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Ordering at the Verwey Transition in Magnetite Fe 3 O 4

Ordering at the Verwey Transition in Magnetite Fe 3 O 4. General. 1. Verwey transition : experiments and the Verwey ionic model 2. C ontroversies with the ionic order. Our contribution. 3 . Magnetite of „ first and second order transition”

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Ordering at the Verwey Transition in Magnetite Fe 3 O 4

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  1. Ordering at the Verwey Transition in Magnetite Fe3O4 General 1. Verwey transition: experiments and the Verwey ionic model 2. Controversies with the ionic order Our contribution 3. Magnetite of „first and second order transition” 4. Main interactions engaged in the transition: electron-electron, electron-lattice?, magnetic?? 5. Conclusions

  2. Compass, China, 220 BC

  3. Main experimental facts Verwey transition, TV= 122 K Latent heat of the transition Discontinuous anomalies in many physical properties

  4. Main experimental facts: structure T<TV O2- (Fe2+, Fe3+) octa monoclinic close to orthorhombic Fe3+ tetra T>TV Tetra (A) site octa (B) site inverse spinel

  5. Main experimental facts: magnetism • anomalies in AC susceptibility and magnetocrystalline anisotropy at the transition M=0.1% S. Chicazumi, AIP Conf. Proc. 29 (1976) 385 • magnetic Properties : • Ferrimagnet: TN=835K; superexchange;Fe3+,Fe3+, Fe2+ • No anomaly in M at TV (bigger than 0.1%) • Anomaly in AC susceptibility • anomaly in MCA energy at TV

  6. Octa positions: mixed valence Tetra positions: Fe3+ T>TV Fe+2.5 Magnetic Test: O2- T<TV Fe+3-Fe+2 (Fe2+, Fe3+) octa Fe3+ tetra m= -5B+ 5 B +4B= 4 B Experiment:4.1 B !! Origin of the transition: due to Coulomb repulsion on octahedral sites high-T dynamic electron disorder (Fe+2.5 ) turns to Fe+3-Fe+2 long range order (mobile electrons from octahedral Fe freeze below TV at specified positions) Verwey idea: order-disorder transformation

  7. Verwey model: conclusions Anderson criterion At all temperatures only those cation arrangements are feasible where two +3 and two +2 iron exist on one tetrahedron of octahedral sites • Strong Coulomb repulsion between octahedral Fe ions drive the transition: • Well defined Fe+2 and Fe+3 ions for T<TV and intermediate valence for T>TV • Well defined cationic order below TV Can those conclusions be tested?

  8. new experiments and the new perspective in the last 4 years Is magnetite really the ionic material dominated by electron repulsion? • physically clear picture • in agreement with magnetic bulk results • low T arrangement is certainly not the one proposed by Verwey and the real charge order has not been determined for over 60 years • strong Coulomb interactions have never been directly proven • NMR results by Novak et al. • X-ray resonant scattering results by Garcia et al. • Combined neutron and X-ray diffraction experiment by Wright et al.

  9. NMR results: octahedral Fe+3 and Fe+2 are very similar below TV P. Novak et al. Phys.Rev. B 61 (2000) 1256 Spin –lattice relaxation time does not distinguish Fe2 cations (but should) „...the NMR relaxation results and also the bond length analysis indicate that below TV the states of iron ions on the B sublattice are mixed so strongly that the notion of 2+ and 3+ valency may lose its meaning...” Fe+3- no orbital moment Long spin-lattice relaxation T1 octahedral Fe+2- orbital moment Fast spin-lattice relaxation T1

  10. X-ray resonant scattering results: no atomic charge ordering occurs below TV A 50K 140K C B theory Exper „... only one kind of tetrahedral and octahedral iron ion (..) exists in magnetite either above or below the Verwey transition. The azimuthal behavior clearly shows that the occurrence of these reflections is due to the presence of local anisotropy of the tetrahedral Fe ions (..) and of the octahedral Fe atoms (..).” „... The absence of any changes in experimental spectra above and below the phase transition...demonstrates that no atomic CO occurs below the phase transition. Moreover, the experimental results can only support a charge disproportionation of 25% at most.” No CO below TV, no fast hoping above TV J. Garcia et al. Phys.Rev.Lett. 85 (2000) 578; Phys. Rev. B63 (2001) 054110; Surf. Rev Lett., 9 (2002) 821 • Forbidden reflections, eg.(006) and (002) visible in resonant scattering experiment due to: • different electronic states (e.g. Fe+2 i Fe+3) • local anisotropy (!!!)

