Mechanism of the Verwey transition

in magnetite Fe3O4

Przemysław Piekarz, Krzysztof Parlinski, and Andrzej M. Oleś

Department of Materials Research by ComputersInstitute of Nuclear Physics Polish Academy of Sciences

Kraków, Poland

Reference:

P. Piekarz, K. Parlinski, and A.M. Oleś, Phys. Rev. Lett. 97, 156402 (2006)

Fe3O4

Verwey Transition, Nature 144, 327 (1939)

Electrical conductivity

122 K

0 TV= 122 K

MetalInsulator

TN= 860 K

MAGNETITE (gr. magnetis) the oldest known magnetic mineral (~1500 B.C.)

Metal – Insulatortransition at 122 K

Fe

3O

4 - ideal material for spintronics aplications

100% spin polarization at room temperature

Spin electronics - Spintronics

Spintronics: manipulate electron spin (or resulting magnetism) to achieve new/improved functionalities -- spin transistors, memories, higher speed, lower power, tunable detectors and lasers, bits (Q-bits) for quantum computing….

 

Fe3O4

Two concepts of Verwey Phase TransitionFe3O4

T > 122K Fe3+ tetrahedral

OFe2.5+ octahedralCubic, Fd-3m, Antiferrimagnet

Metal

Fe3+ tetra

O

Fe3+ octa

Fe2+ octa

Charge order of Fe3+ and Fe2+ in octa

Electronic band structure cal.LDA+UX-ray anomalous scatteringX-ray powder diffractionTransmission electron diffraction

Diffraction methodsX-rays, neutrons,Diffuse scatteringX-ray absorptioin EXAFS octa deform.

Monoclinic distortion P2/c

Metal–insulator transition

Insulator

T < 122K

Citations from highlight articles

on Verwey transitionpublished

in recent years

„... in view of the possible technological importance of this material for spintronics, and because of the still not well understood low-temperature properties, magnetite remains at the focus of active research.„ 1 October 2004, Phys. Rev. Lett. 93, 146404 (2004)

"The classic charge ordering problem is that of magnetite, which, however, has been unresolved for over 60 years.(...) We found an insulating charge ordered ground state whose configuration and charge separation are in good agreement with that inferred from recent powder-diffraction measurements."8 October 2004, Phys, Rev. Lett. 93, 156403 (2004)

"Magnetite, a model system for mixed-valence oxides, does not show charge ordering.„ 8 October 2004, Phys. Rev. Lett. 93, 156408 (2004)

"The fact that if the charge disproportionations found in the insulating phase are of an electronic origin or determined by the structural distortions, is still disputed.„ 5 April 2005, Phys. Rev. B 71, 155103 (2005)

"The question of charge ordering of Fe(2+) and Fe(3+) states on the B sites in the low temperature phase is a matter of continued controversy.„ 10 May 2005, Phys. Rev. B 71, 174106 (2005)

"Magnetite (.) has high potential for applications in spin-electronics, also displays a rather unique electronic phase transition whose explanation has remined a challenge to modern condensed-matter physics."15 June 2005, Europhys. Lett. 70, 789 (2005)

"In spite of a large number of experimental and theoretical efforts, the mechanism governing the conduction and magnetic properties in magnetite is still under debate.„ 29 July 2005, Phys. Rev. B 72, 035131 (2005)

"Despite intensive investigations over half a century, the existence of charge ordering in magnetite remains controversial. The mechanism of the Verwey transition is a fundamental yet unresolved problem."10 March 2006, Phys. Rev. Lett. 96, 096401 (2006)

Symmetry analysis of Verwey phase transitionCubic Fd-3m, unit cell: a x a x a Monoclinic P2/c, unit cell: a/ 2 x a/ 2 x 2a

Searching irreducible representation (IR) of primary order parameter (OP)

Fd-3m => NO SINGLE IR => P2/cVerwey phase transition does NOT have a (single) primary order parameter !!!

(Result of complex and sofisticated symmetry calculations.)

Symmetry reduction:

Fd-3m => 5 => Pbcm (4)Fd-3m => X3 => Pmna (2)

Pbcm (4) Pmna (2) = P2/c (4)

Common symmetry elements:

Fe3O4

Verwey phase transition has TWO primary order parameters

Fd-3m => (5, X3) => P2/c (4) P.Piekarz, K.Parlinski, and A.M.Oles, Phys.Rev.Lett. . 97, 156402 (2006).

kx

ky

kz

X

Ab initio, VASP

Software

Phonon wolf.ifj.edu.pl/phonon/

Software

Computational method

Direct Method K. ParlinskiDirect Method K. Parlinski F(n) F(n) n, m) n, m) (k)(k)

22(k) e(k) = D(k) e(k)(k) e(k) = D(k) e(k)

(k) – phonon dispersions(k) – phonon dispersions

Lattice constants

Atomic positions

Electronic band

structure

Magnetic moments

Ab initio calculated phonon dispersion curves GGA+U Fe3O4

5 phonon mode X3 phonon modeNo soft phonon mode

Experimental points: E.J.Samuelsen and O.Steinsvoll, Phys.Status Sol. B61, 615 (1974).

cubic

Fe3O4 Ground state energy Etot with phonon distorsions

Energy of supercell with 56 atoms.

phonon mode X3 or 5

Cubic

X3 phonon mode

5 phonon mode

P2/c monoclinic

Distorsions with symmetries of X3 and 5 decrease the ground state energy Etot

Further decrease of Etot is possible by fixing the phases between 2- and 4- component order parameters of the X3 and 5, and permitting distorsions defined by the secondary order parameters.

Secondary order parameters: A1g Eg T1g T2g (C44) X1 2 4

parabolaE

Q

Electron density of states for a crystal which is distorted by indicated phonon mode

Fe3O4

X3 phonon mode in cubic crystal induces an electronic gap

GGA + UU = 4 eV

Electron-phonon coupling

Cubicno gap

Cubic + 5

no gap

Cubic + X3

gap

Monoclinicgap

Optimized P2/c structure close to this measured in Reference: J.P.Wright, J.P.Attfield, and P.G.Radaelli, Phys.Rev. B66, 214422 (2002).

Diffraction methodsX-rays, neutrons,Diffuse scatteringX-ray absorptioin EXAFS octa deform.

Two concepts of Verwey Phase TransitionFe3O4

T > 122K

T < 122K

Fe3+ tetrahedral

OFe2.5+ octahedral

Fe3+ tetra

O

Fe3+ octa

Fe2+ octa

Cubic, Fd-3m, Antiferrimagnet

Charge order of Fe3+ and Fe2+ in octa

Monoclinic distortion P2/c

Electronic band structure cal.LDA+UX-ray anomalous scatteringX-ray powder diffractionTransmission electron diffraction

Metal–insulator transition

Metal

Insulator 5

X3

Conclusion

We resolved the long-standing puzzle of the Verwey phase transition

Thank You