is analogous to the band structure of non-magnetic counterpart materials. A band-structure model based on the consistent interpretation of transport, optical, and magnetic

4. Transport and magnetic investigations of Pb1−x−y−zMnxEuySnzTe 28

Fig. 4.1: The band structure model of Pb1−x−yMnxSnyTe mixed crystals

experimental data [16], [17], [18] is presented in Figure 4.1.The band of electrons and the band of light holes (the presence of further L bands is

not included here) are separated by a direct band at the L point of Brillouin zone. Theenergy dispertion relations of electrons and holes are nonparabolic and anisotropic. Thereare four equivalent valleys of both the band of electrons and the band of light holes.Due to the narrow energy gap the energy dispertion relation is nonparabolic and usuallydescribed within Dimmock model [19]. The energy gap of lead chalcogenides increasesrapidly with the content increase of Mn and Eu [20], [14]. In most of IV-VI semimagneticsemiconductors the composition dependence of other band parameters can be neglected.An increase of the energy gap with increasing temperature is observed, similarly to leadchalcogenides. ApproximetelyEΣ = 0.2 – 0.4 eV below the top of the band of light holesthere is a second valence band of heavy holes. The top of this band is located at theΣpoint of the Brillouin zone and there are 12 equivalent energy valleys of this band (Σband). Since the direct energy gap at theΣ point of the Brillouin zone is quite large, theheavy hole band is expected to be parabolic. The electronic properties of p-type IV-VIsemimagnetic semiconductors with very high concentration of carriers (p≥ 5·1019 cm−3)are influenced by the presence of the band of heavy holes. TheΣ band is essential forthe understanding of the correlations between magnetic and transport properties of IV-VIsemimagnetic semiconductors. The effective mass of the carriers in theΣ band is muchhigher than that in the L band (m∗

Σ ≈ 1.7me [18], m∗L ≈ 0.05me [21]).

Mn-based IV-VI semimagnetic semiconductors can be divided in two groups. Thefirst group consists of the materials with relatively low carrier concentration of free carri-ers [22] (in the range 1017 – 1019 cm−3), for instance Pb1−xMnxTe. From a magnetic pointof view these materials are paramagnets aboveT=1K. Their magnetic behaviour closelyresambles that of the Mn containing II-VI SMSC’s and can also be attributed to antifer-romagnetic interactions of the superexchange type, although the interactions are muchweaker than in II-VI semimagnetic semiconductors. Other interspin interaction mecha-nisms (e.g. direct exchange or the RKKY interaction) are expected to be negligible due


Fig. 4.2: Curie-Weiss temperature (Θ) versus free carrier concentration in Pb1−x−yMnxSnyTe.

to the large mean interspin distances and low concentration of carriers. BelowT=1K aspin-glass phase was reported in Pb1−xMnxTe [23]. The second group of IV-VI SMSC’sconsists of the materials with relatively high charge carrier concentrations, of order of1020 – 1021 cm−3, e.g. Pb1−x−yMnxSnyTe (with low Pb content). These compoundsexhibit a ferromagnetic phase transition at low temperatures [1]. The ferromagnetic in-teractions can be explained by RKKY interactions, made effective by the high carrierconcentration and dominating over the superexchange interactions. The ferromagneticphase occurs once the holes start to occupy site bands with a large effective mass. TheRKKY interaction [24], [25], [26] is an indirect interaction between the magnetic ions,which is mediated by the free charge carriers. The interaction strength can be written as:

JRKKY (Rij) = Nm∗J2

sda60k

4F

32π3h2 [sin(2kF Rij)− 2kF Rijcos(2kF Rij)

(2kF Rij)4] (4.1)

wherekF is the Fermi wave number,m∗ the effective mass of the carriers,Jsd the Mn ion-electron exchange integral,a0 the lattice constant,N the number of valleys of the valenceband,Rij the distance between the magnetic ions.

Story et. al. [1] showed that magnetic behaviour of Pb1−x−yMnxSnyTe strongly de-pends on the concentration of free carriers. Figure 4.2 shows the Curie-Weiss temperature(Θ) versus free carrier concentration as reported by Story et. al. for Pb0.25Mn0.03Sn0.72Te.

The nonzero Curie-Weiss temperature is proportional to the sum of all magnetic in-teractions present in the material. The characteristic feature of theTc(p) dependence isthe existance of a certain threshold carrier concentrationp = pt ' 3·1020 cm−3, abovewhich the IV-VI semimagnetic semiconductors show ferromagnetic properties. For car-rier concentration lower than the threshold valuept, the crystals exhibit paramagneticproperties (similarly to low carrier concentration materials like PbMnTe). The observa-tion of concentration dependence of Curie temperature has found an interpretation withinthe frames of the RKKY mechanism and the two valence band model of the band struc-ture of PbSnMnTe and SnMnTe [16], [17]. The strength of the RKKY interaction scaleswith the effective mass of carriers. The RKKY interaction is expected to become stronglyenhanced forp ≥ pt, when the Fermi level enters theΣ band and heavy holes start to


participate in charge transport and in RKKY interaction. Next to the effective mass of thecarriers, the degeneracy of the valence band maxima is also important (as a prefactor ofRKKY interaction). The L band is four-fold degenerate (NL=4), whereas theΣ band istwelve-fold degenerate (NΣ=12)

The RKKY interaction is also responsible for the magnetic behaviour of canonicalmetallic spin-glasses like CuMn. Because of the high carrier concentration of carriers inthese materials (1023 cm−3) the interaction rapidly oscillates between ferromagnetic andantiferromagnetic as a function of the distance between two Mn ions. The period of thisoscillation is short compared to the average Mn-Mn distance. Due to the random positionof the Mn-ions, the interaction will be ferromagnetic or antiferromagnetic at random. Thiscauses a frustration of the spins resulting in a spin-glass state. The ferromagnet/spin-glass phase transition is also observed in the case of IV-VI semimagnetic semiconductors(Pb1−x−yMnxSnyTe, Sn1−xMnxTe) [27], [28]. This effect can be explained in frame ofRKKY interaction. For the ferromagnetism the following condition should be fullfiled:R ≤ R0, whereR is average interspin distance andR0 is characteristic distanceR0 ∼1/kF ∼ 1/p1/3 (in this caseR0 corresponds to the first switch of the RKKY interactionfrom ferromagnetic to antiferromagnetic). ForR ≥ R0 the oscillatorty character of theRKKY interaction is expected and leads to the spin-glass order.

All Eu based IV-VI semimagnetic lead chalcogenides with low carrier concentartions(n,p ≤ 1019 cm−3 are paramagnetic down to aboutT = 1K (similarly to Mn based com-pounds). The very localized character of 4f orbitals of rare earth results in very weakexchange intreractions both between magnetic ions and between magnetic ions and freecarriers. The crystals of Sn1−xEuxTe are not ferromagnetic. The reason of lack of fer-romagnetism in this material is the very small sp–f exchange integral. It was experi-mentally established that theJsf carrier – magnetic moment exchange constants in SnTewith rare earths ions are related to the exchange constant for Mn ions in the followingway: JGd

sf /JMnsd = 1/5 andJEu

sf /JMnsd = 1/8 [29]. It results in 1/25 and 1/64 reduction of

the strength of the RKKY interaction for Gd and Eu based IV-VI SMSC’s making thisinteraction negligible in these materials.

4.2 Transport characterization of Pb1−x−y−xMnxEuySnzTe samples

All the investigated Pb1−x−y−zMnxEuySnzTe samples were characterized by means of lowmagnetic field transport measurements. The aim of the transport characterization was toobtain information about the elementary electric properties of the investigated samples:type as well as concentration of free carriers and their mobility. The Hall voltage VH

as well as conductivity voltage Vσ were measured. In the case of IV-VI semimagneticsemiconductors the carrier concentration is important parameter since the change of thecarrier concentration influences the magnetic behavior of the material.

The Hall bar samples with typical dimensions of 8mm× 2mm× 1mm were used forthe transport measurements. The electrical contacts were prepared always in the sameway. First the surface of the specimens was etched using the solution of Br2 and HBrin the proportion 1 : 20. Next, the gold contacts were deposited by use of gold chloridewater solution on the polished surface of the samples. Finally, the electrical contacts weremade using indium solder and gold wires. Typical resistance of the samples was equal to1 mΩ. This allowed to apply relatively large current (up to 300mA). The Hall as well as


conductivity measurements were performed at the room and liquid nitrogen temperature.The standard DC six probe technique at the static magnetic field up to 1T was used. Allthe investigated samples occurred to be p type.

In the present thesis the nominal hole concentration was determined:

p =1

eRH

(4.2)

where RH is the Hall constant.The nominal value of the hole concentrations results from the value of the Hall con-

stant assuming that Hall coefficient rH is equal to 1. This assumption, widely applied inthe literature is not precise and the nominal Hall concentration p is very often not equalto the real Hall concentration p0:

p0 =rH

eRH

(4.3)

where rH is the Hall scattering factor.It is well known (see e.g. [19], [21], [30]) that the carrier transport in the IV-VI

materials is served through the two hole types: light holes pl and heavy holes ph. Theband structure model that is usually used to analyze the transport effects in PbTe, SnTeand PbMnSnTe crystals with the high carrier concentration is schematically shown inFigure 4.1 and described in section 1 of this Chapter. The low content of europium ionsin the studied samples (see Table 3.1) allows to assume that this model also describe bandstructure of Pb1−x−y−zMnxEuySnzTe crystals. The light hole band (L point of Brillouinzone) is separated from the conduction band by the energy gap E0 ∼ 300 meV. About EΣ∼ 200meV - 400meV below the top of the valence band the heavy holes band is located(Σ point of the Brillouin zone).

Two-carrier transport is the reason for the discrepancy between the calculated nominalhole concentration (by use of Equation 4.2) and the real value of hole concentration inthe investigated samples. In the case of the carrier transport via light and heavy holes,Hall constant is the function of both light and heavy holes carrier concentration, mobilityand Hall scattering factor:

RH =plelrlµ

2l + phehrhµ

2h

(plelµl + phehµh)2(4.4)

where pl, ph - light and heavy hole concentration el, eh - electric charge of carriers rl, rh -Hall scattering factors of carriersµl, µh - mobilities of carriers.

If both the light and heavy holes carry the same elementary charge (+e), Equation 4.4has the following form:

RH =rlpl + b2phrh

e(pl + bph)2(4.5)

where b =µh/µl.The Hall scattering factors rl and rh in the Equation 4.4 depend on both statistical

energy distribution of carriers and band structure anisotropy:

rH = rτra (4.6)

where rτ - standard Hall factor that takes into consideration statistical energy distributionof carriers ra - term related to the anisotropy.


In the strong degenerate systems energy of carriers that participate in transport is equalto Fermi energy (delta type of statistical energy distribution) and rτ=1. For the materialswith anisotropic effective mass or anisotropic time relaxation:

ra =3K(K + 2)

(2K + 1)2(4.7)

whereK = (m‖/m⊥)(τ⊥/τ‖) (4.8)

Anisotropic contribution to the Hall factor (ra) decreases from ra=1 for K=1 to ra=0.75for KÀ1.

The real hole concentration in the sample can be determined by use of the followingequation:

p0 = r∗Hp (4.9)

where

r∗H =(plrl + b2ph)(pl + ph)

(pl + bph)2(4.10)

andp0 = pl+ph - real hole concentration in the samplep = 1/(e RH) - nominal hole concentrationb = µh/µl - heavy hole mobility to light hole mobility ratiopl, ph - light and heavy hole concentrationrl = 3K(K+2)/(2K+1)2 - Hall scattering factor for light holes, K = 10 - anisotropy coeffi-cient for light hole band.

To determine r∗H coefficient, that is function of hole concentration in the sample, oneneeds to know the light as well as heavy hole concentration and ratio of their mobilities.

In the present thesis only nominal Hall concentration was determined at the roomand liquid nitrogen temperature and all experimental data are shown as a function ofnominal concentration (p). The nominal Hall concentration is commonly used in thecharacterization of IV-VI compounds and is unambiguous experimental parameter.

All the investigated samples occurred to be p type with the high almost temperatureindependent hole concentration (in the range between 2·1018 cm−3 and 2·1021 cm−3).

The obtained values of hole concentration, conductivity and mobility measured at theroom and nitrogen temperature are shown in Table 4.1. Typical values of the Hall voltagewere equal from several to several dozen microvolts. Simultaneously, the large valuesof the asymmetry voltage (resulting from non equipotential positions of the Hall probes),exceeding 100µV were observed. The asymmetry voltage as well as influence of the mag-netoresistance on the Hall effect was eliminated by the standard averaging procedure ofresults obtained for the combination of two current as well as magnetic field polarizations.Additionally, using of the Keithley 150B voltometer allowed to reset the asymmetry volt-age at the magnetic field equal to zero. The values of carrier concentration, conductivityand mobility were determined with the uncertainty of 15 percent at the room temperatureand 30 percent at the liquid nitrogen temperature. One of the investigated samples 809−30was isothermally annealed, to increase hole concentration. The procedure of annealingperformed at the telluride atmosphere and temperature of 7000C for 48 hours allowed toincrease hole concentration from 4.22·1020 cm−3 to 8.25 1025 cm−3. The surface of thesample was polished after annealing.


Tab. 4.1: The results of transport characterization of Pb1−x−y−zMnxEuySnzTe samples - hole con-centrationp [1021 cm−3], conductivityσ[(Ωcm)−1], mobility µ [cm2/Vs]) measured atthe room and liquid nitrogen temperature.

sample xPb xMn xEu xSn p σ µ p σ µnumber 300K 300K 300K 77K 77K 77K841_14 - 0.116 0.011 0.873 1.40 3554 15.8 0.93 3029 20.7841_18 - 0.131 0.134 0.735 1.30 3683 15.5 1.04 5598 33.3842_4 - 0.063 0.0045 0.932 1.40 1172 5.2 - - -842_8 - 0.068 0.003 0.929 1.56 3500 14.0 - - -842_14 - 0.070 0.007 0.923 1.56 1933 7.7 1.25 2750 13.7842_20 - 0.091 0.009 0.9 1.21 3480 17.9 1.16 4561 24.6848_4 - 0.061 0.0115 0.927 1.77 4533 16.0 1.70 6648 24.7848_10 - 0.064 0.012 0.924 1.93 1696 5.5 - - -848_16 - 0.050 0.011 0.939 1.24 6435 32.3 1.48 9635 40.60848_22 - 0.065 0.018 0.917 1.37 3557 16.2 - - -848_24 - 0.051 0.019 0.93 1.57 3216 17.4 1.29 4842 23.5848_26 - 0.074 0.023 0.903 1.66 6370 23.9 - - -809_2 0.116 0.031 0.0027 0.85 1.01 5860 29 1.01 19050 76809_4 0.118 0.030 0.0016 0.85 0.501 4050 48.6 0.657 596 30809_10 0.187 0.030 0.0031 0.78 0.601 2920 29 3.0 4983 35809_12 0.215 0.022 0.003 0.76 0.401 3390 49 0.60 6764 69809_30 0.256 0.024 0.010 0.71 0.425 1310 19.2 0.762 2058 16.9809_30 0.256 0.024 0.010 0.71 0.822 3346 25.4 1.04 5307 31.8anneal.809_32 0.27 0.026 0.014 0.69 0.325 2777 53.5 0.49 4731 35.2809_34 0.276 0.027 0.017 0.68 0.449 2970 41.4 0.98 2373 15.2809_36 0.272 0.025 0.013 0.69 0.318 2823 55.4 0.75 4816 40793_2 0.990 0.010 0.000 - 0.002 202 540 0.003 1502 2641793_4 0.989 0.010 0.001 - 0.003 112 263 0.004 807 1399793_6 0.982 0.009 0.009 - 0.002 72 75 0.003 723 1329793_10 0.910 0.005 0.004 - 0.005 11 14 - - -793_12 0.990 0.007 0.003 - 0.005 1910 24.5 0.007 3076 24.4


4.3 Magnetic measurements of Pb1−x−y−zMnxEuySnzTe mixed crystals

In the present section the results of magnetic studies of Pb1−x−y−zMnxEuySnzTe sampleswill be presented. As was shown in the previous section all the investigated samples oc-cured to be p-type with practically temperature independent concentration of carriers.Two groups of IV-VI semimagnetic semiconductors with two types of magnetic ions(Mn2+ and Eu2+) were investigated. First, the samples of Pb1−x−yMnxEuyTe (0.005≤x ≤0.010, 0≤ y ≤0.009) with relatively low free carrier concentration (2.30·1018 cm−3

≤ p ≤ 4.80·1020 cm−3 at T=300K) were studied. Next, the second group of samples:Pb1−x−y−zMnxEuySnzTe (0.022≤ x ≤0.031, 0.002≤ y ≤0.017, 0.0680≤ z ≤0.850 )as well as Sn1−x−yMnxEuyTe (0.055≤ x ≤0.131, 0.003≤ y ≤0.023), characterized bysubstantially larger carrier concentration (3.20·1020 cm−3 ≤ p ≤ 1.01·1021 cm−3, 1.211021 cm−3 ≤ p ≤ 1.93·1021 cm−3 for Pb1−x−y−zMnxEuySnzTe and Sn1−x−yMnxEuyTe,respectively atT=300K) was investigated.

AC magnetic susceptibility studies in the temperature range 1.3-150 K using a mutualinductance method as well as DC magnetization measurements in the magnetic field range0-90 kOe (0-9 T) at various temperatures by use of extraction technique were carried out.The susceptibility measurements were carried out in AC magnetic field of frequency inthe range 7-10000 Hz and amplitude not exceeding 5 Oe (5·10−4 T).

Generally, in the range of high temperatures all IV-VI semimagnetic semiconductorsare Curie-Weiss paramagnets with the temperature dependence of the magnetic suscepti-bility described by the Curie-Weiss law:

χ(T ) = C/(T −Θ) (4.11)

whereC = g2µ2BS(S +1)NM is the Curie constant andkBΘ = 1/3S(S +1)x

∑ziI(Ri)

is the paramagnetic Curie temperature (Curie-Weiss temperature). Here,NM is the con-centration of magnetic ions,zi is the number of magnetic neighbors on i–th crystalo-graphic shell,I(Ri) is the exchange integral between the central ion and its i–th magneticneighbors,S is the spin of the magnetic ion,g is the spin-splittingg factor, kB is theBoltzman constant,µB is the Bohr magneton.

For all the investigated samples the high temperature behaviour of the inverse low-field susceptibilityχ−1 was nearly linear and all data were fitted with Curie-Weiss law ofthe form1:

χ(T ) = C/(T −Θ) + χdia (4.12)

whereχdia is the susceptibility of the host lattice (all IV-VI semiconductors without mag-netic ions are standard diamagnetic materials with magnetic susceptibility aroundχdia

' -3·10−7 emu/g). Figure 4.3 presents the high temperature behaviour of inverse mag-netic susceptibility for a few Pb1−x−yMnxEuyTe samples. The determined values of para-magnetic Curie temperatureΘ, which is proportional to the total strength of exchangeinteractions between magnetic ions and Curie constantC are presented in Table 4.2.

In the case of PbMnEuTe obtained results (the determined negative and relativelysmall values of paramagnetic Curie-Weiss temperatureΘ) indicate that weak antiferro-magnetic superexchange interaction occurs the dominant mechanism in PbMnEuTe crys-tals. The obtained results correspond to those reported in PbMnTe. Inspection of Table

1 The Curie-Weiss law in the form of equation 4.12 describes system with one type of magnetic ions,i.e. PbSnMnTe.


Tab. 4.2: . The results of magnetic measurements for IV-VI mixed crystals.sample xPb x y z C Θ TC Tf

number [emu/g] [K] [K] [K]841_14 - 0.116 0.011 0.873 0.00215 19.65 17.46 -841_18 - 0.131 0.013 0.856 0.00209 18.18 16.63 -842_4 - 0.063 0.0045 0.932 - - 10.90 -842_8 - 0.068 0.003 0.929 - - 13.07 -842_14 - 0.070 0.007 0.923 - - 15.23 -842_20 - 0.091 0.009 0.900 0.00230 17.98 17.10 -848_4 - 0.061 0.0115 0.927 0.00141 11.57 11.57 -848_10 - 0.064 0.012 0.924 - - 8.35 -848_16 - 0.050 0.011 0.939 0.00149 11.02 8.75 -848_22 - 0.065 0.018 0.917 - - 10.75 -848_24 - 0.051 0.019 0.930 0.00222 12.08 10.98 -848_26 - 0.074 0.023 0.903 - - 11.31 -809_2 0.116 0.031 0.003 0.850 0.00047 5.16 - 2.0

(Re(χ)625Hz)

809_4 0.118 0.030 0.002 0.850 0.00050 4.88 - -809_10 0.187 0.030 0.003 0.780 0.00050 4.74 4.13 -809_12 0.215 0.022 0.003 0.760 0.00052 4.55 4.09 -809_30 0.256 0.024 0.010 0.710 0.00080 3.02 2.98 -809_30 0.256 0.024 0.010 0.710 0.00080 4.16 3.55 -anneal.809_32 0.27 0.026 0.014 0.690 0.00082 2.89 2.81 -809_34 0.276 0.027 0.017 0.680 0.00090 2.60 2.60 -809_36 0.272 0.025 0.013 0.690 0.00077 3.13 3.12 -793_2 0.99 0.010 0.000 - 0.00039 -0.93 - -793_4 0.989 0.010 0.001 - 0.00038 -0.69 - -793_4 0.989 0.010 0.001 - 0.00038 -0.69 - -793_6 0.982 0.009 0.009 - 0.00051 -1.12 - -793_10 0.991 0.005 0.004 - 0.00053 -0.42 - -793_12 0.99 0.007 0.003 - 0.00059 -0.39 - -793_14 0.99 0.005 0.005 - 0.00086 -0.41 - -


4.2 shows that no distinct trends inΘ andC dependence on Eu concentration can be ob-served. However, it should be stressed that the values analyzed are determined with ratherlarge error related with considerable uncertainty of chemical compositions of the samples.

