Investigation of the presence of charge order in magnetite by measurement of the spin wave spectrum

McQueeney, R. J.; Yethiraj, M.; Montfrooij, Wouter; Gardner, J. S.; Metcalf, P.; Honig, J. M.

doi:10.1103/physrevb.73.174409

Cited by 26 publications

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“…In this limit, the Zener DE picture of slow and local charge hopping between distinct valence states above T V is appropriate, and the closing of the electronic gap allows the coupling of spin waves to valence fluctuations leading to broadened spin wave line shapes. We also conclude that no features in the spin wave spectrum below T V can be definitively associated with long-range CO, in agreement with the results of our previous study [16].…”

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“…The enhancement of DE above T V can be estimated from the energy of the dispersionless 5 mode, 6J AB S B 8J BB S B . Since J AB does not change [16] Figure 4(a) further illustrates the anomalous 5 mode, which shows a minimum in the measured structure factor whereas the calculation predicts a maximum. Figure 4(b) indicates that A site optical spin waves have little temperature dependence and agree quite well with Heisenberg calculations.…”

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“…Details of sample preparation and characterization are given elsewhere [16]. The sample was mounted with cubic [HK0] as the primary scattering plane, and data were collected with an incident neutron energy of 160 meV and the incident beam at an angle of 25 from the [110] axis.…”

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Zener Double Exchange from Local Valence Fluctuations in Magnetite

et al. 2007

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Magnetite (Fe 3 O 4 ) is a mixed valent system where electronic conductivity occurs on the B site (octahedral) iron sublattice of the spinel structure. Below T V 123 K, a metal-insulator transition occurs which is argued to arise from the charge ordering of 2 and 3 iron valences on the B sites (Verwey transition). Inelastic neutron scattering measurements show that optical spin waves propagating on the B site sublattice ( 80 meV) are shifted upwards in energy above T V due to the occurrence of B-B ferromagnetic double exchange in the mixed valent phase. The double exchange interaction affects only spin waves of 5 symmetry, not all modes, indicating that valence fluctuations are slow and the double exchange is constrained by short-range electron correlations above T V . Magnetite has a cubic inverse spinel crystal structure containing two different symmetry iron sites: the A site resides in tetrahedrally coordinated oxygen interstices and has stable valence (3d 5 , Fe 3 ); the two B sites have octahedral coordination and a fractional average valence of 2:5 . The ferrimagnetic structure consists of ferromagnetic A-and B-sublattices aligned antiparallel to each other (T C 858 K). Below T V 123 K, magnetite undergoes a metal-insulator transition resulting in a decrease of the conductivity by two orders-of-magnitude. The model that has persisted over time is that extra electrons forming Fe 2 ions (3d 6 ) hop to neighboring Fe 3 sites on the cornershared B-sublattice tetrahedral network and give rise to electrical conductivity. Anderson argued that short-range ordering of Fe 2 and Fe 3 exists above T V due to significant intersite Coulomb repulsion and frustration on the B site sublattice [4]. The short-ranged electron correlations maintain local charge ''neutrality'' (2:5 average valence on each tetrahedron), thereby restricting charge hopping and conductivity [5]. In the classic picture of the Verwey transtion, Coulomb repulsions win out at low temperatures, resulting in long-range CO of Fe 2 and Fe 3 [6] in a process reminiscent of Wigner crystallization [7]. However, elastic and orbital interactions [8] induce monoclinic lattice distortions whose complexity has made characterization of the Verwey state difficult [9]. Even the validity of the CO model has been questioned recently [10], but neutron [11] and resonant x-ray scattering measurements [12] now appear to converge on fractional CO.In this Letter, we provide strong evidence for Anderson's original picture of short-ranged electron correlations in the mixed valent (MV) phase. Valence fluctuations occurring on the B-sublattice modify the magnetic exchange and affect spin waves propagating on Fe B sites. Inelastic neutron scattering measurements reveal that B site optical spin waves are shifted up in energy and broadened above T V due to ferromagnetic double exchange (DE). Ferromagnetic DE arises from real charge transfer processes in MV materials, a good example being the ferromagnetic metallic state in the manganites [13]. For fast electron hopping in the band...

