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Ordering at the Verwey Transition in Magnetite Fe
3
O
4 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
Compass, China, 220 BC
Main experimental facts
Verwey transition, T V = 122 K 1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
70 80 90 100 110 T(K) 120 130 140 150 Latent heat of the transition 7.5
6.0
4.5
3.0
1.5
0.0
-1.5
-3.0
4 Fe 3 O 4 8 12 16 1000/T (K -1 ) 20 Discontinuous anomalies in many physical properties 24
Main experimental facts: structure
T
8.40
a m /2 1/2 (Fe 2+ , Fe 3+ ) octa inverse spinel Fe 3+ tetra 8.39
c m /2 8.38
b m /2 1/2 80 100 120 Temperature (K) 140 160 octa (B) site
Main experimental facts: magnetism
anomalies in AC susceptibility and magnetocrystalline anisotropy at the transition 0.08
AC susceptibility 0.06
M=0.1% 0.04
0.02
100 150 Temperature [K] 200 0 -1 -2 -3 Fe 3 O 4 -4 -100 0 100 200 300 400 500 600 700 Temperature (K)
S. Chicazumi, AIP Conf. Proc. 29 (1976) 385
magnetic Properties
Ferrimagnet
Fe 3+
,
Fe 3+ :
,
:
T N =835K;
Fe 2+
superexchange; No anomaly in M at T V (bigger than 0.1%) Anomaly in AC susceptibility anomaly in MCA energy at T V
O 2-
Verwey idea: order-disorder transformation
Octa positions: mixed valence Tetra positions: Fe 3+ T>T V Fe +2.5
(Fe 2+ , Fe 3+ ) octa Fe 3+ tetra Magnetic Test: m= -5 B + 5 B + 4 Experiment: 4.1 B !! B = 4 B T ) turns to Fe +3 -Fe +2 long range order (mobile electrons from octahedral Fe freeze below T V at specified positions) • Strong Coulomb repulsion between octahedral Fe ions drive the transition: • Well defined Fe +2 for T>T V and Fe +3 ions for T 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 new experiments and the new perspective in the last 4 years 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. +3 +2 V P. Novak et al. Phys.Rev. B 61 (2000) 1256 Spin –lattice relaxation time does not distinguish Fe 2 cations (but should) Fe +3 - no orbital moment Long spin-lattice relaxation T 1 „...the NMR relaxation results and also the bond length analysis indicate that below T V 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 +2 - orbital moment Fast spin-lattice relaxation T 1 V 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 (!!!) A 50K 140K C theory Exper B „... 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 T V , no fast hoping above T V V J. P. Wright et al. Phys.Rev.Lett. 87 (2001) 266401; Phys. Rev. B66 (2002) 214422; Bond Valence sums (BVS) and renormalized valences (V) for all sites in the refined 90K structure of Fe 3 O 4 • • Fe arrangement for T< T V Charge difference below 0.2 Anderson criterion violated „...since the magnitude of apparent charge separation in Fe ordered....” 3 O 4 transition- metal oxide is considered to be charge is comparable to that in other charge ordered oxides, it is justifiable to describe magnetite as being charge ordered insofar as any Fe +2.6 Fe +2.4 O -2 V I. Leonov....., V. I. Anisimov, et al.. arXiv:cond-mat/0402363v1 • LSDA (without Coulomb repulsion) gives half metal state below T V even though the realistic monoclinic structure was used • LSDA+U (Coulomb repulsion included) gives charge ordered insulator with E=0.18eV • The same charge order as that of Wright is realized LSDA+U, monoclinic • • Fe octa t 2g 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 gap electron-electron Coulomb repulsion YES!! electron-lattice interaction YES!! magnetic interaction NO! George Honig Purdue University West Lafayette, Indiana USA Don Kim Pukyong National University Pusan, Korea 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 AGH University of Science and Technology, Kraków, Poland The Henryk Niewodniczański Institute Of Nuclear Physics, Kraków, Poland Maria Balanda Krzysztof Parlinski Bruno Lüthi Holger Schwenk Frankfurt University Krankfurt a/Main , Germany ESRF, Grenoble, France Sasha Chumakov Bartek Handke Institute of Catalysis & Surface Chemistry, Polish Academy of Sciences, Kraków, Poland 130 (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 120 110 100 90 Fe 3(1 ) O 4 Fe 3-x Zn x O 4 Fe 3-x Ti x O 4 R. Aragón et. al. J. Magn. Magn. Mat. 54-57, 1335(1986) 80 0.00 0.01 0.02 X, 3 Zn : Fe 3-x Zn x O 4 Ti: Fe 3-x Ti x O 4 nonstoichiometric Fe 3(1 ) O 4 Fe 3 1 x Fe 3 Fe 3 0.03 0.04 2 x Fe 3 1 x Fe 2 1 x Fe 3 1 2 x Fe 2 1 x Ti 4 x Fe 3 1 6 Fe 2 1 9 O 4 O 4 O 4 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 Change of structure at the transition Isotope effect: T V increases when 18 O replaces 16 O ( Terukov et. al., phys. stat. sol. (b) 95, 491(1979) ) 0.8 Fe 3-x Zn x O 4 0.7 0.6 0.5 0.4 550 • The lattice of the first order magnetite becomes more rigid as T falls below T V , in contrast to the unchanged lattice of II order specimens 0.3 500 0.2 0.1 40 x = 0 x = 0.010 x = 0.028 60 80 450 100 80 100 120 Temperature ( K ) 120 140 140 The lattice dynamics is linked to the transition order (also consistent with our EXAFS study) Temperature (K) A. Kozłowski, Z. Kąkol, D. Kim, R. Zalecki, J. M. Honig . Phys.Rev. B54, 12093 (1996). 