Figures 4.4 and 4.5 present high temperature part of inverse AC susceptibility forseveral PbMnEuSnTe and SnMnEuTe samples. The fitting procedure (the Curie–Weisslaw – the same as for PbMnEuTe samples) revealed the positive values of Curie–Weisstemperature in this group of IV-VI mixed crystals. This indicates the presence of fer-romagnetic interactions. The obtained values of Curie–Weiss temperatureΘ and CurieconstantC are shown in Table 4.2.

χ

Fig. 4.3: Inverse AC susceptibility versus temperature measured for Pb1−x−yMnxEuyTe samples(793−2: x=0.010,y=0; 793−4: x=0.010,y=0.001; 793−10: x=0.005,y=0.004; 793−12:x=0.007,y=0.003; 793−14: x=0.005,y=0.005). The solid lines correspond to Curie -Weiss law fits.

The careful inspection of Table 4.2 allows to notice significant changes of Curie-Weiss temperature with the Eu content. The decrease of the paramagnetic Curie temper-atureΘ with the increase of Eu concentration is clearly visible. The three samples ofPb1−x−y−zMnxEuySnzTe: 809−12, 809−30, 809−34 are characterized with very similarvalues of Mn content and concentration of free holes (see Table 4.1). For the Mn concen-tration equal to aroundx ' 0.02 and free hole concentrationp ' 4 1020 cm−3 increaseof Eu content from y=0.003 to y=0.01 leads to the decrease of Curie–Weiss temperaturefrom 4.55K to 3.02K and for y=0.017 paramagnetic Curie temperature is equal to 2.63K.In the case of Sn1−x−yMnxEuyTe crystals such distinct tendency is not observed (see Ta-ble 4.2). However, one needs to realize that obtained values of chemical composition aswell as free carrier concentration are determined with quite large uncertainty.

The low temperature studies revealed the presence of paramagnet/ferromagnet phasetransition in the case of SnMnEuTe as well as the most of PbSnMnEuTe samples. Figures4.6 and 4.7 show the low temperature behaviour of real component of AC susceptibilityRe(χ) for several samples of studied Pb1−x−y−zMnxEuySnzTe and Sn1−x−yMnxEuyTemixed crystals. Typical behaviour of a ferromagnet is observed. Both components of thesusceptibility dramatically increase at the Curie temperatureTC . The Curie temperature


χ

Fig. 4.4: The high temperature inverse AC susceptibility measured for severalPb1−x−y−zMnxEuySnzTe samples (809−2: x=0.031, y=0.003, z=0.850; 809−12:x=0.022,y=0.003,z=0.760; 809−32: x=0.026,y=0.014,z=0.69; 809−34: x=0.027,y=0.017,z=0.680).The solid lines correspond to Curie -Weiss law fits.

was determined by the maximum slope ofdRe(χ)dT

. The obtained values ofTC are shownin Table 4.2.TC values are approximately equal to the Curie-Weiss temperatureΘ de-termined from high temperature susceptibility measurements. The low temperature mea-surements confirmed the described above tendency for studied Pb1−x−y−zMnxEuySnzTecrystals, i.e. the decrease of Curie temperature with the Eu content.

Additionally performed DC magnetization measurements (up to 9T at various tem-peratures) collaborate susceptibility investigations and confirm ferromagnetic orderingobserved for most of PbSnMnEuTe samples. Figure 4.8 presents an example of performedmagnetization studies for 809−10 (x=0.030,y=0.003,z=0.78) ferromagnetic sample sam-ple withp=6·1020 cm−3.

For the sample of PbSnMnEuTe (809−2) the ferromagnetic to spin glass phase tran-sition is observed. Figure 4.9 presents characteristic behaviour of low temperature partof real as well as imaginary component of susceptibility for spin glass (809−2) as wellas ferromagnetic (809−12) samples of Pb1−x−y−zMnxEuySnzTe. In the case of ferro-magnetic sample (with the concentration of free holes equal to 4.0·1020 cm−3) the sharptransitions in both real and imaginary components of susceptibility occur. For spin glasssample (characterized by higher free hole concentrationp=1·1021 cm−3) a cusp inRe(χ)is visible at the freezing temperatureTf . The magnitude of the susceptibility at this cuspis much lower than the susceptibility of the ferromagnetic sample. A corresponding max-imum in the out of phase of susceptibilityIm(χ) is observed at slightly lower tempera-ture. The 809−2 PbMnEuSnTe sample shows an obvious characteristics of spin glass–likephase. The cusp observed in susceptibilityχ versus temperatureT shifts to higher tem-peratures when the frequencyf of the applied AC field is increased. This feature – theincrease of the freezing temperature when the frequency is higher – was observed in the


χ

Fig. 4.5: The high temperature inverse AC susceptibility measured for several Sn1−x−yMnxEuyTesamples (841−18: x=0.131,y=0.013; 841−14: x=0.116,y=0.011; 842−20: x=0.091,y=0.009; 848−4: x=0.061,y=0.0115; 848−16: x=0.050,y=0.011; 848−24: x=0.051,y=0.019).

well-known canonical spin glass systems [31], [32], [33], [34]. The increase ofTf perdecade of frequency is approximately constant and frequency dependence occurs in bothreal and imaginary part of AC magnetic susceptibility. Figures 4.10 and 4.11 present thefrequency dependence of low temperature parts of real and imaginary components of sus-ceptibility for 809−2 sample of PbMnEuSnTe. The relative shift of freezing temperatureTf per decade of frequencyR = ∆Tf/Tf∆logf is equal to 0.021. The rate of the changescorresponding to maximum in imaginary part of susceptibility is higher:R=0.048.

The values ofR reported for known spin glass systems range from 0.005 (Cu) to0.11 (La1−xGdxAl 2 [35]) and the rate of the change inIm(χ) is the same as the rate ofthe change inRe(χ). The values ofR reported for Sn1−xMnxTe are equal:R=0.027(x=0.04) [27], R=0.022 (x=0.008) [36], R=0.027 (x=0.022) [36]. It appears that inthe case of Sn1−xMnxTe mixed crystals the character of the spin glass phase does notdepend on the manganese concentration. In the case of studied in the present thesisPb1−x−y−zMnxEuySnzTe mixed crystals, comparable with Mn-based IV-VI semimagneticsemiconductors, the significant difference is visible in the inequality of frequency shift inRe(χ) andIm(χ). It has to be noted thatIm(χ) in conducting media is distorted becauseof the eddy currents induced by AC magnetic field. Nevertheless, obtained values differfrom those obtained for analogous materials (Sn1−xMnxTe), in particular the differencein the rate of frequency shift of cusp in real and imaginary part of susceptibility seems tobe significant.

Figure 4.12 presents magnetic phase diagram for PbMnSnTe and PbMnEuSnTe sam-ples. The magnetic phase diagram for PbMnSnTe mixed crystals was taken from the Ref.[27] and data for PbMnEuSnTe samples studied in the present thesis were included.

The magnetic phase of the samples at low temperatures is indicated as a functionof both: manganese concentration and free hole concentration. Three regimes can be


χ

!"#$"%

Fig. 4.6: The low temperature behaviour of real part of susceptibility for severalPb1−x−y−zMnxEuySnzTe samples (809−12: x=0.022, y=0.003, z=0.760; 809−36:x=0.025,y=0.013,z=0.690; 809−30: x=0.024,y=0.010,z=0.710 ;809−32: x=0.026,y=0.014,z=0.690; 809−34: x=0.027,y=0.017,z=0.680).

distinguished: a ferromagnetic regime for high manganese and high carrier concentration;a spin glass regime for low manganese and high carrier concentrations; and a reentrantspin glass regime separating the former two. A sample is considered as a reentrant spinglass if in the temperature range two transitions can be observed (ferromagnetic as wellas spin glass). It is clearly visible that the presence of Eu shifts spin glass regime towardslower carrier concentrationp. In the case of Sn1−xMnxTe any changes after introducingEu to semiconductor matrix are not observed in magnetic phase diagram.

The most likely reason of the strong dependence of Curie temperature on Eu content isa variation of the band parameters with the alloy composition. In the qualitative analysisof the above problem the following points should be considered.

• The Eu atom is a magnetic impurity in PbMnSnTe matrix with spin-only groundstate: Eu2+ hasS =7/2. The electrons of the half-filled f-shell, responsible for themagnetic Eu moment, are very weakly coupled to the band electrons. Thus, one cannot expect a substantial contribution of Eu magnetic ions to average magnetization.The coupling constantJs−f is much smaller thanJs−d constant. However thereexists a small contribution to the total energy from s–f coupling between Eu atomsand carriers. One can expect an increase of Curie temperature with the Eu contentfrom this mechanism. Since the experiment shows the opposite behaviour, it can beassumed that the role of Eu as a magnetic impurity is negligible.

• Since EuTe is an antiferromagnet, one can expect a transition from positive (Curie)to negative (Neel) temperature of magnetic ordering of PbMnEuSnTe when chang-ing Eu contenty from 0 to 1. For small Eu content it can lead to a decrease ofTC .


χ

!

Fig. 4.7: The low temperature behaviour of real part of susceptibility for severalSn1−x−yMnxEuyTe samples (841−14: x=0.121,y=0.011; 842−20: x=0.090,y=0.009;841−18: x=0.128,y=0.014; 848−24: x=0.055,y=0.0175; 848−16: x=0.054,y=0.011;848−4: x=0.058,y=0.011).

• Eu is a component of the complex PbMnEuSnTe alloy and one should consider avariation of the band parameters as a function of Eu content. For the qualitativeanalysis, let’s assume here a simplified two-band model with some phenomenolog-ical parameters. It should be stressed that the real spectrum of IV-VI compoundsis rather complicated and one should account for nonparabolicity and anisotropy ofenergy bands.

For a qualitative analysis, the following formula describing RKKY interaction strengthcan be used:

JRKKY (Rij) = Nm∗J2

sda60k

4F

32π3h2

sin(2kF Rij)− 2kF Rijcos(2kF Rij)

(2kF Rij)4(4.13)

wherekF is the Fermi wave number,m∗ the effective mass of the carriers,Jsd the Mn ion-electron exchange integral,a0 the lattice constant,N the number of valleys of the valenceband,Rij the distance between the magnetic ions.

If one will take Rij equal to the mean distance between the magnetic ions (Mn)Rthis formula will give the mean interaction energy between magnetic impurities which isroughly equal to the transition temperatureTC ≈ JRKKY (R)/kB. It should be stressedhere, that Equation 4.13 was obtained for a parabolic energy spectrum and does not takeinto account the anisotropy.

It is assumed that the hole energy spectrum in L points has the form:

EL(k) = (∆2 + v2k2)1/2 (4.14)

and, respectively, inΣ points:

EΣ(k) = ε0 +h2k2

2m∗Σ

(4.15)


0 2 4 6 8 100.0

0.1

0.2

0.3PbSnMnEuTe 809_10

M [

emu/

g]

B [T]

4.3K 12K 30K

Fig. 4.8: Magnetization measured at various temperatures and magnetic fields up to 9T forPb1−x−y−zMnxEuySnzTe 809−10 sample withx=0.030, y=0.003, z=0.780 and holeconcentrationp=6 1020 cm−3.

Here,v is band-coupling constant and it is assumed thatv=5 10−8 eV [37], ∆ = Eg/2andε0 parameters depend on alloy composition,m∗

Σ = 3m0, m0 is free electron mass.It is commonly known that the energy spectrum of Pb1−yEuyTe alloy is very sensitiveto the concentration of Eu. The energy gapEg depends strongly on Eu content - from189.7 meV fory=0 (PbTe) to 248 meV fory=0.013 at the temperatureT=10K [37],dEg/dy=5.788 eV atT=10K fory<0.05 [14]. Considering the energy gapEg dependenceon Sn contentz of Pb1−x−zMnxSnzTe alloy [37], [14] the following formula describingthe energy gap dependence on the alloy composition in Pb1−x−y−zMnxEuySnzTe crystalscan be assumed:

Eg = 0.19(1− z)− 0.3z + 5.788y [eV ] (4.16)

In the present calculations the Mn concentrationx was accepted as equal to 0.02.It is assumed here [19], [37] that the composition dependence ofε0 parameter has the

following form:ε0 = 0.8(1− z) + 0.3z + 4y [eV ] (4.17)

Using Equations 4.14 and 4.15 the hole concentration in L as well asΣ valley can befound:

pL =(E2

F −∆2)3/2

3πv3(4.18)

pΣ =1

3π2(2m∗

Σ

h2 (EF − ε0))3/2 (4.19)

The Fermi energy levelEF is determined by equation:

4pL + 12pΣ = p0 (4.20)


χ

χ

χ

χ

χ

χ

!

"

#$%&$'"

Fig. 4.9: The low temperature behaviour of both realRe(χ) and imaginaryIm(χ) component ofsusceptibility for two samples of Pb1−x−y−zMnxEuySnzTe: 809−2 (x=0.031,y=0.003,p=1·1021 cm−3) and 809−12 (x=0.022,y=0.003,p=4·1020 cm−3). The typical ferro-magnetic characteristics is observed for 809−12 sample and spin glass behaviour for thesample with higher free hole concentration.

which gives the total hole concentrationp0 and takes into account the degeneracy of eachvalley. It is accepted here thatp0 is equal to 4·1020 cm−3.

The Fermi momentum in theΣ bandkΣF = (2m∗

Σ(EF − ε0))3/2 can be found as a so-

lution of Equation 4.20. Next, Equation 4.13 withkF = kΣF , R = (

3a30

4πx)1/3, a0=6.5·10−8

cm,N=12,Jsd=1 eV is used forTC calculations. The obtainedTC dependence on Eu con-centrationy for various values of Sn content (0.6≤ z ≤ 1) is shown in Figure 4.13. It isclearly visible that the obtained results of calculations performed within simple two bandmodel can explain the observed experimentally tendency of Curie temperature decreasewith Eu content. The obtained values of Curie temperature are higher than determinedexperimentally. However, it should be stressed that not all phenomenological parameterswere known precisely. Many assumptions are introduced to the model. Nevertheless, thecalculated dependence of Curie temperature on Eu content very well reflects experimen-tally confirmed effect of theTC decrease with Eu concentrationy.

Since the effect of the decrease of Curie temperature with the increase of Eu contentdue to change of band parameters is pronounced in PbSnMnEuTe mixed crystals, oneshould observe the change ofTC under hydrostatic pressure.

Magnetization measurements under hydrostatic pressure up to 12 kbar were per-formed in the temperature above 4.2K and magnetic fields up to 16 kOe (1.6 T) usingthe vibrating sample magnetometer. A miniature CuBe container with the inner diam-eter of 1.42 mm was used as a pressure cell and a mixture of mineral oil and kerosenewas used as a pressure-transmitting medium. The pressure at low temperatures was de-termined using the pressure dependence of the superconducting transition temperaturefor the pure Sn probe placed near the sample. The experimental setup allows to per-


χ

!" #

Fig. 4.10: The frequency dependence of real component of susceptibilityRe(χ) for the sampleof Pb1−x−y−zMnxEuySnzTe: 809−2: x=0.031,y=0.003,p=1·1021 cm−3. The shift ofthe freezing temperatureTf towards higher temperatures with the frequency increase isclearly visible.

form magnetization studies under hydrostatic pressure in the temperatures aboveT=4.2K. Thus, it was possible to investigate only Sn1−x−yMnxEuyTe samples with Curie tem-peratures higher than 4.2K. Unfortunately, all available Pb1−x−y−zMnxEuySnzTe sampleswere characterized by lower than 4.2K Curie temperature. Two samples were measured:one of Sn1−x−yMnxEuyTe (842−8 with x=0.068,y=0.003,p=1.6·1021 cm−3) and one ofSn1−xMnxTe (x=0.10). Figures 4.14 and 4.15 show the results of zero field cooled (ZFC)low-field magnetization, measured at ambient and equal to 11.2 kbar pressure for SnM-nEuTe and 10.5 kbar for SnMnTe sample. In both cases the decrease of Curie temperatureunder hydrostatic pressure is observed.TC shifts towards low temperatures with the samepressure coefficient for two investigated samples:dTC

dP∼ -0.03 K/kbar.

The ZFC magnetization measurements performed as a function of magnetic field upto 16 kOe (1.6T) at low temperatures (presented in Figures 4.16 and 4.17) revealedthe decrease of spontaneous magnetization in both cases with almost the same pressurecoefficient:dM0

dP∼ -0.026 emu/g kbar for SnMnEuTe sample anddM0

dP∼ -0.03 emu/g kbar

for SnMnTe sample. There is no pressure effect on the coercive field of the hysteresisloops measured for both SnMnEuTe as well as SnMnTe samples.

In fact, performed magnetization measurements under hydrostatic pressure revealedthat introducing Eu ions into semiconductor matrix of SnMnTe does not influence signif-icantly Curie temperature. However, the magnetic studies of SnMnEuTe mixed crystalswith much higher concentration of Eu are needed to form the final conclusions.

The effect ofTC dependence on hydrostatic pressure is well known in PbMnSnTesemimagnetic semiconductor. T. Story [10] observed three different regions of the Curietemperature variation with the pressure - corresponding to three various pressure coeffi-cientsdTC

dP. For the Pb1−x−yMnxSnyTe samples with low free carrier concentration (about

3·1020 cm−3) very significant increase of Curie temperature (approximately 100%) afterapplying the hydrostatic pressure equal to 10kbar is observed. Next, the samples withslightly higher free carrier concentration (6-7·1020 cm−3) reveal no effect in the pressure


χ

!" #

Fig. 4.11: The frequency dependence of imaginary part of susceptibilityIm(χ) for the sample ofPb1−x−y−zMnxEuySnzTe: 809−2 (x=0.031,y=0.003,p=1·1021 cm−3). The maximumof the observed cusp shifts towards higher temperatures with the frequency increase.

dependence of Curie temperature – in this case the values ofdTC

dPare equal to zero. At

least, for the samples with high carrier concentrationp=1·1021 cm−3 the decrease ofTC

with the pressure increase is observed ( negative values ofdTC

dPcoefficient). Simultane-

ously, transport investigations [10] revealed that hydrostatic pressure does not change thetotal free hole concentration, but significantly changes distribution of carriers betweenlight hole (L) and heavy hole (Σ) bands. The experimental results showed that pressurecoefficientdTC /dP (p) dependence reflects the threshold behaviour ofTC as a function ofhole concentrationp. It is presented [10] that for PbSnMnTe mixed crystals energy gapincreases with the hydrostatic pressuredEg/dP=8meV/kbar andε0 energy decreases withhydrostatic pressuredε0/dP=-4meV/kbar. T. Story showed [10] that hydrostatic pressureinduces the changes in the band parameters of PbSnMnTe mixed crystals and this in turnleads to the observed changes in Curie temperature.


Fig. 4.12: Magnetic phase diagram for Pb1−x−yMnxSnyTe [27] and Pb1−x−y−zMnxEuySnzTesamples. Red triangles correspond to PbMnEuSnTe ferromagnets, red circles to PbM-nEuSnTe spin glasses, black circles to PbMnSnTe ferromagnets, green circles to PbMn-SnTe spin glasses, blue circles to reentrant spin glasses. Lines present model calcula-tions of the phase boundary (see Ref. [27]): solid line presents geometric model, dashedand dot dashed lines correspond to Sherrington-Kirkpatrick model, dot line correspondto Sherrington-Southern model

0,000 0,005 0,010 0,0155

6

7

8

z=0.7

z=0.8

z=0.6

z=0.9

z=1

Cur

ie T

empe

ratu

re [

K]

Eu content y

Fig. 4.13: Curie temperature calculated for Pb1−x−y−zMnxEuySnzTe mixed crystals as a functionof Eu contenty for various values of Sn concentration 0.6≤ z ≤ 1 and Mn concentra-tion x=0.02


4 6 8 10 12 14 16 18 20 22 24 26

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

∆TC/dP ~ - 0.03 K/kbar

ZFC B=20 Oe

P=0 P=11.2 kbar

SnMnEuTe 842_8

T [K]

M [

emu/

g]

Fig. 4.14: Zero field cooled magnetization measured as a function of temperature forSn1−x−yMnxEuyTe sample (842−8 with x=0.068,y=0.003,p=1.6·1021 cm−3) at am-bient and equal to 11.2 kbar pressure.

