Anisotropy Energy in MnF2at Low Temperatures

The anisotropy energy in Mn${\mathrm{F}}_2$ is calculated by a spin-wave method. The magnetic dipole interactions and the interactions of individual ions with their surrounding crystalline fields give the anisotropy energy of -4.9×${10}^6$ erg/cc at 0°K. The experimental value extrapolated to 0°K by Foner is -5.0×${10}^6$ erg/cc. The temperature dependence of the anisotropy energy is obtained as $\frac{E_{\mathrm{an}}\mathrm{}\left(T\right)\mathrm{}}{E_{\mathrm{an}}\mathrm{}\left(0\right)\mathrm{}}={\left[\frac{M\left(T\right)\mathrm{}}{M\left(0\right)\mathrm{}}\right]}^{2.9}$, where $E_{\mathrm{an}}\mathrm{}\left(T\right)\mathrm{}$, $M\left(T\right)\mathrm{}$ are the anisotropy energy and the magnetization of the sublattice at $T°$K, respectively, and $E_{\mathrm{an}}\mathrm{}\left(0\right)\mathrm{}$, $M\left(0\right)\mathrm{}$ are the corresponding values at 0°K.