Presentation on theme: "Mechanism of the Verwey transition in magnetite Fe3O4"— Presentation transcript:
1Mechanism of the Verwey transition in magnetite Fe3O4 Przemysław Piekarz, Krzysztof Parlinski, and Andrzej M. OleśDepartment of Materials Research by ComputersInstitute of Nuclear Physics Polish Academy of SciencesKraków, PolandReference:P. Piekarz, K. Parlinski, and A.M. Oleś, Phys. Rev. Lett. 97, (2006)
2Fe3O4 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 KMetalInsulatorTN= 860 K122 KElectricalconductivityMetal – Insulatortransition at 122 K
3Fe3O4 Spin electronics - Spintronics Fe3O4 - ideal material for spintronics aplications100% spin polarization at room temperatureSpintronics: 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….
4Fe3O4 A B Two concepts of Verwey Phase Transition T > 122K MetalT > 122KFe3+ tetrahedralOFe2.5+ octahedralCubic, Fd-3m, AntiferrimagnetFe3+ tetraOFe3+ octaFe2+ octaCharge order ofFe3+ and Fe2+ in octaElectronic band structure cal.LDA+UX-ray anomalous scatteringX-ray powder diffractionTransmission electron diffractionADiffraction methodsX-rays, neutrons,Diffuse scatteringX-ray absorptioin EXAFS octa deform.Monoclinic distortionP2/cBMetal–insulatortransitionInsulatorT < 122K
5Citations 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.) Fe3O4Symmetry analysis of Verwey phase transitionCubic Fd-3m, unit cell: a x a x aMonoclinic P2/c, unit cell: a/ 2 x a/ 2 x 2aSearching 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)Verwey phase transition hasTWO primary order parametersFd-3m => (5, X3) => P2/c (4)P.Piekarz, K.Parlinski, and A.M.Oles, Phys.Rev.Lett. . 97, (2006).kxkykzXPbcm (4) Pmna (2) = P2/c (4)Common symmetry elements:
7Phonon Computational method Software Ab initio, VASP Software Lattice constantsAtomic positionsElectronic band structureMagnetic momentsPhononwolf.ifj.edu.pl/phonon/SoftwareDirect Method K. ParlinskiF(n) n, m) (k)2(k) e(k) = D(k) e(k)(k) – phonon dispersions
8Fe3O4 X3 phonon mode 5 phonon mode Ab initio calculated phonon dispersion curves GGA+Ucubic5 phonon modeX3 phonon modeNo soft phonon modeExperimental points: E.J.Samuelsen and O.Steinsvoll, Phys.Status Sol. B61, 615 (1974).
9Fe3O4 Ground state energy Etot with phonon distorsions Cubic5 phonon modeEnergy of supercell with 56 atoms.parabolaEQX3 phonon modeP2/c monoclinicphonon mode X3 or 5Distorsions with symmetries of X3 and 5 decrease the ground state energy EtotFurther 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
10Fe3O4 Electron-phonon coupling Cubic no gap Cubic + 5 Cubic + X3 gap MonoclinicElectron density of states for a crystal which is distorted by indicated phonon modeGGA + UU = 4 eVX3 phonon mode in cubic crystal induces an electronic gapOptimized P2/c structure close to this measured in Reference:J.P.Wright, J.P.Attfield, and P.G.Radaelli, Phys.Rev. B66, (2002).