2 4 6 8 10 12 14 16 18 20 22 24 26

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

∆TC/dP ~ - 0.03 K/kbar

SnMnTe x=0.10

ZFC B=20 Oe

T [K]

M [

emu/

g]

P=0 10.5 kbar

Fig. 4.15: Zero field cooled magnetization measured as a function of temperature for Sn1−xMnxTesample withx=0.10 at ambient and equal to 10.5 kbar pressure.


-18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18-10

-8

-6

-4

-2

0

2

4

6

8

10

M0

∆M0/dP ~ - 0.026 emu/g/kbar

SnMnEuTe 842_8

ZFC T=5 K

B [kOe]

M [

emu/

g]

P=0 P=11.2 kbar

Fig. 4.16: Zero field cooled magnetization measured as a function of magnetic field at low temper-atureT=5K for Sn1−x−yMnxEuyTe sample (842−8 with x=0.068,y=0.003,p=1.6·1021

cm−3) at ambient and equal to 11.2 kbar pressure.

0 2 4 6 8 10 12 14 160

2

4

6

8

SnMnTe x=0.10

ZFC T=4.2 K

M0

∆M0/dP ~ - 0.03 emu/g/kbarM

[em

u/g

]

B [kOe]

P=0 10.5 kbar

Fig. 4.17: Zero field cooled magnetization measured as a function of magnetic field at low temper-atureT=4.2K for Sn1−xMnxTe sample withx=0.10 at ambient and equal to 10.5 kbarpressure.

5. LOW TEMPERATURE ANNEALING STUDIES OF Ga1−xMnxAs

5.1 Introduction

In this chapter the results of experimental studies of low temperature (LT) Ga1−xMnxAswill be presented. Ga1−xMnxAs has become the focus of current interest because of itshigh Curie temperature and possible spin-electronics applications (see [38] and referencestherein). One of the issues investigated in the presented thesis was the effect of the lowtemperature (LT) annealing on the electronic, magnetic and structural properties of theGa1−xMnxAs. The purpose of this work was to systematically anneal and study the sam-ples over a wide range of Mn concentration. The role of Mn interstitial in GaMnAs isexplored. The as-grown as well as annealed samples were systematically investigated.

This introduction includes briefly review of the physical properties reported for LTGa1−xMnxAs epilayers. Ga1−xMnxAs is the subject of very intense interest, since it be-came a favorite material for spintronics. Many papers present in the literature force togive very brief and selective survey of the reported results.

Typically, the GaMnAs is grown by use of low temperature molecular beam epitaxy(LT MBE, growth temperature<3000C). This allows to overcome the solubility limit ofMn in GaAs, i.e. they are in their non-equilibrium state. The properties of LT GaMnAsdepend on the growth parameters such as As overpressure and substrate temperature (seee.g. [39], [40]). When the growth temperature and/or Mn flux are too high, formationof MnAs phase at the growth front occurs, which can be detected in situ by reflectionhigh-energy electron diffraction (RHEED) allowing one to optimize the growth condi-tions. When substrate temperature is too low, the growth mode changes from the two-dimensional to three-dimensional, resulting in polycrystalline material. The maximumMn concentration, achieved in GaMnAs is equal aboutx≈0.1. Preparation of sampleswith higher Mn content has been proven to be very difficult [41]. Mn ions in the substitu-tional, cation position introduce magnetic moments as well as holes due to their acceptornature. Thus introduced holes mediate ferromagnetic interaction and make resulting alloyGa1−xMnxAs ferromagnetic.

When grown on GaAs, Ga1−xMnxAs shows an in-plane magnetic easy axis. Thiseasy-axis is strain dependent and can be made perpendicular-to-plane by changing thesign of the strain. GaMnAs is under compressive strain when grown on GaAs, which hasa smaller lattice constant than that of GaMnAs. A lattice relaxed InGaAs buffer, havinga larger lattice constant, introduces tensile strain and results in perpendicular anisotropy[42].

The X-ray diffraction measurements show that LT Ga1−xMnxAs has the zinc-blendestructure without detectable second phase (see e.g. [38] and refrences therein). It wasestablished that the lattice constant of Ga1−xMnxAs epilayers increases with the increaseof Mn concentrationx (see [43] and the references therein). While there clearly existsa phenomenological correlation between the experimentally established lattice parameter

5. Low temperature annealing studies of Ga1−xMnxAs 49

andx, it has not been really understood. Particularly, the results of high resolution X-raydiffraction (HRXRD) presented in this thesis show that Mn interstitials are responsible forthe observed expansion of the lattice constant. These measurements are in good agrementwith theoretical predictions proposed by Mašek et al. [44].

It is expected that there are three possible electronic states of the Mn impurity sub-stituting a trivalent cation:A0(d4) andA0(d5+h) for Mn3+ andA−(d5) for Mn2+. Here,A0 denotes the neutral center,A− is negatively charged center, the notation in bracketsis the electronic configuration of d electrons. In the case of theA0(d4) center the holeresides in the 3d shell. However, strong Hund’s intra-site exchange interaction may favora state having five d electrons and a loosely bound hole. This is the case of theA0(d5+h)configuration, whereA0(d4) center traps tightly an electron in the 3d shell forming highspin,S=5/2, 3d5 configuration, and this negatively charged Mn ion binds the hole in aneffective mass state. The variety of experimental results indicate that the ground state ofthe Mn impurity in III-V compounds corresponds toA0(d5+h) configuration [38]. How-ever, no signal ofA0(d5+h) centers is usually detected in MBE grown LT Ga1−xMnxAs.For LT MBE grown Ga1−xMnxAs epilayers withx<0.01 EPR (electron paramagneticresonance) spectra show only one resonance corresponding tog=2.0 (see e.g. [45] andreferences therein). This resonance is attributed toA−(d5) centers. One possible reasonfor the absence ofA0 centers is the high concentration of free holes in the epilayer, whichscreen the Coulomb potential of theA− center and reduce the hole binding energy. Thisway, holes ionize easily and onlyA− centers are left. For Ga1−xMnxAs with still higherMn concentrations (x>0.03), the picture is more complicated and the explanation has notbeen presented so far [45]. However, if the argument of reduced binding hole energy ofA0 center is correct for smallx, it should be even more relevant for the epilayers withhigherx, since the hole concentration increases withx [6].

The hole concentrationp as well as Mn contentx are important parameters for GaM-nAs since Curie temperature of this material increases with the increase ofx andp. Thetransport as well as magnetotransport measurements revealed that the conduction is p-typein the case of GaMnAs (see e.g. [38] and references therein, [46]). The hole concentrationinfluences all major properties of this material [47], [48], [49], [50]. However, the deter-mination of carrier type and concentration is difficult in the case of GaMnAs due to thepresence of anomalous Hall effect (AHE) [38], [51]. To avoid this problem the method ofthe electrochemical capacitance voltage method (ECV) can be used (see e.g. [46], [52],[13]). The Ga1−xMnxAs samples exhibit the negative magnetoresistance al low temper-atures. Recently, F. Matsukura et al. [53] presented that the magnitude of resistancestrongly depend on relative orientations of magnetization and current and their directionsin respect to crystal axes. It was shown (see [38] and references therein) that in termsof metal-insulator transition (MIT), the temperature dependence of resistivity can be costinto two categories. Low- and high-Mn composition samples (x<0.03,x>0.06) are onthe insulator side of MIT, whereas the layers containing intermediate Mn concentrations(0.03≤x≤0.06) are metallic.

Due to the presence of anomalous Hall effect (AHE), magnetotransport measurementsprovide valuable information on magnetism in GaMnAs. Particularly, the anomalous Halleffect studies indicated that the direction of easy axis is mainly controlled by epitaxialstrain in Ga1−xMnxAs [5]. It has been presented that tensile and compressive strains in-duce in-plane and out-of-plane moment orientation respectively. Recently, SQUID mea-surements [54] revealed that GaMnAs epilayers show rich characteristics of magnetic


anisotropy depending not only on epitaxial strain but also on temperature and hole con-centration. These experimental results are corroborated by magnetization measurementsby use of magnetooptical Kerr effect (MOKE) [55]. Theoretical models based on hole-mediated magnetic order [49], [56], [47] give a good account of the observed moment ob-servations, and the formation of magnetic domains is expected [56]. For the out-of-planemagnetized films stripe domain patterns were reported earlier [57]. Recently, magneticdomain structure in Ga1−xMnxAs were studied by means of high resolution magnetoop-tical imaging technique [58]. Large, well defined magnetic domains, on the scale ofhundreds of micrometers, were observed. The clear evidence for a temperature dependentin-plane anisotropy was observed.

The magnetooptical studies of GaMnAs (see e.g. [59]) revealed that the absorptionedge of GaMnAs is not sharp. This is probably due to the impurity band formation causedby the high concentration of ionized Mn and compansating donors [60]. The magnetic cir-cular dichroism (MCD) studies (see [38] and references therein) in the reflectivity modeindicate for a negative value of the p-d exchange integralN0β, similarly to the case of II-VI semimagnetic semiconductors. On the other hand, a positive value of MCD deducedfrom absorption measurements appears to suggest thatN0β is positive [59]. This surpris-ing result is explained if a large Burstein-Moss shift due to the high hole concentrationspecific to III-V SMSC’s is taken into consideration [59].

A detailed theory of ferromagnetism in GaMnAs has not been established yet, butsome important properties such as the Curie temperature, the magnetic anisotropy field,the temperature dependence of the spontaneous magnetization may be derived by use ofmean field theory of ferromagnetism in zinc blende semimagnetic semiconductor [47],[48], [49]. A mean field model based on exchange interaction mediated by delocalizedholes in the ensemble of localized spins has been developed by Dietl et al. [47], [48]. Thebroad range of experiments can be explain by use of this model - assuming an ideal sys-tem without taking into account disorder or formation of impurity band. The model uses aparameterized hole-spin exchange interaction, an exchange integralN0β. The Curie tem-peratureTC is determined by the minimum of the free-energy functional with respect tomagnetizationM at a given hole concentrationp. The hole contribution is computed bysolving a 6×6 Luttinger-Kohn Hamiltonian with the presence of exchange. The theorywith N0β=-1.2±0.2eV taken from photoemission experiments [61] and a carrier-carrierinteraction enhancement of 1.2 [62] explains the large magnitude ofTC=110K [4], [6]for Ga1−xMnxAs with x=0.053 and hole concentrationp=3.5·1020 cm−3 [63]. This mean-field model is also capable of explaining the anomalous magnetic circular dichroism ob-served in GaMnAs [64]. The model explains also the strain dependence of the magneticeasy axis. For experimentally relevant carrier concentrations, the model predicts an in-plane easy axis for compressive strain and a perpendicular axis for tensile strain. It wasestablished experimentally that Curie temperature in Ga1−xMnxAs increases with increas-ing Mn concentrationx (as long as MnAs precipitates are not formed) and with the holeconcentrationp (see e.g. [38] and references therein). These observations are consistentwith the mean-field model of ferromagnetism proposed by Dietl et al., which predicts that

TC = Cxp1/3 (5.1)

whereC is a constant specific to the host material.Recently, T. Jungwirth et al. [65] predicted theoretical calculations of Curie tem-

perature in GaMnAs based on a model with S=5/2 local moments exchange coupled to


itinerant holes in the valence band of semiconductor host. Going beyond the standardmean-field theory of this model the enhancement of theTC due to the exchange and cor-relation in the itinerant-hole system andTC suppression due to collective fluctuations ofthe ordered moments were estimated. The estimated theoretical Curie temperatureTCest

is in good agreement with the experimental transition temperature and very close to mean-field TCMF value justifying the mean-field description of ferromagnetism in this material.

It has been established that the Curie temperature of as-grown GaMnAs epilayers canbe further improved by heat treatment (low temperature annealing). The highest ferro-magnetic transition temperature,TC , observed in GaMnAs (as well as in semimagneticsemiconductors), was for a long time equal to 110K. The results presented in this thesisshowed for the first time that Curie temperature can be enhanced above this limit. The heattreatment (annealing) of the grown by low-temperature molecular beam epitaxy (MBE)Ga1−xMnxAs was the subject of intense studies in a number of laboratories word-wide.First, it was reported that LT annealing improves the Curie temperatureTC and magne-tization M(T) of the annealed samples depending on both the annealing temperature andthe duration of the annealing process [66], [67]. Recently, higher and higher Curie tem-peratures were reported [7], [13], even exceeding 160K [68], [8]. It was also shown that aproper choice of the Mn content and the thickness of GaMnAs epilayer enables a furtherincrease ofTC upon annealing [68], [8].

The Mn ion in the substitutional, cation position in GaAs lattice acts as a acceptor,but in all Ga1−xMnxAs samples the hole concentration is substantially lower than the Mncontent. For a long time this has been ascribed to the formation of arsenic antisites [38]. Itwas shown that the formation of interstitial Mn ions plays here a crucial role [13]. Thesekind of defects play a key role in controlling the ferromagnetic transition in GaMnAs.

5.2 The procedure of annealing

In the present thesis the Ga1−xMnxAs/GaAs epilayers in a wide range of Mn concentra-tion (0.01<x<0.093) were systematically investigated. The procedure of annealing was asfollows. The as-grown wafers were cut into a number of specimens for systematic anneal-ing experiments. The samples were annealed at low temperatures in the range between2600C and 3500C. The time of annealing was between 1 h and 1.5 h. All the samples wereannealed under the flow of N2 gas (in the range between 7.1 10−4 m3/min and 1.42·10−3

m3/min. All post-growth and post-annealing procedures were carried out in the samemanner. After annealing, the samples were cooled down by a rapid quench under the flowof nitrogen gas. Next, the samples annealed at different conditions were characterized bymeans of zero-field resistivity and magnetizationM(T) measurements by use of SQUIDmagnetometer and thus the optimal conditions of annealing were established.

5.3 The results of zero-field resistivity measurements

The zero-field resistivity measurements revealed that annealing leads to large changes inthe transport properties of GaMnAs in the very narrow range of annealing temperatureclose to the growth temperature. The as-grown and annealed samples were character-ized by means of resistivity measurements at zero magnetic field in the temperature rangebetween 10K and room temperature using a helium flow cryostat. The post-growth treat-


ρρ ρρ ΩΩ ΩΩ

Fig. 5.1: The zero-field resistivity of the as-grown GaMnAs epilayers in the wide range of Mnconcentration 0.01≤ x ≤0.093.

ment was in each case the same. For all the samples the electrical contacts for the transportmeasurements were prepared always in the same way. The Hall bar samples with typicaldimensions of 2mm× 6mm were used. The electrical contacts were made using indiumsolder and gold wires. No special precautions were needed to prepare electrical contacts.Typical resistance of the as-grown samples at room temperature was equal from 1 kΩ to2 k Ω. The values of resistivity were obtained with the uncertainty of about 15%. Figure5.1 shows the temperature dependence of zero-field resistivityρ for the as-grown samplesin a wide Mn content 0.01≤x≤0.093.

It is clearly visible that all measured samples reveal metallic type of conductivity.The temperature dependence of the zero-field resistivity shows a broad maximum aroundCurie temperatureTC where negative magnetoresistance also peaks. The hump structureis known to appear at the temperature slightly above the value ofTC obtained from mag-netic measurements. Such critical behavior of resistivity in ferromagnetic GaMnAs wasobserved by many groups (i.e. see [38] and references therein) and suggest the presenceof the critical scattering, in which carriers are scattered by magnetic fluctuation throughexchange interaction. It was shown that hump aroundTC can be interpreted in terms of acritical scattering by packets of ferromagnetically coupled spins, whose correlation lengthis comparable to the wavelength of the carriers at the Fermi level [6], [63].

The measurements of resistivity at zero magnetic field occurred to be very suitablemethod to determine the optimal annealing conditions. Magnetization measurementsM(T) revealed good agreement between transport and magnetic results. For the 10823Cepilayer withx=0.07 annealed for 1 hour at the temperature of 2800C and under flow ofN2 gas (7.1·10−4 m3/min), the value corresponding to the zero-field resistivity hump isequal to 115K, and the SQUID measurements on the same sample yieldedTC=113K (seeFigure 5.2).

For all investigated samples good agreement, within 10%, between zero-field resis-tivity and magnetization results was observed. The optimal time of annealing was in therange between 1h and 1 1/2 h. Figure 5.3 presents the Curie temperature estimated from


ρρρρ

ρρ ρρ

ΩΩ ΩΩ

Fig. 5.2: The temperature dependence of the zero-field resistivity (a hump structure slightlyabove Curie temperature is visible) and magnetization versus temperature measured by aSQUID magnetometer in small magnetic field (B=0.01T) parallel to the sample surface.A good agreement between transport and magnetic data is visible.

the maximum in the temperature dependence of the zero-field resistivity (Tρ) as a functionof the annealing temperature.

All presented samples were annealed for 1 hour under the flow of N2 gas equal to7.1·10−4 m3/min. The large changes in Curie temperature in a very narrow range ofannealing temperatures close to the growth temperature are observed. In the case of allinvestigated epilayers the optimal annealing temperatureTa occurred to be around 2890C.The values of Curie temperature estimated from the zero-field resistivity measurementscorresponding to different annealing temperatures for all studied samples are shown inTable 5.1.

Figure 5.4 shows typical temperature dependences of the zero-field resistivity forthe 10727E Ga1−xMnxAsepilayer withx=0.086 annealed at various temperatures. Theresistivity of the as-grown sample and for samples annealed at relatively low temperatures(2600C, 2890C, 3000C and 3100C) show typical metallic behavior.

For samples annealed at 3500C, an insulating behavior of the resistivity is observed.An increase of both Curie temperature and conductivity is visible after annealing at theoptimal conditions (Ta=2890C, t=1h). For the 10727E sample withx=0.086 the anneal-ing procedure at the optimal temperature shifts theTρ from 88K for the as-grown sampleto 127K, annealing at higher temperature (Ta=3500C) leads to lower Curie temperatureTρ=30K. In general, the large changes of the Curie temperature in the narrow range of theannealing temperature near the growth temperature are accompanied by the large changesof the conductivity. It was found that for the low Mn concentration,x < 0.05, the influ-ence of the annealing procedure on both the Curie temperature and conductivity is weak.Figure 5.5 presents typical zero-field resistivity measured for GaMnAs sample with lowMn contentx=0.027 (10727C) annealed at different thermal conditions. Inset shows theobtainedTρ values versus annealing temperature. It is clearly visible that in this caseannealing procedure leads to the slight changes in both Curie temperature as well as re-sistivity of the sample.


ρρ ρρ

Fig. 5.3: Curie temperatureTρ estimated from the the zero-field resistivity measurements versustemperatures of annealing for GaMnAs samples with different Mn concentration 0.01≤x≤0.093.

Tab. 5.1: Curie temperatureTρ estimated from the zero-field resistivity measurements for as-grown (a.g.) and annealed at different temperaturesTa for 1 hour in nitrogen atmosphereGaMnAs samples with different Mn composition (0.1≤x≤0.093) and various layer thick-nessd.

GaMnAs GaMnAs GaMnAs GaMnAs GaMnAs GaMnAs GaMnAs00811A 00119C 10727C 10727D 10727E 10823C 10823E

d=302nm d=269nm d=131nm d=149nm d=105nm d=111nm d=115nmx=0.01 x=0.032 x=0.027 x=0.062 x=0.086 x=0.07 x=0.093

Ta Tρ Ta Tρ Ta Tρ Ta Tρ Ta Tρ Ta Tρ Ta Tρ

[C] [K] [C] [K] [C] [K] [C] [K] [C] [K] [C] [K] [C] [K]a.g. 41 a.g. 70 a.g. 53 a.g 67 a.g. 88 a.g. 68 a.g. 53260 41 278 72 260 59.5 260 91 280 125 280 115 280 101300 40. 300 72 280 59 280 95 289 127 289 116 289 102350 34 350 42 300 62.5 300 101 300 118 300 113 300 99

- - - - 319 62 320 92 310 103 310 101 310 97- - - - 350 50 350 35 350 30 350 40 350 38


ρ

Ω

Fig. 5.4: Temperature dependence of the zero-field resistivity of GaMnAs sample with high Mnconcentration (x=0.086) annealed at various temperatures.

ρρ ρρ

!"

#

$

%&

ρ Ω

Fig. 5.5: The temperature dependence of zero-field resistivity for as-grown and annealed at var-ious temperatures sample with low Mn concentrationx=0.027. Inset shows the Curietemperature estimated from the resistivity measurements versus annealing temperature.


