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Mechanism of the Verwey transition in magnetite Fe 3 O 4 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)

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Fe 3 O 4 Verwey Transition, Nature 144, 327 (1939) Electrical conductivity 122 K 0 T V = 122 K Metal Insulator T N = 860 K MAGNETITE (gr. magnetis) the oldest known magnetic mineral (~1500 B.C.) Metal – Insulator transition at 122 K

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Fe 3 O 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…. Fe 3 O 4

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Two concepts of Verwey Phase Transition Fe 3 O 4 T > 122K Fe 3+ tetrahedral O Fe 2.5+ octahedral Cubic, Fd-3m, Antiferrimagnet Metal Fe 3+ tetra O Fe 3+ octa Fe 2+ octa Charge order of Fe 3+ and Fe 2+ in octa 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. Monoclinic distortion P2/c Metal–insulator transition Insulator T < 122K

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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.„ 8 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.„ 10 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)

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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 => X 3 => Pmna (2) Pbcm (4) Pmna (2) = P2/c (4) Common symmetry elements: Fe 3 O 4 Verwey phase transition has TWO primary order parameters Fd-3m => ( 5, X 3 ) => P2/c (4) P.Piekarz, K.Parlinski, and A.M.Oles, Phys.Rev.Lett.. 97, (2006). kxkx kyky kzkz X

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

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Ab initio calculated phonon dispersion curves GGA+U Fe 3 O 4 5 phonon mode X 3 phonon mode No soft phonon mode Experimental points: E.J.Samuelsen and O.Steinsvoll, Phys.Status Sol. B61, 615 (1974). cubic

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Fe 3 O 4 Ground state energy E tot with phonon distorsions Energy of supercell with 56 atoms. phonon mode X 3 or 5 Cubic X 3 phonon mode 5 phonon mode P2/c monoclinic Distorsions with symmetries of X 3 and 5 decrease the ground state energy E tot Further decrease of E tot is possible by fixing the phases between 2- and 4- component order parameters of the X 3 and 5, and permitting distorsions defined by the secondary order parameters. Secondary order parameters: A 1g E g T 1g T 2g (C 44 ) X 1 2 4 parabola E Q

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Electron density of states for a crystal which is distorted by indicated phonon mode Fe 3 O 4 X 3 phonon mode in cubic crystal induces an electronic gap GGA + U U = 4 eV Electron-phonon coupling Cubic no gap Cubic + 5 no gap Cubic + X 3 gap Monoclinic 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).

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Diffraction methods X-rays, neutrons, Diffuse scattering X-ray absorptioin EXAFS octa deform. Two concepts of Verwey Phase Transition Fe 3 O 4 T > 122K T < 122K Fe 3+ tetrahedral O Fe 2.5+ octahedral Fe 3+ tetra O Fe 3+ octa Fe 2+ octa Cubic, Fd-3m, Antiferrimagnet Charge order of Fe 3+ and Fe 2+ in octa Monoclinic distortion P2/c Electronic band structure cal. LDA+U X-ray anomalous scattering X-ray powder diffraction Transmission electron diffraction Metal–insulator transition Metal Insulator 55 X3X3

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

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