Temperature Dependence of Anisotropy Energy in Antiferromagnets

The Akulov-Zener classical theory of the temperature dependence of ferromagnetic anisotropy energy is extended to the antiferromagnetic case. The result, for short-range interactions only, is that $\frac{K_n\mathrm{}\left(T\right)\mathrm{}}{K_n\mathrm{}\left(0\right)\mathrm{}}={\left[\frac{M\left(T\right)\mathrm{}}{M\left(0\right)\mathrm{}}\right]}^{\frac{n(n+1\mathrm{})\mathrm{}}{2}},$ where $K_n\mathrm{}\left(T\right)\mathrm{}$ is the $n\mathrm{th}$ order anisotropy constant and $M\left(T\right)\mathrm{}$ is the sublattice magnetization. Here, $K_n\mathrm{}\left(0\right)\mathrm{}$ and $M\left(0\right)\mathrm{}$ refer to the corresponding quantities at absolute zero. The result is verified by a spin-wave calculation.