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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, 156402 (2006)
Fe3O4
MAGNETITE (gr. magnetis)
the oldest known magnetic mineral (~1500 B.C.)
Verwey Transition, Nature 144, 327 (1939)
Insulator
0
Metal
TV= 122 K
Electrical
conductivity
Metal – Insulator
transition at 122 K
122 K
TN= 860 K
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….
Fe3O4
T > 122K
Two concepts of Verwey Phase Transition
Metal
Fe3+ tetrahedral
Fe2.5+ octahedral
O
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.
T < 122K
Charge order of
Fe3+ and Fe2+ in octa
Metal–insulator
transition
Insulator
Fe3+ tetra
Fe3+ octa
Fe2+ octa
O
Monoclinic distortion
P2/c
„... 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)
Citations from
highlight articles
on Verwey transition
published
in recent years
"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)
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)
kz
Common symmetry elements:
Pbcm (4)
Pmna (2) = P2/c (4)
kx
X


ky
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).
Computational method
Software
Ab initio, VASP
Lattice constants
Atomic positions
Electronic band
structure
Magnetic moments
Direct Method K. Parlinski
F(n)
n, m)
(k)
Software
Phonon
wolf.ifj.edu.pl/phonon/
2(k) e(k) = D(k) e(k)
(k) – phonon dispersions
Fe3O4
Ab initio calculated phonon dispersion curves GGA+U
cubic
No soft phonon mode
5
phonon mode
X3
phonon mode
Experimental points: E.J.Samuelsen and O.Steinsvoll, Phys.Status Sol. B61, 615 (1974).
Fe3O4
Ground state energy Etot with phonon distorsions
Cubic
Energy of supercell with 56 atoms.
E
5 phonon mode
parabola
X3 phonon mode
P2/c monoclinic
Q
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 4component 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
Fe3O4
Electron-phonon coupling
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, 214422 (2002).
Cubic
no gap
Cubic + 5
no gap
Cubic + X3
gap
Monoclinic
gap
Fe3O4
T > 122K
Two concepts of Verwey Phase Transition
Metal
Fe3+ tetrahedral
Fe2.5+ octahedral
O
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
Charge order of
Fe3+ and Fe2+ in octa
Fe3+ tetra
Fe3+ octa
Fe2+ octa
O
T < 122K
Insulator
5
Monoclinic distortion P2/c
Conclusion
We resolved the long-standing puzzle of
the Verwey phase transition
Thank You