It was shown that effects of low temperature annealing (at 2400C for 1 hour in anitrogen atmosphere) are more pronounced for the thin layers of Ga1−xMnxAs[69]. Re-cently, K.C. Ku et al. [70] reported that the highestTC in both as-grown and annealed(post-growth annealing for 90 minutes at 2500C in a nitrogen atmosphere) GaMnAs lay-ers occurs for sample thickness between 10nm and 50nm and thatTC is suppressed forthicker layers. The decrease ofTC with the increase of the layer thickness for the as-grown GaMnAs epilayers was observed also by Matsukura et al. [39] and B.S. Sorensenet al. [71]. In present thesis GaMnAs samples with the thickness in the range between105nm and 302nm were systematically annealed and measured. The samples with dif-ferent thickness of GaMnAs layer were characterized simultaneously by different Mnconcentration. This made impossible to verify above suggestions. Nevertheless, the care-ful inspection of Table 5.1 allows to notice that increase of the Curie temperature afteroptimal thermal annealing depends on the Mn concentration and is the most effective forthe high Mn concentration. The observed in the same time enhancement of conductivityis also the most effective for the GaMnAs epilayers with high Mn concentration. Thiseffect is illustrated in the Figure 5.6 where conductivity versus annealing temperature isshown for two samples with low (x=0.027, 10727C) and high Mn concentration (x=0.086,10727E) with similar thickness of GaMnAs layer (131nm and 105nm, respectively). Theannealing procedure is more effective in the case of higher Mn concentration.

5.4 The results of magnetotransport measurements

The magnetotransport measurements were performed in the range of low as well as highmagnetic fields. As grown and annealed at different conditions ferromagnetic GaMnAssamples were investigated in the static (up to 0.5T by use of classical electromagnet andup to 13T using superconducting magnet) as well as pulsed (up to 55T) magnetic fieldsapplied perpendicular to the plane of the film. Both, the anomalous Hall effect as wellas magnetoresistivity (MR) measurements were performed. The DC six probe techniquewas used to perform magnetotransport measurements in the case of low as well as highmagnetic fields.

Magnetotransport measurements provide valuable information on magnetism of thinfilms and are of particular importance in the case of thin films of semimagnetic semicon-ductors in which the magnitude of the total magnetic moment is small. Particularly, theanomalous Hall effect (known also as a extraordinary Hall effect or spin Hall effect) - ifunderstood theoretically - can serve to determine the magnitude of magnetization. How-ever, it should be stressed that the AHE does not provide information about magnetizationof the whole sample but only about its value in the regions visited by the carriers. Particu-larly, near the metal-insulator boundary the carrier distribution is highly nonuniform anddirect magnetic measurements may provide different magnetization values.

The Hall resistanceRHall of a magnetic film of the thicknessd is empirically knownto be a sum of ordinary and anomalous Hall terms [72]:

RHall =Ro

dB +

Rs

dM⊥ (5.2)

whereRo andRs are the ordinary and anomalous Hall coefficients respectively,d is thesample thickness,B is magnetic field andM⊥ is the component of magnetization perpen-dicular to the sample surface.


ΩΩ ΩΩ

!!

ΩΩ ΩΩ

!"##

Fig. 5.6: Conductivity versus annealing temperature for the samples with high Mn concentrationx=0.086 and with low Mn concentrationx=0.027.


The anomalous Hall coefficient is usually assumed to be proportional toRαsheet, where

Rsheet is the sheet resistance. The exponentα is either 1 or 2 depending on the origin ofthe effect. For the skew scattering mechanismα=1, whereas for the side jump mechanismα=2 [72]. A comparison of Hall resistivity and SQUID magnetization data allows toidentify the the dominating mechanism.

Recently, Jungwirth et al. [73] developed theory of the AHE in p-type zinc-blendemagnetic semiconductors and presented numerical results for GaMnAs employing for-mula for the side-jump mechanism in the weak scattering limit.

Moreover, the experimental results demonstrated by Dietl et al. [51] suggested thatthe side-jump mechanism gives the dominant contribution for metallic samples. Also thetheory discussed by the authors [51] indicates that the side-jump mechanism accountsfor AHE in the investigated ferromagnetic material. The authors show that there is agood agreement between their experimental and theoretical [73] magnitude of the Hallconductivity. The theory discussed by Dietl et al. [51] explains the sign of the AHE (thecoefficients of the normal and anomalous Hall effects are expected to have the same sign)and, together with the results obtained by Jungwirth et al. [73] explains the magnitude ofthe Hall conductance.

The presence of the AHE makes the determination of the carrier concentration andtype of carriers very difficult. Determination of the free carrier concentration is compli-cated by the dominance of the anomalous Hall effect term. Generally, in order to obtainfree carrier concentration, the magnetotransport investigations should be performed at lowtemperatures and at magnetic fields sufficiently high so that the magnetization saturates.Then, the ordinary Hall coefficient can be determined from the remaining linear changeof the Hall resistance in the magnetic field. However, the experimental data, i.e. the mag-netization measurements performed by means of magnetooptical Kerr effect up to 25T(see section 6 of this Chapter) revealed that magnetization does not saturate even at thehighest magnetic fields. This makes determination of free carrier concentration difficultand doubtful.

In the present paper, an effort to determine free hole concentration in the as-grown aswell as annealed Ga1−xMnxAs layers was made. The Hall resistivity as well as magne-toresistivity measurements were performed simultaneously in the high pulsed magneticfields up to 55T and low temperatures (T=4.2K) for the epilayers of GaMnAs with vari-ous Mn concentration 0.027≤x≤0.086. Fig 5.7 shows the typical anomalous Hall voltagesignal as a function of magnetic field for two samples of 10727E GaMnAs epilayer withx = 0.086: as-grown and annealed at the optimal temperature 2890C.

The obtained data indicates that the contribution from the ordinary Hall term is rathersmall in the displayed range of temperature and magnetic field - the Hall voltage reflectsM(B) behavior and the significant component to the Hall voltage comes from the anoma-lous Hall effect. It should be stressed that negative magnetoresistance (MR) that is presentin the GaMnAs samples and persists up to high magnetic fields (look in Figure 5.8) addsto the measured signal of anomalous Hall effect. This, in turn, makes the determinationof free carriers difficult.

The magnetotransport measurements (Hall resistivity and conductivity) that were per-formed even in the higher range of magnetic fields (up to 55T) do not give a unique valuefor the hole concentration of the investigated epilayers. As was mentioned before, in therange of high magnetic fields where one may expect magnetization saturation the Hallvoltage should be related to free carrier concentration. In the experiments performed in


ρρρρ

ρρρρ

µµµµ

!" #$%

&"#

Fig. 5.7: The Hall voltage versus magnetic field for two samples of Ga1−xMnxAs with x=0.086,as-grown and annealed at the optimal conditions, measured atT=4.2K. Note that domi-nant contribution to the Hall voltage comes from the AHE term; the Hall voltage reflectstheM(B) behaviour.

the present thesis the difference between the slopes of the Hall voltage in high magneticfields is very small and the data obtained up to 55T do not give the unique value forthe hole concentration of the investigated epilayers. The results obtained by the electro-chemical voltage capacitance voltage (ECV) method in the Lawrence Berkeley NationalLaboratory on the samples annealed and investigated in the present thesis (as-grown andannealed at the optimal conditions samples of 10823C epilayer withx=0.07) [13] clearlyshow that optimal annealing increases the free hole concentration. The increase from 61020 cm−3 for the as-grown sample to 1·1021 cm−3 for the annealed sample was observed.Moreover, further investigations of the as-grown and annealed at the optimal conditionsGaMnAs samples (annealing conditions similarly to these established by author) withvarious Mn concentration by ECV method (see e.g. [52]) confirmed these results. Con-trary to expectation that free hole concentration should increase after annealing at theoptimal conditions (as was shown by electrochemical capacitance voltage (ECV) profil-ing method) the obtained transport data in the high magnetic fields indicate the decreaseof the free carrier concentration. The reason is that the experimental data - Hall voltageversus magnetic field - reflectsM(B) dependence rather then normal Hall effect term. Itshould be also stressed here that performed magnetic investigations - both: direct SQUIDas well as magnetooptical Kerr effect (MOKE) investigations (see sections 5 and 6 ofthis Chapter) indicate that even at low temperatures (T=4.2K) and high magnetic fields(MOKE measurements performed in pulsed magnetic fields up to 25T) the magnetizationis far from being saturated. Also negative magnetoresistance that hardly saturates evenat very high magnetic fields (the measurements ofMR performed up to 55T) makes thedetermination of free carrier concentration in GaMnAs films difficult.

The measurements ofMR were performed in the static (up to 13T) as well as pulsed(up to 55T) magnetic fields applied perpendicular to the plane of the film.

Recently, it has been found that magnetoresistance of Ga1−xMnxAs depends on the


ρ

∆∆ ∆∆

ρρρρ

∆

ρρρρ

∆

Fig. 5.8: Magnetoresistivity (R-R0)/R0, whereR0 is the value of resistivity atB=0, for the epilayerwith high Mn contentx=0.07 measured at various temperatures 4.2K, 40K, 110K, 150Kand 200K for as-grown sample annealed at the optimal conditions (Ta=2890C) and afterannealing at higher temperature (Ta=3500C).


ρρρρ

ρρρρ

ρρρρ

∆∆ ∆∆

!"#!$%

Fig. 5.9: Magnetoresistivity (R-R0)/R0, whereR0 is the value of resistivity atB=0, for the epilayerwith high Mn contentx=0.086: as-grown, annealed at the optimal conditions (Ta=2800C)and after annealing at higher temperature (Ta=3500C).

relative orientation of the current and magnetic field [74], [75], [76], [53]. The observedanisotropic magnetoresistance (AMR) is quite sizable and depends also on the direction ofthe field and current with respect to crystal axis. The measurements ofMR in the presentthesis were performed in the configuration with magnetic fieldB applied perpendicular tothe sample surface and electric currentI flowing randomly with respect to the crystal axis.The effects ofAMRwere not studied. One of the aims of presentedMRmeasurements wasto explore the influance of low temperature annealing on the magnetic field dependenceof resistance.

All investigated samples in a wide range of Mn concentration 0.027≤x≤0.086 ex-hibit negative magnetoresistance above 0.5T. Presently, it is common knowledge (see e.g[38]) that for the Ga1−xMnxAs samples, the negative magnetoresistance peaks aroundTC ,where the temperature dependence of resistance shows a maximum. This effect was alsoobserved for investigated epilayers in the present thesis and is shown in Figure 5.8. Themagnetoresistivity measured up to 13T ((R-R0)/R0, whereR0 is resistivity at zero magneticfield) is shown for three samples: as-grown, annealed at the optimal conditions Ta=2890Cand higher temperature of 3500C of 10823C epilayer with high Mn concentrationx=0.07.It is clearly visible thatMR peaks at the temperature equal to Curie temperature. Furtherinvestigations at higher pulsed magnetic fields (up to 55T) revealed that the negative mag-netoresistance is unsaturated up to the highest value of the investigated field. This effect ispresented in Figures 5.9 and 5.10, where magnetoresistivity is shown for the as-grown andannealed samples with high (10727Ex=0.086) as well as low Mn concentration (10727Cx=0.027).

The author found that annealing of the GaMnAs epilayers with high Mn concentrationleads to very significant changes in magnetoresistivity in the range of low temperatures.As it is clearly visible in Figure 5.9, annealing at the optimal conditions of the epilayerswith high Mn concentration leads to significant decrease ofMR. Annealing at higher tem-peratures (for the 10727E epilayer, the sample annealed at 3500C was investigated) leads


∆∆ ∆∆

ρρρρ

!"#

ρρρρ

Fig. 5.10: Magnetoresistivity (R-R0)/R0, whereR0 is the value of resistivity atB=0, for the epi-layer with low Mn contentx=0.027: as-grown and annealed at the optimal conditions(Ta=3000C).

to the substantial increase of magnetoresistance. It should be recalled here (see section 2of this Chapter), that zero-field resistivity measurements (resistance versus temperature)revealed metallic type of conductivity for the samples annealed at the optimal conditionsand insulating type of conductivity for the samples annealed at higher temperatures. Alarge negative magnetoresistance was observed and reported on the insulating side andin the vicinity of the metal-insulator transition in GaMnAs samples [77], [78]. For theGaMnAs samples with lower Mn content (x=0.027) theMR is not affected by the heattreatment at the optimal conditions. It should be stressed that also the influence of anneal-ing procedure on both the Curie temperature and conductivity is weak in this case. For10727C epilayer withx=0.027 the observed changes in magnetoresistance after annealingat the optimal conditions are very small.

Recently, the negative high field magnetoresistance was studied experimentally anddiscussed by F. Matsukura et al. [53] and T. Dietl et al. [51]. The authors show that theresistance maximum and the associated negative magnetoresistance in the vicinity ofTC

seem to result from effects of thermally disordered spins upon localization and scatter-ing. As is underline in the papers, there is a number of effects that can produce a sizablemagnetoresistance in magnetic semiconductors, especially at the localization boundary[79]. In particularly, spin disorder scattering shifts the MIT (metal to insulator transition)towards higher carrier concentration. Since the magnetic field orders the spins, negativemagnetoresistance occurs, sometimes leading to the field-induced insulator-to-metal tran-sition [80]. Negative magnetoresisstance and resistance maximum atTC persist deeplyin the metallic phase owing to critical scattering [63]. The negative magnetoresistancehardly saturates even at high magnetic fields and occurs also at low temperatures. Inorder to explain this observation, the authors note that the giant splitting of the valenceband makes both spin-disorder and spin-orbit scattering relatively inefficient. Under suchconditions, weak localization magnetoresistance can show up at low temperatures, whereinelastic scattering ceases to operate. The low-temperature negative magnetoresistanceappears to do not be any spin phenomenon but an orbital effect resulting from the destruc-


ΩΩ ΩΩ

!"#

Fig. 5.11: MagnetoresistivityR for the sample withx=0.01 in low magnetic fields atT=20K. Themagnetic fieldB was applied perpendicular to the film. Note that hysteretic behavior isvisible. The arrows and numbers indicate the history and direction of applied magneticfield.

tive influence of the magnetic field on interference of scattered waves.In the range of low magnetic fields the positive magnetoresistance is present. TheMR

curves exhibit hysteretic behavior for the configuration with the perpendicular directionof magnetic field and samples under compressive strain. This effect is shown in Figures5.11 and 5.12.

The low magnetic field data can provide information on process of field-induced ro-tation of magnetization in respect to magnetic field direction, crystal and easy axis. Re-cently, [53] showed that behaviour of magnetoresistance in the low magnetic field rangedepends on the character of the strain and on the field and current directions. In particu-lar, for the magnetic field pointed along the growth direction, the values of the magneticfield corresponding to resistance maxima are of order of the anisotropy field (∼0.2T) thataligns magnetization along the growth direction.

The values ofB corresponding to the maxima of magnetoresistance for the samplesinvestigated in the thesis are of the same order as reported in Ref. [53].

The hysteretic behaviour of low magnetic fieldMR is correlated with the low magneticfield behavior of SQUID magnetization - hysteresis loops of magnetization (see section5 of this Chapter). As the temperature is reduced below Curie temperature, an increasein the coercive field is observed that collaborates the low field hysteretic behavior ofMR.With the decrease of temperature the low field hysteretic feature of the magnetoresistivityis much stronger (see Figures 5.12).

Moreover, the LT annealing affects also the magnetoresistivity and hysteresis loops.The decrease of both the coercive field and negative magnetoresistivity is pronouncedafter annealing at the optimal conditions (the SQUID magnetization data are describedand discussed in details in section 5 of this Chapter). Only speculative and phenomeno-logical interpretation is possible at present. Recently, T. Fukumura et.al. [81] showedthat the films of GaMnAs with in-plane magnetization has unconventional domain struc-ture that show random arrangement of the domains. It is obvious that hysteresis loop


Fig. 5.12: Low magnetic field magnetoresistivity for the Ga1−xMnxAs sample withx=0.01 mea-sured at various temperatures. The magnetic fieldB was applied perpendicular to thefilm. The arrows and numbers indicate the history and direction of applied magneticfield.

features, specifically coercive field, shape, saturation magnetization are correlated withdomain structure. The transport properties of the ferromagnetic materials can be modi-fied by domain walls, particularly domain wall can increase or decrease the resistance ofthe system [82]. Moreover, it was shown that the shape and positions of the peaks ofMRdepend on domain structure and squareness of the hysteresis loops [83]. The observedlarge changes of theMR and magnetization can be related with the change of domainstructure of GaMnAs system.

Matsukura et al. [53] assigned the effect of hysteretic resistance jumps to a large ratioof the anisotropy and coercive fields, which makes that even a rather small misalignment,and thus a minute in-plane field, can result in magnetization switching between in-planeeasy-directions.

5.5 The results of SQUID measurements

Magnetic properties of Ga1−xMnxAs thin layers can be measured by direct magnetizationmeasurements as well as magnetooptical studies (Magnetooptical Kerr Effect - MOKE)and magnetotransport investigations. In this section the results of direct magnetizationmeasurements will be shown and discussed. Direct measurements of the magnetizationM of GaMnAs epilayers as a function of magnetic fieldB and temperatureT were per-formed by use of a commercially available superconducting quantum interference device(SQUID) magnetometer. The temperature independent diamagnetic response of GaAssubstrate was determined from separate measurement of only the same GaMnAs sub-strate used for epitaxial growth. Next, the diamagnetic component was subtracted from


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Fig. 5.13: Magnetization versus temperatureM(T) measured in small magnetic fieldB = 10Gs forthe as-grown and annealed at 2890C GaMnAs sample withx=0.07. It is clearly visiblethat annealing procedure at the optimal conditions leads to the increase of saturationmagnetization.

the total response to obtain magnetization of the magnetic layer. The as-grown and an-nealed at different conditions samples were measured when magnetic fieldB was appliedparallel to the GaMnAs layer.

Two types of magnetization measurement were performed. First, the temperaturedependence of magnetizationM(T) was measured in small magnetic fields (i.e., 10 Gauss)after the sample has been magnetized at higher magnetic field (1000 gauss) parallel tothe sample surface. These measurements allowed to determine paramagnet/ferromagnetphase transition temperature. As an example the magnetization curves versus temperaturemeasured for two samples withx=0.07 (10823C epilayer), as-grown and annealed at theoptimal conditions (Ta=2890C) are shown in Figure 5.13.

The magnetization measurementsM(T) revealed good agreement between transportand magnetic results. The values of Curie temperature determined from SQUID measure-ments are in good agreement, within 10% with the values estimated from the zero-fieldresistivity. It is clearly visible that, the saturation magnetizationMS increases after heattreatment at the optimal conditions, indicating that annealing increases the concentrationof magnetically active Mn ions. Such effect is observed for all investigated samples in thewhole range of Mn concentration.

The second aim of the SQUID measurements was to investigate the hysteresis loopsof as-grown and annealed epilayers of GaMnAs. Figure 5.14 shows magnetization curvesat several temperatures of as grown and annealed at the optimal conditions (Ta=2890C,t=1h, under flow of N2) samples of a 111nm thick GaMnAs layer with Mn contentx =0.07 (10823C epilayer) grown on GaAs substrate. When magnetic fieldB is applied par-allel to the sample surface,M(B) curves show a clear hysteresis below Curie temperature(TC=67K for as-grown sample,TC=112K for annealed sample - as indicated fromM(T)measurements).

The measurements ofM(B) showed that the annealing process also affects the hystere-


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Fig. 5.14: Magnetization versus temperatureM(T) measured in small magnetic fieldB = 10Gs forthe as-grown and annealed at 2890C GaMnAs sample withx=0.07. It is clearly visiblethat annealing procedure at the optimal conditions leads to the increase of saturationmagnetization.


Fig. 5.15: The hysteresis loopM(B) for the as-grown and annealed at the optimal conditions sam-ple with x=0.07 measured atT=5K. The decrease of coercive field is visible after opti-mal annealing.

sis loops particularly, the coercive field decreases when the samples are annealed at theoptimal temperatures around 2890C. This effect is shown in Figure 5.15. Simultaneously,the increase of the saturation magnetizationMS is also observed after heat treatment at theoptimal conditions, indicating that annealing increases the concentration of magnetically-active Mn ions. Thermal annealing at higher temperature leads to increase of the coercivefield and decrease of the saturation magnetization. Figure 5.16 presentsM(T) curves forthe three samples with Mn concentrationx=0.061: as-grown, annealed at the temperature2800C and higher temperature 3500C measured at small magnetic fieldB=10Gs.

Annealing at high temperature of 3500C leads to the significant decrease of both theCurie temperature as well as the saturation magnetization. This effect is accompaniedby the large increase of the coercive field. This effect is shown in Figure 5.17, wherehysteresis loops for as-grown and annealed at 2800C and higher temperature of 3500Csamples withx=0.062 (10727D epilayer) are presented.

