Magnetization and exchange in nonstoichiometric magnetite

Measurements of saturation magnetization and remanence in ${\mathrm{Fe}}_{3\left(1\mathrm{-}\mathrm{\delta }\right)}$ ${\mathrm{O}}_4$ single crystals with (0.000 ${\mathit{J}}_{\mathit{A}\mathit{B}}$, evaluated with spin-wave theory in the harmonic approximation, agree with those derived from low-temperature heat-capacity investigations. A discontinuous change in behavior for δ>0.0039 is consistent with the change from a first- to second-order Verwey transition, associated wtih splitting of the octahedral electronic levels. A self-reversal of the remanent moment is observed at ${\mathit{T}}_{\mathit{V}}$, in the second-order regime. Simple nearest-neighbor models, in the mean-field approximation, suffice to account for all electronic and magnetic critical temperatures, in the Ising two-state and Heisenberg formulations, respectively.