Zener double exchange from local valence fluctuations in magnetite

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 $T_V=122$ 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 ($\sim$80 meV) are shifted upwards in energy above $T_V$ due to the occurrence of B-B ferromagnetic double exchange in the mixed valent metallic phase. The double exchange interaction affects only spin waves of ${\mathrm{\Delta }}_5$ symmetry, not all modes, indicating that valence fluctuations are slow and the double exchange is constrained by electron correlations above $T_V$.