Verwey transition in magnetite (Fe3O4), unveiled?

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1 Verwey transition in magnetite (Fe3O4), unveiled? J.E. Lorenzo Keywords: Charge, orbital orderings; lattice distortion; spin reorientation; resonant X ray scattering S. Grenier N. Jaouen Y. Joly D. Mannix C. Marin C. Mazzoli E. Nazarenko IN-Grenoble Synchrotron-SOLEIL IN-Grenoble IN-Grenoble CEA-Grenoble ESRF-Grenoble IN-Grenoble/Rostov State University, Russia E. Nazarenko, J.E. Lorenzo, Y. Joly, J.L. Hodeau, D. Mannix and C. Marin, Phys. Rev. Lett. 97, (2006) J.E. Lorenzo, C. Mazzoli, N. Jaouen, C. Detlefs, S. Grenier, Y. Joly, and C. Marin, submitted to PRL Y. Joly, J.E. Lorenzo, E. Nazarenko, J.L. Hodeau, D. Mannix and C. Marin, submitted to PRB

2 Self organization of correlated electrons (CE)

3 Outline What do we know about Fe3O4 Lattice distortion Magnetic order Charge order Orbital order Fe2+ How do these orderings are intertwined? Conclusions Lattice distortions

4 Magnetite

5 Verwey transition in magnetite: How did this saga start? Fe3+ Fe2.5+δ Fe2.5 δ O4 Verwey 1939

6 What do we know about magnetite? Lattice distortions

7 Verwey phase transition in Fe3O4 Cubic (a * a * a) to monoclinic ( 2a * 2a * 2a) a=8.385 A (4 0 4) Wright, PRB 2002

8 What do we know about magnetite? Magnetic ordering

9 Verwey phase transition in Fe3O4 Polarized neutron diffraction H=2T ILL IN20 Itinerant and valence electrons are antiferromagnetically coupled

10 Verwey phase transition in Fe3O4 Spin reorientation takes place at TK=130K from 111 to 100

11 Verwey phase transition in Fe3O4 Spin reorientation takes place at TK=130K from 111 to 100

12 magnetocrystalline anisotropy Isotropy point

13 What do we know about magnetite? Charge ordering

14 Verwey model of CO

15 Charge ordering: previous experiments (0, 4, 7/2)

16 Charge ordering in Fe3O4 Experimental data Fit with CO Fit without CO 150 ( 4,4,1) Photon energy (ev) Nazarenko et al., Phys. Rev. Lett 97, (2006)

17 Results charge ordering in magnetite Agreement with theoretical calculations (LSDA+U) and bond valence method (1) : I. Leonov et al., Phys. Rev. Lett. 93, (2004) TBLMTO (2) : H. T. Jeng, et al., Phys. Rev. Lett. 93, (2004) FLAPW P. work BVS (1) (2) n3d n3d n3d M n3d M Fe Fe Fe Fe Resonant X ray scattering can give quantitative values of electronic parameters Charge ordering : ± 0.12 (Fe1 and Fe2) and ± 0.08 (Fe3 and Fe4) electron for Fe3O4 ± 0.04 for NaV2O5

18 Results charge ordering in magnetite Fe1 : : 2.5 δ 12 Fe2 : : δ 12 Fe3 : : 2.5 δ 34 Fe4 : : δ 34 Conclusion: Complex charge ordering, magnitude in agreement with BVS and electronic band structure calculations.

19 From charge ordering to ferroelectricity??? Efremov et al., Nature Materials 3, 853, (2004) Site centered charge order TM O Bond centered charge order Ferroelectric intermediate state

20 Ferroelectricity and multiferroicity in magnetite Magnetite is ferroelectric at low T Kato and Iida, J. Phys.Soc. Jpn 51, 1225 (1982) K Magnetite is multiferroic at low T Rado and Ferrari, Phys. Rev. B12, 5166 (1975) R

21 What do we know about magnetite? orbital ordering

22 Orbital order in magnetite cubic trigonal eg eg t2g e'g a1g Fe2+ (d6) Gap~0.18 ev Band width~0 0.4eV (2002) LDA+U calculations first showed the occurrence of orbital ordering and thus suggested that orbital degrees of freedom do play a rôle at the Verwey transition

23 Phase diagram : inter-site Coulomb (V) and hopping (tpd) Electron hopping tpd On-site Coulomb Inter-site Coulomb U=4 ev V Spinless 3-band Hubbard (Hartree-Fock approximation) Trigonal crystal field D=0.25 ev Spin-orbit ζ=0.052 ev (CD-)ROO-I: orbital order a1g (with) without CO (CD-)ROO-II: orbital order eg, (with) without CO COO: OO with complex numbers coefficients Uzu and Tanaka, J. Phys. Soc. Jpn., (2006)

24 Orbital order in magnetite Observation of orbital ordering by resonant X ray scattering at Fe L edges Observation of orbital ordering by resonant X ray scattering at Fe K edges Schlappa PRL 2008 (0 0 2n+1/2)

25 How do these electronic degrees of freedom interact?

26 Resonant diffraction in Fe3O4 (00 l) (004) ( (007/2) (003) ( (005/2) (002) ( (003/2) ( (001) ( (001/2) Bragg reflection of cubic Extinct Bragg reflection of cubic Charge ordering + lattice distortion Orbital ordering (Extinct Bragg reflection of LT struct)

27 Temperature dependence or CO, OO, LT Bragg diffraction spans over nearly 11 orders of magnitude!!!!. OO very weak peaks, and rather short correlation length, 130Å (orbital disorder?). CO peaks shows shorter correlation length than LT. CO and OO peaks shows no 1st order phase transition but a kink at TV

28 Temperature dependence or CO, OO, LT TV TV Tk Tk LT peaks displays 3 different regimes of fluctuations Above TV both intensity CO and OO peaks follow identical T-dependence. Between TV and TK CO peaks shows longer correlation length than LT.

29 Conclusions Pure electronic degrees of freedom are the important variables above TV. Fe2+ cations lead the game in charge, orbital and spin orderings. TK (and the spin reorientation) seems to play a fundamental role on the onset of charge/orbital orderings. Between TK and TV CO fluctuations are of longer LRO than lattice, thus hinting the possibility of a Wigner crystal between these two temperatures. Band structure calculations suggest charge-orbital ordering and hence the Verwey metal-insulator transition is driven by the on-site Fe d-electron correlation. OO is probably disordered, probably reflecting a phenomenally complex orbital ground state with site dependent orbital occupancies. We believe that the Verwey transition at TV sets in to disrupt a growing charge disproportionation and to prevent the CO to become unstable.

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