It has been found by anomalous Hall effect studies [42], [5], that the direction of theeasy axis is mainly controlled by epitaxial strain in Ga1−xMnxAssystem. The direct mag-netization studies by use of SQUID magnetometer (see e.g. [38] and references therein)confirmed that for GaMnAs layer grown on GaAs substrate (i.e. under compressive bi-axial strain) in-plane magnetic easy axis is observed. The hard magnetic axis lies in theperpendicular direction. In the present work the SQUID magnetization curves were mea-sured applying magnetic field parallel to the sample surface. An effort to measure SQUIDmagnetization in the magnetic field perpendicular to the sample surface was made for theas-grown and annealed 10727E epilayer withx=0.086, but unfortunatelly the signal of105 nm thick layer was too small in this case. Recently, it was demonstrated by SQUIDmagnetization measurements [54] that GaMnAs films can exhibit rich characteristics ofmagnetic anisotropy depending not only to the epitaxial strain but being strongly influ-enced by the Mn as well as hole concentration and temperature. The temperature-inducedreorientation of the easy axis from [001] to [100], and then to [110] or equivalent di-


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Fig. 5.16: Magnetization versus temperature measured by SQUID magnetometer at small mag-netic fieldB=10Gs for three samples withx=0.062 (10727D epilayer): as-grown, an-nealed at the temperature 2890C and 3500C.

Fig. 5.17: The hysteresis loopsM(B) for the sample withx=0.062 as-grown, annealed at the tem-perature equal to 2890C and higher temperature 3500C.


x

y

Ei

Magnetic material

x

y

θθK

ab

Fig. 5.18: The principle of magnetooptical Kerr effect method.

rections occurs in films of (001) GaMnAs grown on GaAs substrate with appropriatelylow values ofp. The data collected nearTC revealed a non-equivalence of the [110] and[-110] crystal directions, the latter corresponding to hard axis. This kind of anisotropydevelops independently of free hole concentration and was reported by other groups [80],[55]. Finally Sawicki et al. reported, that for the samples with relatively high values offree hole concentration the hard axis remains oriented along [-110] direction but the threeother main directions ([100], [110] and [010]) become equally easy.

5.6 The results of magnetooptical Kerr effect measurements

The magnetooptical Kerr effect (MOKE) measurements were performed in order to studythe magnetic properties of the investigated GaMnAs layers. The experiments were carriedout in the polar configuration under pulsed magnetic fields up to 25T and at temperatures5K≤T≤250K for the as-grown and annealed at the optimal conditions epilayers.

First, the briefly outline of the MOKE method and next, the results of the performedmeasurements are presented.

5.6.1 Introduction - magnetooptical Kerr effect

The magnetooptical Kerr effect corresponds to a change in the polarization of light re-flected from a magnetic material. Reflection of a beam of linearly polarized light from amagnetized material causes the polarization to become elliptical, with the main axis ro-tated over a small angleθK with respect to the incident light. Figure 5.18 shows schemat-ically the principle of the magnetooptical Kerr effect.

The elipticity of the reflected light is quantified byε (ellipticity angle):

ε = arctan(e) (5.3)

wheree (ellipticity) is equal to the ratio of the length of the semi-minor axis of the ellipse(b) to the length of its semi-major axis (a): e= b

a.

The change in the polarization of light is described by Kerr complex angle:

ΦK = θK + iε (5.4)


whereθK is Kerr rotation angle andε is ellipticity angle.The magnetooptical Kerr effect can be measured in three different configurations.

• Longitudinal Kerr effect: the magnetic field is applied in the plane of the sample aswell as in the plane of incidence.

• Transverse Kerr effect: the magnetic field is applied in the plane of the sample andperpendicular to the incidence plane.

• Polar Kerr effect: the applied magnetic field is perpendicular to the sample surface.

Both longitudinal as well as polar magnetooptical Kerr effect configurations have in com-mon that the magnetization lies in the plane of incidence. This is not the case anymore intransverse configuration. No Kerr rotation and ellipticity are expected in this configura-tion. Figure 5.19 illustrates possible configurations of MOKE.

LongitudinalKerr effect

PolarKerr effect

TransverseKerr effect

Fig. 5.19: Three configurations for magnetooptical Kerr effect measurements: longitudinal, trans-verse, polar.

In the present thesis MOKE measurements were carried out in the polar configuration.A simple interpretation of MOKE can be achieved using a macroscopic point of view. TheKerr effect appears because left- and right-circularly polarized light waves propagatesdifferently in the magnetic material. A linearly polarized beam of light can be thought asa superposition of such two kinds of waves.

The constants pertaining to the MOKE (polar) in the special case of normal incidencehave the following form [84]:

θK = Im N+ −N−1−N+N−

(5.5)

and

ε = Re N+ −N−1−N+N−

(5.6)

where: θK is Kerr rotation angle,N is the complex index of refraction (N=n-ik; n=realindex of refraction;k=extinction coefficient),N+ andN− are the complex indexes of re-fraction for the right-circularly and left- polarized light respectively,ε is ellipticity angle.

The magnetooptical Kerr effect arises from antisymmetric, off-diagonal elements inthe optical conductivity tensorσxy [84]. The off-diagonal elements of conductivity tensorlead to different indices of refraction for right- and left-circular light in a medium and arethus responsible for mantetooptical effects (for instance magnetooptical Kerr effect).

MOKE is proportional to the net magnetization of ferromagnetic sample. In the caseof a nonferromagnetic material MOKE is proportional to the external magnetic field.


The calculations performed by H. S. Bennet and E. A. Stern [85] revealed that forferromagnetic material:

ΦferroK ∝ σxy ∝ M (5.7)

whereM is magnetization.For nonferromagnetic material:

ΦnonferromagneticK ∝ σxy ∝ B (5.8)

whereB is magnetic field.Another difference between these two types of materials is the order of magnitude.

The rotation for nonferromagnet is much smaller then for a ferromagnetic material.A real microscopic explanation of magnetooptical Kerr effect in ferromagnetic mate-

rials was initiated by Hulme in 1932 and completed by P. Argyres in 1955 [84]. Argyresshowed that including the interaction between an electron and an effective field that it"feels" as it moves through a material leads to non-zero of-diagonal elements in the con-ductivity and polarizability tensors that determine the index of refraction. The key stepwas introduction of spin-orbit interaction. The calculations of Argyres show that tensorsof conductivity and poarizability have non-zero off diagonal elements which come di-rectly from included spin-orbit term. Knowledge of these tensor elements allowed him tocalculate the difference in the index of refraction in right- and left- circular modes. TheKerr constantsθK andε can be obtained using the following relationship:

N+ −N−1−N+N−

=1

ε0ω

σxy

N(1−N2)(5.9)

5.6.2 The results of MOKE measurements for the as-grown and annealed GaMnAsepilayers

In order to study the magnetic properties of GaMnAs layers the magnetooptical Kerr ef-fect (MOKE) measurements were performed. The experiments were carried out in thepolar configuration for four epilayers in a wide range of Mn concentration: as grown andannealed 10727E samples withx=0.086, as grown 11127A sample withx=0.048 and asgrown 10529A sample with x=0.014. The experimental setup used for these measure-ments is schematically shown in Figure 2.7 and described in details in Chapter 2.

The MOKE measurements were performed for two wavelengths of incident light:λ=632.8 nm (red HeNe laser) andλ=540.5 nm (green HeNe laser). The magnetoopti-cal studies were carried out under pulsed magnetic fields up to 25T and at temperaturesranging from 5K up to 250K.

Figure 5.20 presents Kerr rotation angleθK versus magnetic field up to 6T for the asgrown epilayer with high Mn contentx=0.086 and a Curie temperatureTC=88K.

The data were collected at various temperatures - below and above Curie temperature.The magnetic field dependence of Kerr rotation angleθK at different temperatures for thesame epilayer withx=0.086 annealed at the optimal conditionsTa= 2890C is shown in theFigure 5.21.

It is clearly visible that belowB=1T and forT belowTC , θK(B) exhibits a non mono-tonic field dependence. This non monotonic behavior is observed in the Kerr rotationcurves for all of the investigated samples: as grown and annealed 10727E epilayer with


θθ θθ

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Fig. 5.20: Kerr rotation angleθK versus magnetic field up to 6T for the as grown epilayer withhigh Mn contentx=0.086 and a Curie temperatureTC=88K.

θθ θθΚΚ ΚΚ

!

Fig. 5.21: The magnetic field dependence of Kerr rotation angleθK at different temperatures forthe epilayer withx=0.086 annealed at the optimal conditionsTa= 2890C

, λ=632.8nm.


λ λ λ λ

θθ θθ ΚΚ ΚΚ// // θθ θθ

ΚΚ ΚΚ

! "

! "#

! "#

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Fig. 5.22: The results of MOKE obtained atT=5K for λ=632.8nm for all investigated samplesas grown and annealed 10727E epilayer withx=0.086 and for epilayers with lower Mnconcentration: 11127A (x=0.048) as well as 10529A (x=0.014).

x=0.086 and for epilayers with lower Mn concentration: 11127A (x=0.048) as well as10529A (x=0.014). The results obtained atT=5K for two wavelengths of incident lightλ=632.8nm andλ=540.5nm are presented in Figure 5.22 and Figure 5.23 respectively.

These figures indicate very clearly that low magnetic field feature shifts towards highermagnetic fields after annealing. The low magnetic field dependence of Kerr rotation an-gle was measured systematically at different temperatures (below as well as above Curietemperature) for two samples - as grown and annealed at the optimal conditions 10727Eepilayer. These measurements showed that the non monotonic low magnetic field behav-ior is related to the magnetic properties of the studied epilayers. The observed feature ispresent up to temperatures nearTC - it disappears at the temperatures just below Curietemperature. The shift towards higher magnetic field with the increase of Mn contentis also visible. The comparison ofθK(B) behaviour for two used wavelengths (look inFigures 5.24 and 5.25 where magnetic field dependence of Kerr rotation angle for twoas grown epilayers withx=0.086 andx=0.014 for red as well as green laser lines is pre-sented) indicates that the position in the magnetic field is the same for red as well as greenlaser, however the change in the shape of the low magnetic field feature is visible.

To compare the measured magnetic field dependence of Kerr rotation angle with theabsolute magnetizationM, additionally the SQUID investigations were performed for asgrown 10727E sample withx=0.086. The measurements were performed in the perpen-dicular configuration at low temperatureT=5K. The diamagnetic component of diamag-netic GaAs substrate was subtracted from the total response to obtain magnetization ofthe GaMnAs layer. As was mentioned in the previous section, the signal of the 105 nm


λ λ λ λ


ΚΚ ΚΚ

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Fig. 5.23: The results of MOKE obtained atT=5K for λ=540.5nm for all investigated samplesas grown and annealed 10727E epilayer withx=0.086 and for epilayers with lower Mnconcentration: 11127A (x=0.048) as well as 10529A (x=0.014).

λ λ λ λ

λλλλ


ΚΚ ΚΚ

!"#$

Fig. 5.24: The comparison ofθK(B) behaviour for two used wavelengths (two wavelengths ofincident lightλ=632.8nm andλ=540.5nm) for as grown epilayer withx=0.086.


λλλλ

λ λ λ λ


ΚΚ ΚΚ

!"#$

Fig. 5.25: The comparison ofθK(B) behaviour for two used wavelengths (two wavelengths ofincident lightλ=632.8nm andλ=540.5nm) for as grown epilayer withx=0.014.

thick GaMnAs layer was small and noisy for this configuration (hard axis). Figure 5.26presents measured magnetizationM versus magnetic field at 5K. Unfortunately, this datadoes not give the unique answer about the existence of low magnetic field feature in theSQUID magnetization.

At present only very speculative interpretation of the measured data is possible. Itis known (see previous section) that GaMnAs films exhibit rich characteristics of mag-netic anisotropy [54], [80], [55]. The low magnetic field behavior of Kerr rotation angledescribed above can be related with the magnetic anisotropy observed in GaMnAs epi-layers. However, up to now the MOKE measurements as a function of wavelength werenot investigated.

Nevertheless, the SQUID measurements performed in the perpendicular configurationtogether with MOKE studies indicate that even at low temperatures and high magneticfields the measured magnetization is far from being saturated. In addition, comparison ofthe two data sets: Kerr rotation angle with the SQUID magnetizationM (look in Figure5.27) collected in the same field range indicates that the usual relationθK ∝ M, observede.g. for metallic magnetic metals, is not valid for GaMnAs.

The magnetic field dependence of Kerr rotation angle was also studied in the rangeof high magnetic fields. Figure 5.28 presentsθK(B) curves measured up to 25T at lowtemperature equal to 5K.

For all the investigated samples in the wide range of Mn concentration the oscillatoryterms are clearly visible in the range of high magnetic fields. For high magnetic fields,where the following condition is satisfied:s=ωCτ À 1 (ωC is cyclotron frequency andτis life time), the quantum phenomena can be observed - in optics the resonance optical


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Fig. 5.26: SQUID magnetizationM versus magnetic field at 5K. The magnetic field was appliedperpendicular to the sample surface.

θθ θθΚΚ ΚΚ

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Fig. 5.27: The comparison of the two data sets: Kerr rotation angle with the SQUID magnetizationM(B) collected atT=5K.


λ λ λ λ

θθ θθ

ΚΚ ΚΚ

!"

#!"

$#!"

Fig. 5.28: The results of MOKE obtained atT=5K for λ=632.8nm in the range of high magneticfields for all investigated samples as grown and annealed 10727E epilayer withx=0.086and for epilayers with lower Mn concentration: 11127A (x=0.048) as well as 10529A(x=0.014)


transitions. The oscillatory terms visible in the Figure 5.28 can be related to the interbandoptical transitions between Landau levels, i.e. resonance interband transitions from heavyholes, light holes, spin-split-of bands to conduction band. The similar oscillatory behaviorof Kerr rotation angle in high magnetic fields for GaMnAs epilayers was observed by N.Négre [86]. The author studied MOKE under high pulsed magnetic fields (up to 32T) forGaMnAs epilayers with low Mn concentration - up tox=0.034. The performed Fouriertransform analysis ofθK(1/B) curves measured atT=5K for GaMnAs epilayers as wellas for low temperature epilayers of GaAs allowed to obtain the resonance frequencies.In the case of GaAs three frequencies of the measured oscillations were clearly visible:F1=276T,F2=182T andF3=42T. Additionally, the first harmonic of frequencyF3 equalto 80T was observed. These three frequencies author assigned to the following interbandtransitions:F1 - from heavy holes band to conduction band,F2 - from light hole bandto conduction band andF3 - from spin-split-of band to conduction band. For GaMnAsepilayers the same frequencies were observed as for GaAs sample. Additional frequencyF equal to 141T was visible for GaMnAs sample with the highest Mn concentration.

In the present thesis all measured curves characterized by oscillatory terms at highmagnetic fields were analyzed by use of Fourier transform. Figures 5.29 and 5.30 presentKerr rotation angle oscillatory terms as a function of inverse magnetic field measured atT=5K. The results of Fourier transform analysis are gathered in Figures 5.31 and 5.32.

For the sample 10529A withx=0.014 (look in Figure 5.31 the following frequen-cies are distinct:F1=277±5T, F2=179±5T, F3=93±5T andF4=45T±4T. For the sam-ple 11127A withx=0.048 the frequencies:F1=286±5T, F2=186±5T, F3=72±5T andF4=49T±4T are distinct (see Figure 5.31). In the case of as grown 10727E epilayerwith the higest Mn concentration (x=0.086) clearly three frequencies can be separated:F1=172±5T, F2=93±5T, F3=38±4T (Figure 5.32). In the range of higher frequenciesany distinct peak can be isolated from the background. Finally, for the annealed at the op-timal conditions 10727E epilayer one can distinguish the following distinct frequencies:F1=278±5T, F2=179±5T,F3=71±5T andF4=53T±4T. (Figure 5.32)

There is no distinct peak around 141T for all investigated GaMnAs samples in a widerange of Mn concentration. The determined values of oscillations frequencies are veryclose to these observed for GaAs by N. Négre. One needs to realize that in the performedexperiment the incident beam of light can penetrate deeper then the thickness of GaMnAsepilayer and reflections from GaAs are also possible. The observed interband transi-tions can correspond to GaMnAs thin film as well as GaAs. Nevertheless, the performedFourier transform analysis does not definitively settle this question.

Additionally, the shift of oscillating terms with magnetic field after thermal annealingis observed. This effect is presented in Figure 5.33.

The shift towards higher magnetic fields is clearly visible. The high resolution X-ray diffraction measurements showed (see section 8 of this Chapter) that annealing at theoptimal conditions changes strain relations. The strain is reduced by annealing process.The induced by annealing changes in the strain relations modify the band structure ofGaMnAs (bands splitting, anisotropy) and this in turn may be responsible for the observedshift of magnetic fields oscillating terms.


!" #$

!"#$%!

Fig. 5.29: The oscillatory terms of Kerr rotation angle as a function of inverse magnetic fieldmeasured at T=5K for two epilayers: 10529A (x=0.014) and 11127A (x=0.048).


!" #$

!"#

Fig. 5.30: The oscillatory terms of Kerr rotation angle as a function of inverse magnetic fieldmeasured atT=5K for as-grown as well as annealed sample of 10727E epilayer withx=0.086.


!"#$

%

!"#$

%

&

Fig. 5.31: The results of Fourier transform analysis of Kerr rotation angle curves measured atT=5K for two epilayers: 10529A (x=0.014) and 11127A (x=0.048)


!"#$%

&''

!

"

#

Fig. 5.32: The results of Fourier transform analysis of Kerr rotation angle curves measured atT=5K for as-grown as well as annealed sample of 10727E epilayer withx=0.086.


λ λ λ λ

!

!"#

Fig. 5.33: The oscillatory terms of Kerr rotation angle as a function of magnetic fieldB measuredat T=5K for as-grown as well as annealed sample of 10727E epilayer withx=0.086.The shift of oscillating terms towards higher magnetic field after thermal annealing isvisible.


ΨΨΨΨ

Fig. 5.34: Schematic view of the channeling of ions directed at an angleΨ to a close-packed rowof atoms in a crystal.

5.7 The channeling experiments - the results of c-RBS and c-PIXEmeasurements

The channeling experiments i.e. channeling Rutherford backscattering (c-RBS) and chan-neling particle-induced X-ray emission (c-PIXE) measurements were performed on theas-grown and annealed samples of Ga1−xMnxAs.

The results of channeling measurements [13] [52] indicated that low temperature an-nealing introduces a rearrangement of Mn sites in Ga1−xMnxAs lattice. The combinedc-RBS and c-PIXE studies revealed the important role of interstitial Mn atoms in ferro-magnetic epilayers of Ga1−xMnxAs. The channeling experiments clearly established cor-relation between the arrangement of Mn sites in Ga1−xMnxAs and experimental effectsobserved after low temperature annealing performed at the optimal conditions (describedin the previous sections of this Chapter), i.e., the increase of the Curie temperature, theincrease in the saturation magnetization observed at low temperatures, the increase ofthe conductivity and the increase of the hole concentration (measured by means of ECVmethod [46], [13], [52], [87]).

Mn atoms incorporated into ferromagnetic Ga1−xMnxAs lattice can occupy three dis-tinct types of lattice site: substitutional positions in Ga sublattice MnGa, where Mn++

ions act as acceptors and also contribute to uncompensated spins; interstitial positionsMnI , commensurate with the zinc-blende lattice structure, where they act as a donors andtend to passivate MnGa acceptors; and random locations Mnran incommensurate with thezinc-blende lattice, i.e. that form clusters of Mn or MnAs clusters.

In Ga1−xMnxAs only substitutional Mn++ ions act as acceptors, so Mn concentrationx and free hole concentrationp are closely related.

Channeling is the steering of a beam of energetic ions into open spaces (channels)between close-packed rows or planes of atoms in a crystal, as shown schematically inFigure 5.34 and Figure 5.35.

The steering is the result of a correlated series of small-angle screened Coulomb col-lisions between an ion and the atoms bordering the channel. Thus, channeled ions donot penetrate closer than the screening distance of the vibrating atomic nuclei, and theprobability of large-angle Rutherford collisions (back-scattering), nuclear reactions, orinner-shell X-ray excitation is greatly reduced compared with the probability of such in-


ΨΨΨΨ

χχχχ

Fig. 5.35: The normalized yieldχh of ions that are backscattered from host atoms (the RBS yield)shows a strong dip atΨ=0. If 50% of solute atoms are displaced into the channel, thenormalized yieldχs of ions backscattered from the solute atoms is approximately halfthe random yield; i.e.,χs=0.5 atΨ=0 (broken curve). If displaced solute atoms arelocated near the center of the channel, a peak in yield may occur (dotted line).

teractions from a non-channeled (random) beams of ions. For the ions incident at smallanglesΨ to a close-packed direction, a large reduction in yield from such interactionswith host atoms is observed (look in Figure 5.35). The normalized yieldχh from hostatoms for such interactions is defined by the ratio of the yield for ions incident at an angleΨ to the yield for a "randomly" directed beam.

The position of solute atoms in a crystal lattice can be determined quite directly andprecisely from channeling experiments by measuring the normalized yieldsχh from hostatoms andχs from solute atoms for the same depth increment in the crystal [88], [89]. Ifsolute atoms are in the same lattice sites as host atoms, thenχs

∼= χh for any angleΨ. Ifsolute atoms project into a given channel, the channeled ions interact with them, causingan increased yieldχs. If, for example, 50% of solute atoms project into a given channel,the value ofχs for that channel would be 0.5 if the ion flux distribution were uniform ina channel (look in Figure 5.35). Because of the steering action involved in channeling,the ion flux is peaked near the center of a channel. Thus, if the solute atoms are displacedto positions near the center of a channel, a peaking inχs occurs near perfect alignment(Ψ=0). Such a peaking effect is unambiguous evidence that the solute atoms lie near thecenter of the channel. By comparing yields for different channels, the position of soluteatoms can be determined rather accurately by a triangulation procedure.

