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 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

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 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

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, 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) "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)

(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, 156402 (2006). kx ky kz X   Pbcm (4) Pmna (2) = P2/c (4) Common symmetry elements:

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

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).

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

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, 214422 (2002).

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

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