  11. Neutron and X-ray powder diffraction: charge ordering occurs below TVbut charge difference is low Bond Valence sums (BVS) and renormalized valences (V) for all sites in the refined 90K structure of Fe3O4 J. P. Wright et al. Phys.Rev.Lett. 87 (2001) 266401; Phys. Rev. B66 (2002) 214422; • Fe arrangement for T< TV • Charge difference below 0.2 • Anderson criterion violated „...since the magnitude of apparent charge separation in Fe3O4 is comparable to that in other charge ordered oxides, it is justifiable to describe magnetite as being charge ordered insofar as any transition- metal oxide is considered to be charge ordered....” • Fe +2.6 Fe +2.4 O -2

  12. Theory: charge ordering occurs below TVbut charge difference is low I. Leonov....., V. I. Anisimov, et al.. arXiv:cond-mat/0402363v1 • LSDA (without Coulomb repulsion) gives half metal state below TV even though the realistic monoclinic structure was used • LSDA+U (Coulomb repulsion included) gives charge ordered insulator with E=0.18eV gap LSDA+U, monoclinic • The same charge order as that of Wright is realized • Fe octa t2g orbital difference as large as 0.5, but total 3d charge difference is 0.2 • Anderson criterion violated since both Coulomb and elastic energy should be minimized

  13. What interactions are involved in the transition? • electron-electron Coulomb repulsion YES!! • electron-lattice interaction YES!! • magnetic interaction NO!

  14. What interactions participate in the transition; Magnetite of first and second order Purdue University West Lafayette, Indiana USA George Honig Don Kim Zbigniew Kąkol, Józef Korecki Zbigniew Tarnawski, Andrzej Kołodziejczyk, Ryszard Zalecki, Czesław Kapusta, Janusz Przewoźnik, Adrian Wiechec, Danuta Owoc, Vit Prochazka, Colin Oates, Marta Borowiec, Andrzej Kozłowski Maria Balanda Krzysztof Parlinski Bruno Lüthi Holger Schwenk Sasha Chumakov Bartek Handke Pukyong National University Pusan, Korea AGH University of Science and Technology, Kraków, Poland The Henryk Niewodniczański Institute Of Nuclear Physics, Kraków, Poland Frankfurt University Krankfurt a/Main , Germany ESRF, Grenoble, France Institute of Catalysis & Surface Chemistry, Polish Academy of Sciences, Kraków, Poland

  15. Zn :  Fe3-xZnxO4 Ti:  Fe3-xTixO4 nonstoichiometric Fe3(1-) O4 Tetra (A) Octa (B) With increasing number of vacancies or doped atoms the nature of the transition changes from first order to the continuous one “Magnetite of first and second order” (a) δ = -0.00053 (b) δ = -0.00017 (c) δ = 0.00021 (d) δ = 0.00035 (e) δ = 0.0017 (f) δ = 0.0035 (g) δ = 0.0050 (h) δ = 0.0068 (i) δ = 0.0097 R. Aragón et. al. J. Magn. Magn. Mat. 54-57, 1335(1986)

  16. Can lattice dynamics participate in the transition? • The lattice of the first order magnetite becomes more rigid as T falls below TV, in contrast to the unchanged lattice of II order specimens • The lattice dynamics is linked to the transition order (also consistent with our EXAFS study) M. Borowiec, V. Procházka, C.J. Oates, M. Sikora, D. Zając, D. Rybicki, D. Nowak, B. Sobanek, D. Owoc, A. Kozłowski, Z. Kąkol, Cz. Kapusta, E. Welter submitted to J. Alloys - Comp A. Kozłowski, Z. Kąkol, D. Kim, R. Zalecki,J. M. Honig. Phys.Rev. B54, 12093 (1996). Studies of elastic constants Studies of structure by neutron and X-ray scatterring Studies of lattice dynamics by NIS • Change of structure at the transition • Isotope effect: TV increases when 18O replaces 16O ( Terukov et. al., phys. stat. sol. (b) 95, 491(1979) ) Electron-phonon interactions vital to the mechanism of the transition?

