Temperature Dependence of the Resonance Frequency of Ferrimagnets and Antiferromagnets

A spin-wave calculation of the temperature dependence of the resonance frequency of a two-sublattice ferrimagnet leads to a modification of the macroscopic result at low temperatures which may be conveniently represented by a temperature-dependent Weiss field parameter $\lambda \mathrm{}\left(T\right)={\lambda }_W{\left(\frac{{\gamma }_2{M}_1\mathrm{}\left(0\right)+{\gamma }_1{M}_2\mathrm{}\left(0\right)\mathrm{}}{{\gamma }_2{M}_1\mathrm{}\left(T\right)+{\gamma }_1{M}_2\mathrm{}\left(T\right)\mathrm{}}\right)}^{\frac{1}{2}}.$ The analysis for the antiferromagnet is consistent with the Kanamori-Tachiki semiphenomeno-logical spin-wave theory. The complete Nagamiya-Keffer-Kittel formula is recovered provided that ${\chi }_{\perp }$ takes the value predicted by linear spin-wave theory rather than molecular field theory.