The Ga1−xMnxAs samples studied in the present thesis were investigated by directlycomparing the Mn Kα X-ray signals (c-PIXE) with the c-RBS signals of GaAs from theGa1−xMnxAs film simultaneously obtained using a 1.95 MeV4He+ beam. The locationof Mn sites in Ga1−xMnxAs lattice was studied by comparing of these two signals fordifferent channels.

The channeling experiments revealed that in LT MBE grown ferromagneticGa1−xMnxAs with high Mn concentrationx a significant fraction of incorporated Mn


Fig. 5.36: Schematic of the tetrahedral interstitial positions for a zinc-blende lattice along the var-ious axial directions.

atoms (14% for the as-grown 10823C GaMnAs epilayer withx=0.092 as determined byPIXE measurements) occupies well defined, commensurate with the GaAs lattice inter-stitial positions. The most important experimental result is the fact that low temperatureannealing performed at the optimal conditions leads to the significant reduction of Mninterstitial atoms (to 7% of the total Mn content for Ga0.908Mn0.092)[13] [52]. An increasein Mn interstitials and a decrease in substitutional Mn acceptors is observed with theincrease of Mn content [52].

In the zinc-blende lattice structure there are two possible interstitial positions, i.e. thetetrahedral interstitial positions with the four nearest neighbors cations and the hexagonalinterstitial positions with the six (three cations and three anions) nearest neighbors. Im-purity atoms in the interstitial sites in a diamond lattice are shadowed by the host atomsin the 〈100〉 and〈111〉 directions but are exposed in the〈110〉 axial channel. They canbe distinguished by studying angular scans around the〈110〉 axial direction. Schematicof the tetrahedral interstitial positions for a zinc-blende lattice along the various axialdirections are shown in Figure 5.36.

The arrangement of the tetrahedral interstitial positions in a zinc-blende lattice along〈110〉 gives rise to a double-peak feature due to the flux peaking effect of the ion beamin the channel. Figures 5.37, 5.38, 5.39 show the PIXE and RBS angular scans aboutthe 〈100〉, 〈110〉 and 〈111〉 axes for as-grown sample withx=0.092. The normalizedyield for the RBS (χGaAs) or the PIXE Mn X-ray signals (χMn) is defined as the ratioof the channeled yield to the corresponding unaligned yield. The higher (χMn) for theas-grown film observed in the〈110〉 direction as compared to those in〈111〉〈100〉 di-rections suggest that non-random fraction of Mn ions in these samples do not all sit insubstitutional sites. A double-peak feature is observable in the〈110〉 scan (indicated byarrows in Figure 5.38). These results indicate that a fraction of non-random Mn atomsis located at the tetrahedral interstitial sites in which the interstitial is surrounded by fournearest neighbors. The fraction of these interstitial Mn atoms can be roughly estimatedto be∼14%, assuming that flux peaking in the〈110〉 channel of GaAs is∼1.5 [90], [89].The PIXE and RBS angular scans taken about the〈110〉 and〈111〉 axes for annealed atthe optimal conditions (T=2890C) sample (see Reference [13]) show that the double-peakfeature is less prominent for the sample annealed at the optimal conditions, indicating areduced concentration of interstitial Mn in this sample. This suggest that Mn interstitialsare highly unstable. The interstitial Mn atoms are reduced to 7% of the total Mn content.For the sample annealed at high temperature equal to 3500C [13] the normalized yield(χMn) values are high and nearly equal in all three channeling scans. This suggest thatnot only all of the interstitial Mn, but also a significant fraction of the Mn atoms originallyat the substitutional positions leave their positions. It was shown [52] that Mn interstitials


No

rmal

ized

yie

ld, χχ

2.0 0.0

0.2

0.4

0.6

0.8

1.0

1.2

host (RBS) Mn (PIXE)

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

<100>

tilt angle (degree)

x=0.092

Fig. 5.37: The PIXE and RBS angular scans about the〈100〉 axes for as-grown sample withx=0.092.

increase (from 5% to 14%) as the Mn content increases (fromx=0.02 tox=0.092).Figure 5.40 shows the fraction of nonrandom Mnfnr, calculated by comparing nor-

malized yieldsχMn andχGaAs using the following relation [89]:

fnr =1− χMn

1− χGaAs

(5.10)

For both the as-grown GaMnAs epilayer and annealed at the optimal conditions(2890C), thefnr values are similar for the〈100〉 and〈111〉 projections but show a muchlower value for〈110〉 axial direction. This is due to the flux peaking effect, i.e. Mnatoms are visible in the〈110〉 channel and X-rays coming from these interstitial Mn areenhanced. Thus, non-random fraction of Mn atomsfnr calculated fromχMn does notrepresent the true non-random Mn fraction. For the sample annealed at 3500C the fnr

values are similar in all axial directions. The significant decrease offnr is visible afterthermal annealing at higher temperature (higher then 3000C), suggesting that post-growthannealing promotes random precipitation of Mn. 35% of the Mn atoms is estimated asa forming random precipitates after thermal annealing at high temperature 3500C. It wasreported that Mn removed from ordered sites forms MnAs inclusions after annealing atthe temperatures higher then 3000C [91].

The most important experimental fact is that in the as-grown sample∼ 14% of theMn atoms reside on the tetrahedral interstitial sites. One should realize that the intersti-tial MnI donor is both positively charge and relatively mobile. It is therefore expectedto drift toward the negatively charged MnGa acceptor centers, thus forming MnGa-MnI

pairs. The electrostatic attraction between positively charged Mn interstitials MnI andnegative substitutional MnGa acceptors stabilizes highly mobile MnI in intersitial sitesadjacent to MnGa, i.e. the tetrahedral position between four cations is preferred. Re-


No

rmal

ized

yie

ld, χχ

2.0

<110>

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

tilt angle (degree)

x=0.092


0.0

0.2

0.4

0.6

0.8

1.0

1.2


No

rmal

ized

yie

ld, χχ

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0

tilt angle (degree)

<111> x=0.092


0.0

0.2

0.4

0.6

0.8

1.0

1.2



!"#

$%

$%

$%

Fig. 5.40: The fraction of nonrandom Mnfnr, calculated by comparing normalized yieldsχMn

andχGaAs for the〈100〉, 〈110〉 and〈111〉 projections.

cently, this was confirmed by a calculation of the total energy of Mn ions located at dif-ferent interstitial sites, which has shown that the tetrahedral interstitial position betweencations is energetically favorable in strongly p-type material [92]. However it should bementioned that, K. W. Edmonds et al. claim that according to their calculations, in p-type samples the tetrahedral interstitial site between the four As anions should be favored[93]. Annealing the sample at the optimal conditions (at the temperatures only slightlyabove the growth temperature) breaks relatively weak MnI-MnGa. The decrease of thecompensating MnI donors leads to increase of the number of electrically-active MnGa,and thus also the hole concentration. The electrochemical capacitance-voltage profiling(ECV) method measurements [13], [52] showed an increase in the free hole concentra-tion from 6·1020 cm−3 observed in the as-grown sample to 1·1021 cm−3 for the GaMnAsepilayer annealed at the optimal conditions. As is well known, the increase in the holeconcentration will automatically result in an increase ofTC . Because removal of MnIby annealing is accompanied by an increase of saturation magnetization (as evidencedby magnetization studies), this suggest that the MnGa-MnI pairs are coupled antiferro-magnetically i.e., the magnetic moment of MnI "neutralizes" the contribution of MnGa tothe magnetization. Removal of MnI from such a pair should thus automatically renderthe substitutional Mn++ magnetically-active, increasing the saturation magnetization, asis indeed observed experimentally. Theoretical predictions [94], [95] revealed that Mninterstitials make some of the substitutional Mn ions magnetically inactive by formingwith them close pairs, with the spins antiferromagnetically coupled by the superexchangemechanism.

The lattice rearrangement of Mn atoms in Ga1−xMnxAs system provides a clear expla-nation of the experimental effects, i.e. the increase of the conductivity, the increase of theCurie temperature, and the increase in the saturation magnetization observed at low tem-peratures for the samples annealed at the optimal conditions. The results of channelingexperiments (c-PIXE, c-RBS) revealed that in the as-grown ferromagnetic Ga1−xMnxAs


samples a fraction of incorporated Mn atoms occupies interstitial tetrahedral positions, themore significant the higher the Mn content (∼14% for the epilayer withx=0.092, whereas5% for x=0.02 [52]). K. M. Yu et al. [46] uses thermodynamical arguments to explainwhy the amount of interstitials in the sample, and subsequently the sample’s reaction tothe annealing, depend on the Mn content: the Fermi level is pushed towards or into thevalence band by the increasing number of Mn substitutional acceptors, the formation ofinterstitiasls becomes energetically favorable.

5.8 The results of diffraction (HRXRD) measurements

In the present thesis the structural investigation of as-grown as well as annealedGa1−xMnxAs epilayers was carried out using high resolution X-ray diffraction (HRXRD)measurements for a wide range of Mn concentrations (0.027≤ x≤ 0.086), with a specialattention on how the interstitial Mn atoms (MnI) influence the lattice parameter of thismaterial.

It was experimentally established that the lattice constant of Ga1−xMnxAs layers in-creases with the increase of Mn concentration [43].

The lattice constanta0 measurements have often been used as a method of determiningthe Mn concentrationx in Ga1−xMnxAs. While there clearly exists a phenomenologicalcorrelation betweena0 andx, based on the remarks just made it is now clear that thiscorrelation is quite complex and is not really understood. For example, it was recentlyreported that epilayers of Ga1−xMnxAs with the same composition but prepared usingdifferent growth parameters have quite different lattice constants [96]. Moreover, it wassuggested that Ga1−xMnxAs is an example of a system does not obey Vegard’s law in thetraditional sense of a linear variation between the two end-point compounds, i.e., betweenzinc blende GaAs and (hypothetical) zinc blende MnAs [96].

Recently, first-principles theoretical calculations [44] have predicted that the presenceof Mn interstitials atoms can be the reason of the observed expansion of the lattice con-stant of Ga1−xMnxAs. It is also well known that a high arsenic antisite concentrations(AsGa) in low temperature GaAs (LT-GaAs) also leads to an increase in the lattice con-stant. The AsGa defects are expected to be present in Ga1−xMnxAs layers, since theseare grown at low temperatures similar to those used for growing LT-GaAs. It has beenshown that the lattice constant of Ga1−xMnxAs additionally depends in a sensitive way onthe growth conditions, quite possibly due to excess As incorporation, the degree of whichmay in itself depend on the presence of Mn in the system [40], [96].

One of the aims of the performed structural investigations was to explore the influ-ence of Mn interstitials atoms on the lattice constant of Ga1−xMnxAs which, as noted inReference [44], is expected to strongly affect the lattice parameter.

The as-grown as well as annealed at the optimal conditions samples (Ta ≈ 2890 C)with x=0.027 (10727C),x=0.062 (10727D), andx=0.086 (10727E), were studied.

The measurements were performed using a Philips X’Pert-MRD diffractometerequipped with a parabolic X-ray mirror and four-bounce Ge 220 monochromator at theincident beam, and a three-bounce Ge analyzer at the diffracted beam.

Figure 5.41 shows theω/2Θ scans obtained for the symmetric (004) reflection for theas-grown samples withx=0.027,x=0.062 andx=0.083. Figure 5.42 showsω/2Θ scan forthe sample withx=0.083 before and after annealing.


ωωωω

ωωωω

Fig. 5.41: Theω/2Θ scan for the symmetric (004) Bragg reflection for as-grown samples withx=0.027, 0.062, and 0.086.

ωωωω

ωωωω

!

Fig. 5.42: Theω/2Θ scan for the symmetric (004) Bragg reflection for as-grown and annealedsample withx=0.086.


Tab. 5.2: The measured values of perpendicular to the layer plane lattice parameter(a⊥), in-planelattice parameter (a‖), the calculated values of the relaxed mismatch (arelax-as)/as, andthickness of the GaMnAs epilayers determined from both RHEED oscilations and XRDmeasurements before and after annealing.

sample a‖ a⊥ arelaxed ∆a/a d [nm] d [nm]x [Å] [Å] [Å] [ppm] XRD RHEED

0.027 5.65348 5.66941 5.661243 1373 122 131as-grown

0.027 5.65348 5.66829 5.660697 1277 123 -annealed

0.062 5.65348 5.68431 5.668505 2658 140 149as-grown

0.062 5.65348 5.68049 5.666643 2328 136 -annealed

0.083 5.65348 5.6953 5.67386 3605 98 105as-grown

0.083 5.65348 5.68783 5.67022 2961 101 -annealed

For both as-grown and annealed samples the profiles ofω/2Θ scan exhibit clear inter-ference fringes, attesting to the high structural perfection of the layers. It is clearly visiblethat annealing procedure performed at the optimal conditions does not change the struc-tural quality of the investigated epilayers. These oscillations also provide a very directmethod for determining the Ga1−xMnxAs layer thickness. Thickness values estimatedfrom the thickness fringes in theω/2Θ curves are collected in Table 5.2. The values ofthe layer thickness obtained by this method agree rather well with those obtained fromRHEED oscillations, thus providing an added measure of internal consistency of the per-formed experiments.

The good agreement of the experimental values of full width at half maxima (FWHM)observed for the (004) Bragg reflections (from 170 to 180 arcsec) with the FWHM valuesobtained from the simulated curves (∼ 187 arcsec) shown in Figure 5.43 also indicatethat the crystalline quality of the Ga1−xMnxAs layers is rather high. Finally, the lack ofasymmetry in the profiles indicates the absence of detectable strain gradients within theentire thickness of the Ga1−xMnxAs film.

The reciprocal lattice maps measured for the (004) and (224) reflections revealed highcrystalline perfection of the as-grown Ga1−xMnxAs epilayers and showed that annealingdoes not alter the crystalline quality of the investigated layers. Figures 5.44 and 5.45present the reciprocal lattice maps obtained for the (004) and (224) reflections, respec-tively.

The very narrow inQx direction peaks corresponding to the Ga1−xMnxAs layers (un-changed by the annealing process), along with the presence of the interference peaks dueto multiple reflections within the Ga1−xMnxAs layer, indicate a sharp interface betweenthe Ga1−xMnxAs layer and the GaAs substrate. This, together with the relative sharpnessof the Ga1−xMnxAs peak, suggests that the Mn content is uniform (negligible gradient


ω

ω

Fig. 5.43: Comparison of the measuredω/2Θ scan for the symmetric (004) Bragg reflection(dashed curve) with simulation results (solid curve) for the annealed sample withx=0.086.

in x) throughout the epilayer. The fact that the value ofQx in the asymmetric reciprocallattice maps (see Figure 5.45) is the same for the Ga1−xMnxAs layer and for the GaAssubstrate also reveal that the Ga1−xMnxAs films (as-grown as well as annealed) are fullystrained to the (100) GaAs substrate (i.e., fully pseudomorphic), with no detectable re-laxation throughout the thickness of the film. The cross shown in Figure 5.45 indicatesthe position where the peak from the hypothetical relaxed Ga1−xMnxAs would occur onthe (224) reciprocal map, thus serving to illustrate the degree of tetragonal distortion uni-formly experienced by the Ga1−xMnxAs alloy along the growth direction.

Measurements of the (004) Bragg reflections allowed to calculate the lattice parame-ters perpendicular to the layer plane (a⊥) for all samples studied. The combination of thisand the measurements of the asymmetric (224) Bragg reflections were then used to de-termine the in-plane lattice parameter (a‖). The values of relaxed layer lattice parameterarelax (calculated from the measured values ofa⊥ anda‖), and the calculated values ofthe relaxed mismatch (arelax − as)/as before and after annealing (whereas is the latticeparameter of the GaAs substrate), are shown in Table 5.2.

The lattice parametersarelax for relaxed Ga1−xMnxAs were obtained using the relation

arelax =a⊥ + 2ba‖

1 + 2b(5.11)

where b=C11/(C11+2C12). Here C11 and C12 are elastic constants for GaAs(C11=11.82·1010 Pa, C12 = 5.326 1010 Pa [97]).

As seen from the reciprocal maps for the (224) reflection shown in Figure 5.45,aparallel is essentially identical to the lattice parameter of GaAs. Analogous results were


Fig. 5.44: Reciprocal space maps of the symmetric (004) reflection for the as-grown and annealedsample withx=0.086. (Qx andQy represent reciprocal space vectors (Qx is in the direc-tion <110> parallel to the surface,Qy is in the direction perpendicular to the surface),both given inλ/2d units,λ=0.15406 nm,d denotes the interplanar spacing).


Fig. 5.45: Reciprocal space maps of the asymmetric (224) reflection for the as-grown and annealedsample with x=0.086. (Qx andQy represent reciprocal space vectors (Qx is in the direc-tion <110> parallel to the surface,Qy is in the direction perpendicular to the surface),both given inλ/2d units,λ=0.15406 nm,d denotes the interplanar spacing).


obtained for the samples with the lower Mn content,x=0.062 andx=0.027. As in thecase ofx=0.086, theω/2Θ scans, the reciprocal lattice maps for the symmetric (004)and asymmetric (224) reflections indicate high crystalline perfection of the samples, andsystematically reveal a distinct decrease of the perpendicular lattice parameter after an-nealing.

The primary result of the high resolution X-ray diffraction measurements is the obser-vation that the Ga1−xMnxAs lattice parameter decreases when the epilayers are annealedat the optimal conditions i.e. the interstitial Mn atoms are removed from the alloy [13],[7]. As has been noted, such a result has been foreseen by Mašek et al. [44].

As was noted in the previous section of this Chapter the channeling studies: c-RBSand c-PIXE revealed that optimal annealing leads to the significant reduction of Mn inter-stitial Mn atoms (to 7% of the total Mn content for Ga1−xMnxAs with Mn concentrationx=0.07 as determined from RHEED oscillations) [13]. The c-PIXE measurements distin-guish between contributions from Mn in substitutional, interstitial and random positions(i.e., those in the form of random precipitates, such as MnAs inclusions). The total Mnconcentration determined from c-PIXE investigations is always higher by 15 to 20% thanthe values obtained from RHEED in as-grown samples. As was noted in Chapter 3 itcan be assumed that RHEED oscillations provide a measure of substitutional Mn cationsMnGa. The PIXE measurements revealed that sample withx determined by RHEED as0.07 has total of Mn concentration equal to 0.092, of which 0.072 was in substitutionalpositions, 0.013 in the form of interstitials, and 0.007 occurred as random precipitates. Ifone will use the above results on the sample withx=0.086 (as determined from RHEEDoscillations) and will ascribex=0.086 to substitutional Mn, then the total concentrationof Mn in this sample can be estimated asxtot ∼0.109, with the atomic fraction of Mninterstitials (xint) estimated as 0.015 in as-grown material and 0.008 after the sample wasannealed, for a change in interstitial concentration estimated at∆xint=0.007. The calcu-lation of Mašek et al. [44] indicate that the relaxed lattice parameter of Ga1−xMnxAs hasthe following form (in Å):

a = a0 + 0.02xsub + 1.05xint + 0.69y (5.12)

wherea0 is the lattice parameter of GaAs,xsub andxint are the concentrations of substi-tutional and interstital Mn, andy is the concentration of As antisites AsGa.

It is safe to assume that after low-temperature annealingxsub andy remain unchanged(the temperatureT<3000C is too low to "kick out" these atoms from the crystallographicGa sites), so that the only significant effect of such annealing is the removal of MnI .Assumingxsub andy to remain constant, and using the values ofa0 before and after an-nealing from Table 5.2, Equation 5.12 gives a change of the interstitial concentration∆xint=0.004. This is smaller, but of the same order of magnitude as the change inxint

estimated from the RBS/PIXE experiments. Applying a similar analysis to the remain-ing lattice parameter changes listed in Table 5.2, we consistently get lower values fromEquation 5.12 for the change of the MnI concentration (by a similar factor of about 2)than those obtained if one makes the (admittedly very rough) assumption that the value ofxint is reduced from 14 to 7% of the total Mn content.

The observed trend is quite systematic: not only is the lattice parameter consistentlylower for annealed samples, but the degree by which it is lower is proportional to the Mnconcentration. It can be seen from Figure 5.46, where the relaxed lattice constant beforeand after annealing as a function of the substitutional Mn concentrationx is plotted. There


Fig. 5.46: Relaxed lattice parameter of Ga1−xMnxAs plotted as a function of the Mn concentrationx for as-grown and annealed samples.

are two interesting features which emerge from Figure 5.46. First, when one extrapolatesthe as-grown and annealed points tox=1.0, one obtains, respectively, the values of 5.90Åand 5.86 Åfor the hypothetical zinc blende MnAs. It is interesting that a theoreticalcalculation of thea0 for hypothetical zinc blende MnAs using covalent radiirc (for Asrc =1.225 Å; for Mnrc = 1.326 Å) (see e.g. [98]), one obtains a value of 5.89Å. Whilethis agreement may be to some coincidental, this is probably the reason why the increaseof a0 with x, along with the use of Vegard’s law, has been rather widely accepted forGa1−xMnxAs, and has been initially interpreted as the effect of substitutional Mn in thisalloy.

