Green's-Function Theory of Ferrimagnetism, with an Application to Magnetite

Abstract

A Green's-function theory of magnetic properties of an $n$-sublattice ferrimagnet is derived in the random-phase approximation. The magnitude and relative orientation of the sublattice magnetizations, the renormalized magnon spectra, the zero-point motion and the Curie temperature as functions of the spin magnitudes, the exchange constants and the geometry are derived. These properties have been computed for magnetite. It is concluded that magnitudes of the exchange constant $J_{\mathrm{AB}}$ between sites of tetrahedral and octahedral coordination of about 2.5×${10}^{-3\mathrm{}}$ eV above 119°K, and about 1×${10}^{-3\mathrm{}}$ eV below that temperature, are consistent with present experimental data for magnetite.