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Zener Double Exchange from Local Valence Fluctuations in Magnetite

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“…The observed charge disproportionation [7] results from the modified d-p hybridization due to the EP coupling. Finally, a gap in the magnon spectrum at k ∆ point below T V [32] indicates a large spin-phonon interaction and confirms that k ∆ becomes a point on the Brillouin zone surface.…”

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Mechanism of the Verwey Transition in Magnetite

2006

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By combining ab initio results for the electronic structure and phonon spectrum with the group theory, we establish the origin of the Verwey transition in Fe3O4. Two primary order parameters with X3 and ∆5 symmetries are identified. They induce the phase transformation from the hightemperature cubic to the low-temperature monoclinic structure. The on-site Coulomb interaction U between 3d electrons at Fe ions plays a crucial role in this transition -it amplifies the coupling of phonons to conduction electrons and thus opens a gap at the Fermi energy. Published in Phys. Rev. Lett. 97, 156402 (2006). PACS numbers: 71.30.+h, 64.70.Kb, 75.50.Gg The discovery of the remarkable discontinuous drop of the electrical conductivity by two orders of magnitude in magnetite (Fe 3 O 4 ) below the Verwey transition (VT) at T V = 122 K [1] triggered intensive studies of its microscopic origin which have been continued for more than six decades. Verwey suggested explaining it by a metalinsulator transition due to the reduction of electron mobility caused by ordering of Fe 3+ and Fe 2+ ions below T V . In spite of great experimental effort, however, the existence of ionic-like charge ordering at T < T V could not be confirmed, and the origin of the VT in magnetite remains still puzzling [2].Magnetite is a ferrimagnetic spinel with anomalously high critical temperature T c ≃ 860 K. Hence, it is viewed as an ideal candidate for room temperature spintronic applications. It crystalizes in the inverse spinel cubic structure, Fd3m, with two types of Fe sites: the tetrahedral A sites and the octahedral B ones, see Ref. There are also other arguments against simple ionic mechanism of the VT. Firstly, the replacement of oxygen O 16 by O 18 isotope increases T V by a few degrees [9], indicating that the transition cannot be purely electronic.Secondly, signals in diffuse neutron scattering observed above T V at k ∆ = (0, 0, 1 2 ), halfway between Γ and X points with k X = (0, 0, 1), and equivalent points of the reciprocal lattice [10] (in units of 2π a , where a is the cubic lattice constant), change into Bragg peaks below T V . The intensity of critical scattering was succesfully calculated on the basis of the transverse acoustic (TA) phonon mode with the ∆ 5 symmetry. Further neutron studies discovered diffuse scattering with large intensities close to Γ and X points, and the dominant component of X 3 symmetry [11]. Other observations from Raman [12], X-ray [13] and nuclear inelastic scattering measurements [14] suggest that phonons play an essential role in the VT. But phonons alone cannot explain the metal-insulator nature of the transition either. Actually, if they alone were responsible, a phonon soft mode would have been found for the cubic phase, while the present ab initio calculations do not imply such a soft mode behavior.The purpose of this Letter is to resolve the above controversies and to demonstrate a cooperative scenario of the VT. Following the pioneering work of Ihle and Lorenz [15], who considered weak intersite Coulom...

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“…On the other hand the Fe 2+ has a ground state 5 D 4 that will be split by spin-orbit interactions. 50 Therefore the charge ordering produces an enhancement of the effect of the spin-orbit interaction. Since the anisotropic magnetoresistance is a consequence of this interaction 14,15,18 it can be expected that the the effect of polaron formation, thus charge ordering in the system can be observed by anisotropic magnetoresistance measurements as evidence from our observations.…”

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