Figure 5.46 also reveals another interesting feature. Note that the decrease ofa0 afterannealing appears to be proportional tox, suggesting that the annealing-induced drop inthe concentration of MnI increases with the Mn concentration. Since it is known fromthe c-PIXE results that annealing reduces the MnI concentration by roughly a factor oftwo, this would suggest that the difference between the lattice parameter of as-grownmaterial and of the hypothetical material in which there are no Mn interstitials wouldbe approximately twice as large as that seen in Figure 5.46 between the as-grown andannealed cases. Extending this logic tox=1.0, we obtain an estimate of 5.83Åfor thelattice parameter of zinc blende MnAs with only substitutional Mn. This is of course indisagreement with Reference [44], in which it is predicted that the effect of substitutionalMn on the lattice constant of Ga1−xMnxAs is practically negligible (in stark contradictionto the estimated value obtained by using covalent radii). It is possible that this points tovery physical insights: if one assumes zinc blende Ga1−xMnxAs with only substitutionalMn, one must take into account that every Mn produces an uncompensated hole, and forMnAs (or even Ga1−xMnxAs with a large value ofx) one automatically has a metal. It islikely that the Coulomb interaction between the hole gas and the positive ions experiencea Coulomb attraction, exactly as in a metallic bond, which causes the lattice parameterto shrink. One would assume that this effect is present in the first-principles calculationsdiscussed in Reference [44] (although it may be over-estimated in the calculations). Thetendency fora0 to decrease further with decreasing concentration of MnI signaled by


the results plotted in Figure 5.46 may thus be a qualitative indication of the physicalprocesses implicitly taken into account in the first-principles calculation of Mašek et al.[44].

The presented data indicate that the samples are uniformly strained. The degree ofstrain, defined as (arelax − as)/as (whereas is the lattice parameter of the underlyingsubstrate) is also listed in Table 5.2. As expected, the degree of strain in the specimensincreases with the Mn content; but the strain is reduced by the annealing process.

6. CONCLUSIONS AND SUMMARY

In this thesis the results of magnetic and transport study of multinary alloys:Pb1−x−y−zMnxEuySnzTe and Ga1−xMnxAs are reported. For lead chalcogenides, thepresence of two types of magnetic ions (Mn and Eu) on magnetic properties of the re-sultant semimagnetic semiconductor was studied. The effect of the low temperatureannealing on the transport, magnetic, magnetooptical and structural properties of theGa1−xMnxAs was investigated.

6.1 Pb1−x−y−zMnxEuySnzTe

The transport measurements revealed p-type of conductivity for all investigated samplesof Pb1−x−y−zMnxEuySnzTe. The samples are characterized with high almost temperatureindependent hole concentration (in the range between 2·1018 cm−3 and 2·1021 cm−3). Theparamagnet/ferromagnet as well ferromagnet/spin glass phase transitions were observed.The following most important results were obtained for Pb1−x−y−zMnxEuySnzTe mixedcrystals:

1. The presence of two types of magnetic ions (Mn and Eu) in IV-VI semiconduc-tor matrix influences magnetic properties of the resultant semimagnetic semicon-ductor. The results of magnetic measurements show that Curie temperatureTC aswell as Curie - Weiss temperatureΘ decrease with the increase of Eu content inPb1−x−y−zMnxEuySnzTe samples. The magnetic susceptibility measurements re-vealed also that Eu changes spin glass dynamics in this material. The differencein the rate of frequency shift of cusp in real and imaginary part of susceptibilityis visible. Such behaviour was not observed for Mn-based IV-VI semimagneticsemiconductors. Magnetic phase diagram of investigated Pb1−x−y−zMnxEuySnzTeshows that the presence of Eu shifts glass regime towards lower carrier concentra-tion p (as compared to Pb1−x−yMnxSnyTe system).

2. The qualitative analysis showed that a variation of the band parameters with thealloy composition (i.e. shift ofε0 as well asEg parameter with Eu concentrationy- see Chapter 4 ) is responsible for the observed strong dependence of Curie tem-perature on Eu content. Introduced simple two band model explains both the orderof the transition temperature values as well asTC dependence on Eu concentration.The calculated dependence of Curie temperature on Eu content very well reflectsexperimentally confirmed effect ofTC decrease with Eu concentrationy.

6.2 Ga1−xMnxAs

The annealing studies on GaMnAs in the wide range of Mn concentration (up to highvaluesx∼0.09) were performed. The systematic transport, magnetotransport, magnetic,

6. Conclusions and Summary 100

magnetooptical, structural and channeling measurements were carried out. Significantannealing-induced changes in the magnetic, electronic as well as structural propertiesof this semimagnetic material, that depend on the Mn concentration and on annealingconditions were observed. In summary:

1. The optimal conditions (temperature, time, flow of N2 gas of post-growth annealingwere established for studied samples. A method of increasing TC , was developed.For the first time it is shown that by a proper choice of annealing conditions the limitof TC in GaMnAs (∼110K) [6] can be shifted to much higher values (up to 127K forx∼0.08). Simultaneously, an increase in saturation magnetization, conductivity andfree hole concentration is observed for samples annealed at the optimal conditions.

2. The most important experimental fact is that low temperature annealing performedat the optimal conditions leads to the significant reduction of Mn interstitial atoms(7% of the total Mn content for GaMnAs epilayer withx=0.092). LT post-growthannealing leads to a rearrangement of the Mn ions in the host lattice, in particularto the removal of Mn from the interstitial sites. The presented channeling mea-surements showed that in the process of LT annealing the MnI ions are movedto random, incommensurate with GaAs lattice positions (e.g. MnAs clusters), inwhich the Mn ions are electrically inactive, what increases the hole concentration,conductivity andTC . According to theab initio calculations [93], this is due tothe out diffusion of Mn intersitials towards the surface - the biding energy for MnI

in GaMnAs allows for significant diffusion of this effect at temperatures above∼1500C. Recently, it was presented [99], [95], [100] that spins in the formed MnI-MnGa pairs are expected to be antiferromagnetically aligned, thus cancelling themagnetic contribution of MnGa to the magnetization of the GaMnAs system as awhole. Removal of MnI from such a pair should thus automatically render the sub-stitutional Mn++ magnetically-active, increasing the saturation magnetization, as isindeed observed experimentally and shown in the thesis. The magnetic propertiesof the Mn ion in interstitial sites, i.e. the negligible kinetic exchange constant andstrong antiferromagnetic superexchange with the adjacent substitutional Mn ion,act towards diminishing the transition temperature. Mn interstitial act against theferromagnetism in Ga1−xMnxAs, not only due to the compensating character of thisdefect, but also because of their distinct magnetic behaviour.

Here, it should be mentioned that fact of inequality between the hole concentrationand the Mn content (hole concentration is substantially lower than the Mn contentin all Ga1−xMnxAs samples) has been ascribed for a long time to the presence ofcompensating donors, in particular to the formation of arsenic antisites (AsGa) dur-ing the eptaxial growth of GaMnAs at As overpressure. The LT annealing inducedchanges of the hole concentration and, therefore, Curie temperature were attributedto the decrease of the concentration of arsenic antisites. These antisites, however,are relatively stable defects - it was shown that to remove AsGa from LT MBEgrown GaAs annealing temperatures above 4500C are needed [101].

3. It is shown that the lattice parameter decreases when the epilayers of GaMnAsare annealed at the optimal conditions, i.e. when the interstitial Mn atoms are re-moved from the alloy. The results of high resolution X-ray diffraction (HRXRD)


are agreement with the theoretical predictions [44]. Using the values of lattice con-stant before and after annealing obtained from HRXRD measurements a change ofthe interstitial concentration was estimated. The obtained values are smaller butof the same order of magnitude as the change in concentration of intersitial Mnestimated from RBS/PIXE measurements.

4. Magnetic investigations (SQUID measurements) revealed a decrease of the coer-cive field after heat treatment at the optimal conditions. Thermal annealing at ahigher temperature leads to an increase of the coercive field. This can be related tothe domain structure in the investigated material. It is easy to imagine that properannealing diminishes the coercive field. The MOKE measurements showed thenon monotonic low magnetic field behaviour. The observed features are connectedwith the magnetic properties of studied epilayers. At present very speculative inter-pretation is possible. Such behaviour can be related with the magnetic anisotropyobsrerved in GaMnAs epilayers. The oscillatory terms in the range of high mag-netic fields are visible in the range of high magnetic fields (up to 25T). The shifttowards higher magnetic fields is pronounced after thermal annealing at the opti-mal conditions. The induced by annealing changes in the strain relations modifythe band structure of GaMnAs and this in turn may be responsible for the observedshift of oscillation terms.

5. All investigated samples indicated unsaturated negative magnetoresistance (MR)up to the highest value of investigated field (55T). A sizable negative magnetore-sistance in the regime of strong magnetic fields can be assigned to the weak lo-calization effect [51]. It was found that annealing of the Ga1−xMnxAs epilayerswith high Mn concentration leads to very significant changes in magnetoresistiv-ity. Particulary, a pronounced decrease of magnetoresistivityMR after annealing atthe optimal conditions and a substantial increase ofMR after annealing at a highertemperature was observed. For samples with lower Mn content (x∼0.03) theMR isnot affected by the heat treatment at the optimal conditions. It was also shown thatfor low Mn concentration the influence of annealing procedure on both the Curietemperature and conductivity is weak. The annealing induced large changes of themagnetoresistivity can be related with the change of the domain structure of GaM-nAs system. In the range of low magnetic fields the hysteretic behaviour ofMRis observed. The low field hysteretic feature is much more pronounced with thetemperature decrease.

6.3 Suggestions for further studies

1. Magnetic studies of Pb1−x−y−zMnxEuySnzTe mixed crystals were performed forsamples with relatively low Eu concentration. More distinct effect of the influenceof the second type of magnetic ion on the magnetic properties of the resultant mate-rial should be visible for higher Eu concentration. The ideal samples for these kindof investigation should be characterized by the same content of Mn and high scatterof Eu content.

The measurements of magnetization under hydrostatic pressure were performedonly for Sn1−x−yMnxEuyTe samples. For samples of PbSnMnEuTe the very pro-


nounced effect of the decrease ofTC with the Eu concentration related to the varia-tion of the band parameters with the alloy composition was visible. One can expectthat for these samples the change in the magnetization measured under hydrostaticpressure with the Eu content.

2. The measurements of MOKE were not performed as a function of the wavelength.This kind of investigations could be helpful to explore the origin of oscillating termsin the high magnetic field range of MOKE curves as well as low magnetic fieldbehaviour of MOKE.

3. Magnetization measurements in the perpendicular configuration (magnetic field di-rected perpendicular to the sample surface) would be very helpful in the furtherstudies of the magnetic properties of GaMnAs epilayers. Particularly, SQUID mea-surements in this configuration in the range of low magnetic fields could throw thelight on the low magnetic field behaviour of magnetooptical Kerr effect. The per-formed in the thesis measurements revealed that usual relationθK ∝M is not validin GaMnAs. Further studies are necessary to explore the relation between SQUIDmagnetizationM and Kerr rotation angleθK .

7. APPENDICES

7.1 Appendix 1

The Jones vector[102] provides a concise representation of the electric vibration of atransverse-electric (TE) plane wave. The two-component complex Jones vector carriersinformation about the amplitudeA, absolute phaseδ, azimuthθ and ellipticity angleε ofthe elliptic vibration of the electric-field vector of a uniform monochromatic TE planewave of light (look in Figure 7.1).

Let’s assume that uniform, TE travelling plane wave of arbitrary polarization propa-gates along the positive direction of the z axis of an xyz orthogonal, right-handed, Certe-sian coordinate system, then the electric vector of such a wave becomes:

−→E (z, t) = Ex cos[ωt− 2π

λz + δx)]

−→ex + Ey cos[ωt− 2π

λz + δy)]

−→ey (7.1)

,whereEx andEy represent the amplitudes of the linear, simple-harmonic oscillations

of the electric-field components along x and y axes;δx andδy represent the respectivephases of these oscillations,−→ex and−→ey are unit vectors in the positive directions of the xand y axes.

The Jones vector−→E (0) (in the form of 2×1 column vector (matrix)) of the wave

(Equation 7.1) has the following form:

−→E (0) =

(fExeiδx

fEyeiδy

)(7.2)

The vector−−→E(0) is the concise representation of a single plane wave which is known to be

monochromatic, uniform and transverse-electric and contains complete information aboutthe amplitudes and phases of the field components, so about the polarization of the wave.From the Jones vector the time and space dependence of the entire wave can be obtainedby using the following equation:

−→E (z, t) = Re[

−→E (0)ei(ωt− 2πz

λ)] (7.3)

The full explicit expression of the wave (Equation 7.1) can be obtained by reintroducingthe units vectors−→ex and−→ey . In simplified notation the Jones vector has the followingform:

−→E =

(Ex

Ey

)(7.4)

where Ex=Exeiδx and Ey=Eye

iδy .For an elliptical vibration which amplitude A, phaseδ, azimuthθ and ellipticity angle

ε are given a Jones vector can be constructed.

7. Appendices 104

εεεε

θθθθδδδδ

Fig. 7.1: The parameters that define the ellipse of polarization in its plane: 1) the azimuthθ, thatdefines orientation of the ellipse in its plane (−π

2 ≤ θ ≤ π2 ); 2) the ellipticity e=b

a ; 3)

the ellipticity angleε=arctan(e) (−π4 ≤ ε ≤ π

4 ); 4) the amplitudeA = (a2+b2)12 ); 5)

the absolute phaseδ defined by the initial electric field and auxiliary (dashed) circle (-π ≤ δ ≤ π), it determines the angle between the initial position of the electric vector att=0 and major axis of the ellipse.

The Cartesian Jones vector of a given elliptical polarization state has the followingform: (

Ex

Ey

)= Aeiδ

(cos(θ) cos(ε)−i sin(θ)sin(ε)

sin(θ) cos(ε)+i cos(θ) sin(ε)

)(7.5)

The circular Jones vector of a given elliptical polarized state has the following form:(

El

Er

)= Ae

iδ√2

(cos(ε)−sin(ε)eiθ

cos(ε)+sin(ε)e−iθ

)(7.6)

When a polarized light passes through optical elements, its polarization state is in gen-eral modified. This can be described in the framework of the Jones formalism. Assuming,that the polarization response of optical elements such as the sample, mirror, polarizer,etc. is linear it can be expressed by a matrix product. Let the incident and the outgo-ing plane waves be described by their appropriate Jones vectors

−→Ei and

−→Eo, respectively.

The following equation express the law of interaction between the incident wave and theoptical system as a simple linear matrix transformation of the Jones vector of the wave:

−→Eo =

(T11 T12

T21 T22

)−→Ei (7.7)

7. Appendices 105

Eg

B=0

k=0

Fig. 7.2: 1 Energy bands for a simple semiconductor for B=0.

7.2 Appendix2

Let’s consider a simple case of two parabolic energy bands in the effective mass approx-imation (look in Figure 7.2, where the upper curve represents the energy wave vectorrelation of the conduction electrons with effective massmc and the lower curve, the va-lence electrons, or holes, with effective massmv).

The simplification follows from the effective mass approximation. The Schrödingerequation for electrons moving through the periodic potentialV(r) of the lattice, i.e.,

[−→p 2/2m + V (−→r )]Ψ = EΨ (7.8)

is replaced by the simpler equation:−→p 2Ψ/2mc = EcΨ (7.9)

where−→p is the momentum operator. The solution of the above solution is:

Ec = h2−→k 2/2mc (7.10)

For the valence band, which is separated from the conduction band by the energy gap, Eg,one obtains:

Ev = −Eg − h2−→k 2/2mv (7.11)

In a magnetic field, the Schrödinger equation, neglecting spin, for Bloch electrons is:

[1

2m(−→p + e

−→A )2 + V (−→r )]Ψj(

−→r ) = EjΨj(−→r ) (7.12)

where−→A is the vector potential for the magnetic field. The solution here is:

Ψj(−→r ) = Φj(

−→r )Fj(−→r ) +

1

m

∑

i6=j

pαij

(Ej − Ei)(pα +

e

cAα)Fj(

−→r )Φi(−→r ) (7.13)

7. Appendices 106

whereΦj(−→r )is the Bloch functionujkexp[i(

−→k ·−→r ) at the bottom of the band, i.e.uj0; the

summation is over all the other bandsi, pαij is theα component of the momentum matrix

element, i.e.,

pαij ≡

∫u∗i0(

−→r )pαuj0(−→r )dτ (7.14)

andF(−→r ) is obtained from the solution of the equation:

1

2m∗ (−→p +

e

c

−→A )2Fj(

−→r ) = EjFj(−→r ) (7.15)

Assuming the magnetic fieldB in the z-direction and−→A = (0, Bx, 0), the latter equation

becomes:1

2m∗ [−→p 2 + 2

eB

cxpy +

e2B2

c2x2]Fj(

−→r ) = EjFj(−→r ) (7.16)

Choosing a solution of the form:

Fj(−→r ) = g(x)exp[i(kyy + kzz)] (7.17)

results in the simplified equation:

− h2

2mast

d2g

dx2+ [

1

2m∗ (hky +eB

cx)2 +

h2k2z

2m∗ ]g = Eg (7.18)

that represents the motion of a one-dimensional simple harmonic oscillator. The eigen-values of above equation are:

E = (n +1

2)hωc + h2k2

z/2m∗, (7.19)

where n=0, 1, 2, 3..., andg(x) = φn(x− chky/eB) (7.20)

the one dimensional simple harmonic oscillator wave function. Thus, to the first order:

Ψj(−→r ) = uj0Fj(

−→r ) =uj0√(LyLz)

exp[i(kyy + kzz)]φn(x− ch

eBky) (7.21)

whereLx, Ly, Lz are the crystal dimensions.In a magnetic field the energy levels of the electrons and holes can be represented as:

Ec = (n +1

2)hωc + h2k2

z/2mc (7.22)

and

Ev = −Eg − (n′ +1

2)hωv − h2k2

z/2mv (7.23)

respectively. These energy levels are shown in Figure 7.3.The electromagnetic wave can be represented by a time-varying field, of frequencyω

and polarization−→ε , which has a negligible space variation since the wavelength of theradiation is much longer than the lattice spacing. The probability of electron transitions

7. Appendices 107

n'=0n'=1

n'=2

n=1

n=2

n=0

1/2 hωv

hωv

1/2 hωc

hωc

B>0

k=0

Fig. 7.3: Energy bands for a simple semiconductor for B>0.

from an initial state, i, to a final state, f, is proportional to the square of the matrixPif

which to first order equals:

Pif = 〈Ψ∗fH

′Ψi〉 =

∫u∗f0(

−→r )F ∗f (−→r )−→ε · (−→p +

e

c

−→A )ui0(

−→r )Fi(−→r )dτ (7.24)

whereH’ is the perturbing Hamiltonian (H’=−→ε · (−→p + e/c−→A )sin(ωt)).

A simplification of above expansion is possible because the harmonic oscillator func-tionsFi(

−→r ), Ff (−→r ), as well as the vector potential

−→A of the wave, vary slowly compared

to the periodic band edge functionsui0 andui0. Consequently the former functions can betreated as constant over a unit cell so that:

Pif = [

∫

crystal

F ∗f (−→r )−→ε · (−→p +

e

c

−→A )Fi(

−→r )dτ

∫

cell

u∗f0ui0dτ+

∫

crystal

F ∗f (−→r )Fi(

−→r )dτ

∫

cell

u∗f0−→ε · −→p ui0dτ ] (7.25)

For the case of interband transitions (transitions between two bands), the first term ofEquation 7.2 goes to zero because of the orthogonality ofui0, uf0 and the second term isusually non-vanishing.

The simple harmonic oscillator functions, i.e.Fc andFv do not involve properties ofthe energy bands. Consequently, because of orthogonality, the selections rules are:

∆ky = ∆kx = 0 (7.26)

and∆n = 0 (7.27)

7. Appendices 108

The energy for a transition (the spin is neglected) is:

∆E = Ec − Ev = Eg + (n +1

2)h(ωc + ωv) + h2k2

z/2µ (7.28)

whereµ ≡ mcmv/(mc + mv) is the reduced effective mass.When spin is included, Equation 7.19 can be written as:

E = (n +1

2)hωc + MµBgB + h2k2

z/2m∗ (7.29)

whereµB is the Bohr magneton;g is the effective spectroscopic spin factor, which is equalto 2 for a free electron;M is the component of angular momentum along the magneticfield, characterized by values± 1

2, corresponding to the two possible values of electron

spin.If spin is included, the momentum matrix term (

∫u∗c0−→ε ·−→p uv0dτ ) yields an additional

selection rule∆M=0, or±1. For propagation of the electromagnetic wave parallel tothe magnetic field, then

−→E ⊥ −→

B and∆M=±1 corresponding to the senses of circularpolarization. For propagation perpendicular to

−→B , then∆M=0 for

−→E ‖ −→B and∆M=±1

for−→E ⊥ −→

B . These selectional rules are determined from the Bloch functions with spinincluded.

