Zener Double Exchange from Local Valence Fluctuations in Magnetite

Abstract

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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