  17. Lattice dynamics: elastic constant studies • Clear difference in lattice stiffnes for the „first and the continuous type” magnetite H.Schwenk, S.Bareiter, B.Luthi, Z.Kakol, A. Kozłowski, J.M. Honig. Eur.Phys.J. B13, 491(2000)

  18. Lattice dynamics: elastic constant studies • c44is well fitted by the Landau identical formula for continuous phase transitions  (=56K) temperature of the phase transition predicted by Landau theory, TC(=66K) critical temperature resulting from coupling of the order parameter to the strain. • All systems prepare for continuous low temperature transition in the same manner, irrespective of its later order (same ) • the coupling to the elastic degrees of freedom is comparable (same TC). High temperature properties are not so susceptible to departures from stoichiometry or doping and do not differentiate between I and II order type transition The correlations which ultimately trigger the Verwey transition set in just above TV.

  19. Nuclear Elastic/Inelastic Resonant X-Ray Scattering/Absorption Usuall Mossbauer effect 6 5 3 4 3 Counts *10 2 1 0 - 80 - 60 - 40 - 20 0 20 40 60 80 Energy [meV] 1000 100 Counts 10 6 1 0 20 40 60 80 100 120 140 160 NIS 5 Time [ns] E 4 Phonon anihilation 3 Counts /103 -10 -5 0 5 10 Phonon creation 2 velocity [mm/s] Energy 1 0 - 80 - 60 - 40 - 20 0 20 40 60 80 Energy[meV] 57Fe nuclear energy level E0 E<100meV Sample: 57Fe3O4 storage ring e- APD 2 APD 1 lens undulator 57Fe absorbs E0 - E Phonon anih. 57Fe absorbs E0 + E Phonon creat.

  20. Low energy vibration spectrum 300K 1.2 100K 105K 110K 1.0 115K 120K 130K 0.8 140K Normalized intensity 25K 50K 0.6 80K 95K 0.4 0.2 0.0 4 6 8 10 12 14 16 18 20 22 24 26 28 30 E(meV) B. Handke, A. Kozłowski,K. Parliński,J.Przewoźnik, T. Ślęzak, A. I.Chumakov, L. Niesen, Z.Kąkol,J.Korecki. submitted to Phys.Rev. . B, Octahedral iron vibration spectrum changes discontinuously at TV

  21. Magnetic interactions Although magnetization does not have a step at the transition, AC susceptibility does change. May it mean that magnetic interactions play a role in the Verwey transition? susceptibility temperature 200 400 600 800 1000 1200 1400 heating time (s)

  22. Magnetic interactions Although magnetization does not have a step at the transition, AC susceptibility does change. May it mean that magnetic interactions play a role in the Verwey transition? Magnetic interactions do not actively participate in the Verwey transition Z. Tarnawski et al. submitted to Acta Phys. Pol.

  23. Conclusions • Fe3O4 is a simple, model material where the concepts of charge ordering and phase transitions may be tested • there is some charge order at low temperatures, but orthodox meaning of integer ionic states is not valid • the lattice feels the continuous transition from highest temperatures; the interactions that actually trigger first order Verwey transition set in very close to the transition. • Intervening interactions are Coulomb repulsion Electron-lattice Magnetic interactions do not participate in the transition

  24. Phonon DOS: theory vs. experiment the sudden loweringof low energy DOS at TV is due to the change of octahedral Fe vibration Octahedral iron vibration spectrum changes discontinuously at TV

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