Spin Wave Spectra of Magnetite

Expressions for spin wave energies in normal and inverse spinel have been obtained which are exact to all orders in the spin wave momentum. These dispersion curves have been compared with existing experimental data on magnetite and good agreement found if the principal exchange interaction is taken to be 2.4×{}10^-3 eV. The surprisingly small range of validity of the usual k² approximation is pointed out and possible effects of the deviation from k² behavior on the magnetic part of the heat capacity are discussed. The small (like-like) exchange interactions have been included (also to all orders in the spin-wave momentum) with the most important result that agreement with the experimental dispersion curves is improved.