The energy for a transition with spin is:

∆E = Ec − Ev = Eg + (n +1

2)h(ωc + ωv) + h2k2

z/2µ + (Mcgc −Mvgv)µBB (7.30)

By the fixing the photon energy of the incident radiation at a value somewhat above theenergy gap and varying the magnetic field B, one will obtain a series of peaks in theabsorption (or in MOKE curves - as was observed in the present thesis) which are periodicin 1/B:

1

B= F =

(n + 1/2) heµc± 1

2(gc + gv)µB

∆E − Eg

(7.31)

Figure 7.4 shows schematically the interband transitions for Landau levels of twosimple parabolic bands, the conditions for resonance transitions are visible.

7. Appendices 109

Ec

Ev

4

4

3

3

2

1

1

2

0

0

EG

B

E

Fig. 7.4: The intrerband transitions between Landau levels (n=0,1,2,3,4) of two simple parabolicbands ( the left side of the picture represents simple energy bands for B=0). The arrowsindicate the conditions for resonance transitions.

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LIST OF FIGURES

2.1 The schematic view of the Tracor X-ray Spectrace 5000. . . . . . . . . . 112.2 The experimental setup for magnetotransport measurements. . . . . . . . 132.3 The experimental setup for magnetotransport measurements (configura-

tion with 7001 Keithley Scanner and 7065 Hall Card). . . . . . . . . . . . 142.4 The configuration with two power suppliers (Oxford Instruments and

Lake Shore power supplier) connected in parallel. This configuration al-lowed to reverse fluently the direction of magnetic field. . . . . . . . . . . 14

2.5 Experimental setup for AC susceptibility/DC magnetization measure-ments - 7229 LakeShore Susceptometer/Magnetometer system. . . . . . 17

2.6 The cross-sectional view of the coil assembly. The two sensing coils areconnected in opposition in order to cancel the voltages induced by the ACfield itself or voltages induced by unwanted external sources. . . . . . . . 18

2.7 The schematic view of experimental setup for magnetooptical Kerr effectmeasurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.1 Chemical composition distribution along the crystal growth direction forthe crystal of PbSnMnEuTe. . . . . . . . . . . . . . . . . . . . . . . . . 23

3.2 RHEED oscillations observed during the growth of a Ga1−xMnxAs filmwith x = 0.062. The first 7 periods correspond to LT-GaAs. The "jump"in the signal occurs at the point when the Mn shutter has been opened andthe rate of oscillations increased. . . . . . . . . . . . . . . . . . . . . . . 24

4.1 The band structure model of Pb1−x−yMnxSnyTe mixed crystals . . . . . . 284.2 Curie-Weiss temperature (Θ) versus free carrier concentration in

Pb1−x−yMnxSnyTe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294.3 Inverse AC susceptibility versus temperature measured for

Pb1−x−yMnxEuyTe samples (793−2: x=0.010, y=0; 793−4: x=0.010,y=0.001; 793−10: x=0.005, y=0.004; 793−12: x=0.007, y=0.003;793−14: x=0.005,y=0.005). The solid lines correspond to Curie -Weisslaw fits. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.4 The high temperature inverse AC susceptibility measured for severalPb1−x−y−zMnxEuySnzTe samples (809−2: x=0.031,y=0.003,z=0.850;809−12: x=0.022, y=0.003, z=0.760; 809−32: x=0.026, y=0.014,z=0.69; 809−34: x=0.027,y=0.017,z=0.680).The solid lines correspondto Curie -Weiss law fits. . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.5 The high temperature inverse AC susceptibility measured for sev-eral Sn1−x−yMnxEuyTe samples (841−18: x=0.131,y=0.013; 841−14:x=0.116, y=0.011; 842−20: x=0.091, y=0.009; 848−4: x=0.061,y=0.0115; 848−16: x=0.050,y=0.011; 848−24: x=0.051,y=0.019). . . . 38

List of Figures 117

4.6 The low temperature behaviour of real part of susceptibility for severalPb1−x−y−zMnxEuySnzTe samples (809−12: x=0.022,y=0.003,z=0.760;809−36: x=0.025, y=0.013, z=0.690; 809−30: x=0.024, y=0.010,z=0.710 ;809−32: x=0.026, y=0.014, z=0.690; 809−34: x=0.027,y=0.017,z=0.680). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.7 The low temperature behaviour of real part of susceptibility for sev-eral Sn1−x−yMnxEuyTe samples (841−14: x=0.121,y=0.011; 842−20:x=0.090, y=0.009; 841−18: x=0.128, y=0.014; 848−24: x=0.055,y=0.0175; 848−16: x=0.054,y=0.011; 848−4: x=0.058,y=0.011). . . . 40

4.8 Magnetization measured at various temperatures and magnetic fields up to9T for Pb1−x−y−zMnxEuySnzTe 809−10 sample withx=0.030,y=0.003,z=0.780 and hole concentrationp=6 1020 cm−3. . . . . . . . . . . . . . 41

4.9 The low temperature behaviour of both realRe(χ) and imaginaryIm(χ)component of susceptibility for two samples of Pb1−x−y−zMnxEuySnzTe:809−2 (x=0.031, y=0.003, p=1·1021 cm−3) and 809−12 (x=0.022,y=0.003,p=4·1020 cm−3). The typical ferromagnetic characteristics isobserved for 809−12 sample and spin glass behaviour for the sample withhigher free hole concentration. . . . . . . . . . . . . . . . . . . . . . . . 42

4.10 The frequency dependence of real component of susceptibilityRe(χ)for the sample of Pb1−x−y−zMnxEuySnzTe: 809−2: x=0.031,y=0.003,p=1·1021 cm−3. The shift of the freezing temperatureTf towards highertemperatures with the frequency increase is clearly visible. . . . . . . . . 43

4.11 The frequency dependence of imaginary part of susceptibilityIm(χ)for the sample of Pb1−x−y−zMnxEuySnzTe: 809−2 (x=0.031,y=0.003,p=1·1021 cm−3). The maximum of the observed cusp shifts towardshigher temperatures with the frequency increase. . . . . . . . . . . . . . 44

4.12 Magnetic phase diagram for Pb1−x−yMnxSnyTe [27] andPb1−x−y−zMnxEuySnzTe samples. Red triangles correspond to PbM-nEuSnTe ferromagnets, red circles to PbMnEuSnTe spin glasses, blackcircles to PbMnSnTe ferromagnets, green circles to PbMnSnTe spinglasses, blue circles to reentrant spin glasses. Lines present modelcalculations of the phase boundary (see Ref. [27]): solid line presentsgeometric model, dashed and dot dashed lines correspond to Sherrington-Kirkpatrick model, dot line correspond to Sherrington-Southern model . 45

4.13 Curie temperature calculated for Pb1−x−y−zMnxEuySnzTe mixed crystalsas a function of Eu contenty for various values of Sn concentration 0.6≤ z ≤ 1 and Mn concentrationx=0.02 . . . . . . . . . . . . . . . . . . 45

4.14 Zero field cooled magnetization measured as a function of temperature forSn1−x−yMnxEuyTe sample (842−8 with x=0.068,y=0.003,p=1.6·1021

cm−3) at ambient and equal to 11.2 kbar pressure. . . . . . . . . . . . . . 464.15 Zero field cooled magnetization measured as a function of temperature

for Sn1−xMnxTe sample withx=0.10 at ambient and equal to 10.5 kbarpressure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

4.16 Zero field cooled magnetization measured as a function of magnetic fieldat low temperatureT=5K for Sn1−x−yMnxEuyTe sample (842−8 withx=0.068,y=0.003,p=1.6·1021 cm−3) at ambient and equal to 11.2 kbarpressure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

List of Figures 118

4.17 Zero field cooled magnetization measured as a function of magnetic fieldat low temperatureT=4.2K for Sn1−xMnxTe sample withx=0.10 at am-bient and equal to 10.5 kbar pressure. . . . . . . . . . . . . . . . . . . . 47

5.1 The zero-field resistivity of the as-grown GaMnAs epilayers in the widerange of Mn concentration 0.01≤ x ≤0.093. . . . . . . . . . . . . . . . . 52

5.2 The temperature dependence of the zero-field resistivity (a hump struc-ture slightly above Curie temperature is visible) and magnetization versustemperature measured by a SQUID magnetometer in small magnetic field(B=0.01T) parallel to the sample surface. A good agreement betweentransport and magnetic data is visible. . . . . . . . . . . . . . . . . . . . 53

5.3 Curie temperatureTρ estimated from the the zero-field resistivity mea-surements versus temperatures of annealing for GaMnAs samples withdifferent Mn concentration 0.01≤ x≤0.093. . . . . . . . . . . . . . . . . 54

5.4 Temperature dependence of the zero-field resistivity of GaMnAs samplewith high Mn concentration (x=0.086) annealed at various temperatures. . 55

5.5 The temperature dependence of zero-field resistivity for as-grown andannealed at various temperatures sample with low Mn concentrationx=0.027. Inset shows the Curie temperature estimated from the resistivitymeasurements versus annealing temperature. . . . . . . . . . . . . . . . . 55

5.6 Conductivity versus annealing temperature for the samples with high Mnconcentrationx=0.086 and with low Mn concentrationx=0.027. . . . . . 57

5.7 The Hall voltage versus magnetic field for two samples of Ga1−xMnxAswith x=0.086, as-grown and annealed at the optimal conditions, measuredat T=4.2K. Note that dominant contribution to the Hall voltage comesfrom the AHE term; the Hall voltage reflects theM(B) behaviour. . . . . . 59

5.8 Magnetoresistivity (R-R0)/R0, whereR0 is the value of resistivity atB=0,for the epilayer with high Mn contentx=0.07 measured at various temper-atures 4.2K, 40K, 110K, 150K and 200K for as-grown sample annealedat the optimal conditions (Ta=2890C) and after annealing at higher tem-perature (Ta=3500C). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

5.9 Magnetoresistivity (R-R0)/R0, whereR0 is the value of resistivity atB=0,for the epilayer with high Mn contentx=0.086: as-grown, annealed at theoptimal conditions (Ta=2800C) and after annealing at higher temperature(Ta=3500C). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

5.10 Magnetoresistivity (R-R0)/R0, whereR0 is the value of resistivity atB=0,for the epilayer with low Mn contentx=0.027: as-grown and annealed atthe optimal conditions (Ta=3000C). . . . . . . . . . . . . . . . . . . . . 62

5.11 MagnetoresistivityR for the sample withx=0.01 in low magnetic fields atT=20K. The magnetic fieldB was applied perpendicular to the film. Notethat hysteretic behavior is visible. The arrows and numbers indicate thehistory and direction of applied magnetic field. . . . . . . . . . . . . . . 63

5.12 Low magnetic field magnetoresistivity for the Ga1−xMnxAs sample withx=0.01 measured at various temperatures. The magnetic fieldB was ap-plied perpendicular to the film. The arrows and numbers indicate thehistory and direction of applied magnetic field. . . . . . . . . . . . . . . 64

List of Figures 119

5.13 Magnetization versus temperatureM(T) measured in small magnetic fieldB = 10Gs for the as-grown and annealed at 2890C GaMnAs sample withx=0.07. It is clearly visible that annealing procedure at the optimal con-ditions leads to the increase of saturation magnetization. . . . . . . . . . 65

5.14 Magnetization versus temperatureM(T) measured in small magnetic fieldB = 10Gs for the as-grown and annealed at 2890C GaMnAs sample withx=0.07. It is clearly visible that annealing procedure at the optimal con-ditions leads to the increase of saturation magnetization. . . . . . . . . . 66

5.15 The hysteresis loopM(B) for the as-grown and annealed at the optimalconditions sample withx=0.07 measured atT=5K. The decrease of coer-cive field is visible after optimal annealing. . . . . . . . . . . . . . . . . 67

5.16 Magnetization versus temperature measured by SQUID magnetometer atsmall magnetic fieldB=10Gs for three samples withx=0.062 (10727Depilayer): as-grown, annealed at the temperature 2890C and 3500C. . . . . 68

5.17 The hysteresis loopsM(B) for the sample withx=0.062 as-grown, an-nealed at the temperature equal to 2890C and higher temperature 3500C. . 68

5.18 The principle of magnetooptical Kerr effect method. . . . . . . . . . . . . 695.19 Three configurations for magnetooptical Kerr effect measurements: lon-

gitudinal, transverse, polar. . . . . . . . . . . . . . . . . . . . . . . . . . 705.20 Kerr rotation angleθK versus magnetic field up to 6T for the as grown

epilayer with high Mn contentx=0.086 and a Curie temperatureTC=88K. 725.21 The magnetic field dependence of Kerr rotation angleθK at different tem-

peratures for the epilayer withx=0.086 annealed at the optimal conditionsTa= 2890C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

5.22 The results of MOKE obtained atT=5K for λ=632.8nm for all investi-gated samples as grown and annealed 10727E epilayer withx=0.086 andfor epilayers with lower Mn concentration: 11127A (x=0.048) as well as10529A (x=0.014). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

5.23 The results of MOKE obtained atT=5K for λ=540.5nm for all investi-gated samples as grown and annealed 10727E epilayer withx=0.086 andfor epilayers with lower Mn concentration: 11127A (x=0.048) as well as10529A (x=0.014). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

5.24 The comparison ofθK(B) behaviour for two used wavelengths (two wave-lengths of incident lightλ=632.8nm andλ=540.5nm) for as grown epi-layer withx=0.086. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

5.25 The comparison ofθK(B) behaviour for two used wavelengths (two wave-lengths of incident lightλ=632.8nm andλ=540.5nm) for as grown epi-layer withx=0.014. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

5.26 SQUID magnetizationM versus magnetic field at 5K. The magnetic fieldwas applied perpendicular to the sample surface. . . . . . . . . . . . . . . 76

5.27 The comparison of the two data sets: Kerr rotation angle with the SQUIDmagnetizationM(B) collected atT=5K. . . . . . . . . . . . . . . . . . . 76

5.28 The results of MOKE obtained atT=5K for λ=632.8nm in the range ofhigh magnetic fields for all investigated samples as grown and annealed10727E epilayer withx=0.086 and for epilayers with lower Mn concen-tration: 11127A (x=0.048) as well as 10529A (x=0.014) . . . . . . . . . . 77

List of Figures 120

5.29 The oscillatory terms of Kerr rotation angle as a function of inverse mag-netic field measured at T=5K for two epilayers: 10529A (x=0.014) and11127A (x=0.048). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

5.30 The oscillatory terms of Kerr rotation angle as a function of inverse mag-netic field measured atT=5K for as-grown as well as annealed sample of10727E epilayer withx=0.086. . . . . . . . . . . . . . . . . . . . . . . . 80

5.31 The results of Fourier transform analysis of Kerr rotation angle curvesmeasured atT=5K for two epilayers: 10529A (x=0.014) and 11127A(x=0.048) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

5.32 The results of Fourier transform analysis of Kerr rotation angle curvesmeasured atT=5K for as-grown as well as annealed sample of 10727Eepilayer withx=0.086. . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

5.33 The oscillatory terms of Kerr rotation angle as a function of magneticfield B measured atT=5K for as-grown as well as annealed sample of10727E epilayer withx=0.086. The shift of oscillating terms towardshigher magnetic field after thermal annealing is visible. . . . . . . . . . . 83

5.34 Schematic view of the channeling of ions directed at an angleΨ to aclose-packed row of atoms in a crystal. . . . . . . . . . . . . . . . . . . 84

5.35 The normalized yieldχh of ions that are backscattered from host atoms(the RBS yield) shows a strong dip atΨ=0. If 50% of solute atoms aredisplaced into the channel, the normalized yieldχs of ions backscatteredfrom the solute atoms is approximately half the random yield; i.e.,χs=0.5at Ψ=0 (broken curve). If displaced solute atoms are located near thecenter of the channel, a peak in yield may occur (dotted line). . . . . . . . 85

5.36 Schematic of the tetrahedral interstitial positions for a zinc-blende latticealong the various axial directions. . . . . . . . . . . . . . . . . . . . . . 86

5.37 The PIXE and RBS angular scans about the〈100〉 axes for as-grown sam-ple with x=0.092. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87



5.40 The fraction of nonrandom Mnfnr, calculated by comparing normalizedyieldsχMn andχGaAs for the〈100〉, 〈110〉 and〈111〉 projections. . . . . . 89

5.41 Theω/2Θ scan for the symmetric (004) Bragg reflection for as-grownsamples withx=0.027, 0.062, and 0.086. . . . . . . . . . . . . . . . . . . 91

5.42 Theω/2Θ scan for the symmetric (004) Bragg reflection for as-grown andannealed sample withx=0.086. . . . . . . . . . . . . . . . . . . . . . . . 91

5.43 Comparison of the measuredω/2Θ scan for the symmetric (004) Braggreflection (dashed curve) with simulation results (solid curve) for the an-nealed sample withx= 0.086. . . . . . . . . . . . . . . . . . . . . . . . . 93

5.44 Reciprocal space maps of the symmetric (004) reflection for the as-grownand annealed sample withx=0.086. (Qx andQy represent reciprocal spacevectors (Qx is in the direction <110> parallel to the surface,Qy is in the di-rection perpendicular to the surface), both given inλ/2d units,λ=0.15406nm,d denotes the interplanar spacing). . . . . . . . . . . . . . . . . . . . 94

List of Figures 121

5.45 Reciprocal space maps of the asymmetric (224) reflection for the as-grown and annealed sample with x=0.086. (Qx andQy represent recipro-cal space vectors (Qx is in the direction <110> parallel to the surface,Qy

is in the direction perpendicular to the surface), both given inλ/2d units,λ=0.15406 nm,d denotes the interplanar spacing). . . . . . . . . . . . . . 95

5.46 Relaxed lattice parameter of Ga1−xMnxAs plotted as a function of the Mnconcentrationx for as-grown and annealed samples. . . . . . . . . . . . . 97

7.1 The parameters that define the ellipse of polarization in its plane: 1) theazimuthθ, that defines orientation of the ellipse in its plane (−π

2≤ θ ≤

π2); 2) the ellipticity e=b

a; 3) the ellipticity angleε=arctan(e) (−π

4≤ ε ≤

π4); 4) the amplitudeA = (a2+b2)

12 ); 5) the absolute phaseδ defined by

the initial electric field and auxiliary (dashed) circle (-π ≤ δ ≤ π), itdetermines the angle between the initial position of the electric vector att=0 and major axis of the ellipse. . . . . . . . . . . . . . . . . . . . . . . 104

7.2 1 Energy bands for a simple semiconductor for B=0. . . . . . . . . . . . 1057.3 Energy bands for a simple semiconductor for B>0. . . . . . . . . . . . . 1077.4 The intrerband transitions between Landau levels (n=0,1,2,3,4) of two

simple parabolic bands ( the left side of the picture represents simple en-ergy bands for B=0). The arrows indicate the conditions for resonancetransitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

LIST OF TABLES

2.1 Specifications of 7229 LakeShore Susceptometer/Magnetometer system. 15

3.1 The chemical composition of Pb1−x−y−zMnxEuySnzTe samples deter-mined by means of X-ray dispersive fluorescence analysis technique. . . 22

3.2 The lattice constanta0 of Pb1−x−y−zMnxEuySnzTe samples determinedby the standard powder X-ray measurements and the values of the latticeconstant of Pb1−x−yMnxSnyTe a [11] with similar content of Mn and Snas for the samples investigated in the thesis. . . . . . . . . . . . . . . . . 22

3.3 The parameters of the LT MBE growth of GaMnAs samples - substratetemperatureTS and temperature of the Mn effusion cellTMn, thicknessof the GaMnAs layersdGaMnAs determined from RHEED oscillations andMn composition of investigated samplesx (determined from RHEED os-cillations, X-ray diffraction and high resolution X-ray diffraction mea-surements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.1 The results of transport characterization of Pb1−x−y−zMnxEuySnzTe sam-ples - hole concentrationp [1021 cm−3], conductivityσ[(Ωcm)−1], mobil-ity µ [cm2/Vs]) measured at the room and liquid nitrogen temperature. . . 33

4.2 . The results of magnetic measurements for IV-VI mixed crystals. . . . . 35

5.1 Curie temperatureTρ estimated from the zero-field resistivity measure-ments for as-grown (a.g.) and annealed at different temperaturesTa for 1hour in nitrogen atmosphere GaMnAs samples with different Mn compo-sition (0.1≤x≤0.093) and various layer thicknessd. . . . . . . . . . . . . 54

5.2 The measured values of perpendicular to the layer plane latticeparameter(a⊥), in-plane lattice parameter (a‖), the calculated values ofthe relaxed mismatch (arelax-as)/as, and thickness of the GaMnAs epilay-ers determined from both RHEED oscilations and XRD measurementsbefore and after annealing. . . . . . . . . . . . . . . . . . . . . . . . . . 92

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