1. Mechanism of the Verwey transition in magnetite Fe3O4
Przemysław Piekarz, Krzysztof Parlinski, and Andrzej M. Oleś
Department of Materials Research by Computers
Institute of Nuclear Physics Polish Academy of Sciences
Kraków, Poland
Reference:
P. Piekarz, K. Parlinski, and A.M. Oleś, Phys. Rev. Lett. 97, (2006)

2. Fe3O4 Verwey Transition, Nature 144, 327 (1939) Metal Insulator
MAGNETITE (gr. magnetis)
the oldest known magnetic mineral (~1500 B.C.)
Verwey Transition, Nature 144, 327 (1939)
TV= 122 K
Metal
Insulator
TN= 860 K
122 K
Electrical
conductivity
Metal – Insulator
transition at 122 K

3. Fe3O4 Spin electronics - Spintronics
Fe3O4 - ideal material for spintronics aplications
100% spin polarization at room temperature
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….

4. Fe3O4 A B Two concepts of Verwey Phase Transition T > 122K
Metal
T > 122K
Fe3+ tetrahedral O
Fe2.5+ octahedral
Cubic, Fd-3m, Antiferrimagnet
Fe3+ tetra O
Fe3+ octa
Fe2+ octa
Charge order of
Fe3+ and Fe2+ in octa
Electronic band structure cal.
LDA+U
X-ray anomalous scattering
X-ray powder diffraction
Transmission electron diffraction A
Diffraction methods
X-rays, neutrons,
Diffuse scattering
X-ray absorptioin EXAFS octa deform.
Monoclinic distortion
P2/c B
Metal–insulator
transition
Insulator
T < 122K

5. Citations from highlight articles on Verwey transition published
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, (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, (2004)
"Magnetite, a model system for mixed-valence oxides, does not show charge ordering.„ October 2004, Phys. Rev. Lett. 93, (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, (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.„ May 2005, Phys. Rev. B 71, (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, (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, (2006)

6. (Result of complex and sofisticated symmetry calculations.)
Fe3O4
Symmetry analysis of Verwey phase transition
Cubic 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/c
Verwey 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)
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, (2006). kx ky kz X  
Pbcm (4) Pmna (2) = P2/c (4)
Common symmetry elements:

7. Phonon Computational method Software Ab initio, VASP Software
Lattice constants
Atomic positions
Electronic band structure
Magnetic moments
Phonon
wolf.ifj.edu.pl/phonon/
Software
Direct Method K. Parlinski
F(n) n, m) (k)
2(k) e(k) = D(k) e(k)
(k) – phonon dispersions

8. Fe3O4 X3 phonon mode 5 phonon mode
Ab initio calculated phonon dispersion curves GGA+U
cubic
5 phonon mode
X3 phonon mode
No soft phonon mode
Experimental points: E.J.Samuelsen and O.Steinsvoll, Phys.Status Sol. B61, 615 (1974).

9. Fe3O4 Ground state energy Etot with phonon distorsions
Cubic
5 phonon mode
Energy of supercell with 56 atoms.
parabola E Q
X3 phonon mode
P2/c monoclinic
phonon mode X3 or 5
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

10. Fe3O4 Electron-phonon coupling Cubic no gap Cubic + 5 Cubic + X3 gap
Monoclinic
Electron density of states for a crystal which is distorted by indicated phonon mode
GGA + U
U = 4 eV
X3 phonon mode in cubic crystal induces an electronic gap
Optimized P2/c structure close to this measured in Reference:
J.P.Wright, J.P.Attfield, and P.G.Radaelli, Phys.Rev. B66, (2002).

12. Fe3O4 5 A B X3 Two concepts of Verwey Phase Transition T > 122K
Metal
T > 122K
Fe3+ tetrahedral O
Fe2.5+ octahedral
Cubic, Fd-3m, Antiferrimagnet
Electronic band structure cal.
LDA+U
X-ray anomalous scattering
X-ray powder diffraction
Transmission electron diffraction
Diffraction methods
X-rays, neutrons,
Diffuse scattering
X-ray absorptioin EXAFS octa deform.
Metal–insulator transition X3
T < 122K
Charge order of
Fe3+ and Fe2+ in octa
Monoclinic distortion P2/c 5
Insulator A B
Fe3+ tetra O
Fe3+ octa
Fe2+ octa

13. We resolved the long-standing puzzle of the Verwey phase transition
Conclusion
We resolved the long-standing puzzle of
the Verwey phase transition
Thank You