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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