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 Electron-phonon interactions vital to the mechanism of the transition? Studies of elastic constants Studies of structure by neutron and X-ray scatterring Studies of lattice dynamics by NIS 2,0 x = 0 1,6 x = 0.006 x = 0.010 1,2 x = 0.020 0,8 x = 0.032 0,4 Fe 3-x Zn x O 4 0,0 40 60 80 100 120 140 160 180 T (K) H.Schwenk, S.Bareiter, B.Luthi, Z.Kakol, A. Kozłowski, J.M. Honig . Eur.Phys.J. B13, 491(2000) Fig. 9 Kąkol Clear difference in lattice stiffnes for the „first and the continuous type” magnetite 1,1 1,0 0,9 0,8 x=0.02 x=0 Fe 3-x Zn x O 4 0,7 x=0.032 0,6 0 50 100 150 200 T [K] 250 300 350 c 44 is well fitted by the Landau identical formula for continuous phase transitions c 44 c 0 44 T T T C (=56K) temperature of the phase transition predicted by Landau theory, T C (=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 T C ). 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 T V . e - Usuall Mossbauer effect 57 Fe nuclear energy level E 0 6 5 E<100meV 4 3 2 storage ring 1 Sample: 57 Fe 3 O 4 0 -80 -60 -40 -20 0 20 Energy [meV] 40 60 80 undulator 57 Fe absorbs E 0 E 57 Fe absorbs E 0 + E lens Phonon anih. Phonon creat. APD 2 APD 1 6 5 NIS E 4 3 2 1 Phonon anihilation 0 - 80 - 60 - 20 0 20 - 40 Energy [meV] 40 Phonon creation 60 80 1000 100 10 1 0 20 40 60 80 100 120 140 160 Time [ns] -10 velocity [mm/s] Energy 5 10 B. Handke , A. Kozłowski , K. Parliński , J. Przewoźnik , T. Ślęzak , A. I. Chumakov , L. Niesen , Z. Kąkol, J. Korecki . submitted to Phys.Rev. . B, 1.2 1.0 0.8 0.6 0.4 0.2 0.0 4 6 8 1012141618202224262830 E(meV) 300K 140K 130K 120K 115K 110K 105K 100K 95K 80K 50K 25K 1.5 1.0 0.5 0.0 0 5 296 K 140 K 120 K 100 K 25 K 10 15 Energy [meV] 20 25 Octahedral iron vibration spectrum changes discontinuously at T V 100000 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? 10000 1000 75 100 125 150 175 200 225 250 275 300 325 T(K) 126,00 125,75 125,50 125,25 125,00 124,75 124,50 124,25 124,00 123,75 susceptibility temperature 14 12 10 8 6 4 123,50 2 123,25 123,00 200 400 600 800 1000 1200 1400 heating time (s) 100000 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? 10000 1000 75 100 125 150 175 200 225 250 275 300 325 T(K) 126,00 125,75 125,50 125,25 125,00 124,75 124,50 124,25 124,00 123,75 123,50 123,25 123,00 200 H ext =0 kOe 400 H ext 600 =2 kOe 800 1000 heating time (s) 1200 14 12 10 8 6 4 2 1400 Z. Tarnawski et al. submitted to Acta Phys. Pol. Fe 3 O 4 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 0.26 0.24 0.22 0.20 0.18 0.16 0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.00 0 NIS DOS @ 296 K NIS DOS @ 25 K Fe total Fe octa Fe tetra 10 20 30 40 E (meV) 50 60 70 80 the sudden lowering of low energy DOS at T V is due to the vibration Octahedral iron vibration spectrum changes discontinuously at T VVerwey model: conclusions
Is magnetite really the ionic material dominated by electron repulsion?
NMR results: octahedral Fe
and Fe
similar below T
are very
X-ray resonant scattering results: no atomic charge ordering occurs below T
Neutron and X-ray powder diffraction: charge ordering occurs below T
but charge difference is low
Theory: charge ordering occurs below T
charge difference is low but
What interactions are involved in the transition?
What interactions participate in the transition; Magnetite of first and second order
“Magnetite of first and second order”
Can lattice dynamics participate in the transition?
Lattice dynamics: elastic constant studies
Lattice dynamics: elastic constant studies
Nuclear Elastic/Inelastic Resonant X-Ray Scattering/Absorption
Low energy vibration spectrum
Magnetic interactions
Magnetic interactions
Magnetic interactions do not actively participate in the Verwey transition
Conclusions