Short-Range Order Effect on the Magnetic Anisotropy near the Transition Point

Abstract

The temperature dependence of the magnetic anisotropy with tetragonal symmetry is studied classically for antiferromagnets near $T_N$, by developing a refined statistical theory. It appears that the magnetic anisotropy has a singularity of ${(T-T_N)}^{-\frac{1}{2}}$, where $T_N$ denotes the Néel point to be determined from the exchange energy. Because the actual Néel point ${T_N}^{*}$ shifts from $T_N$ to the higher temperature by $T_A$ which is proportional to the anisotropy constant, the magnetic anisotropy at ${T_N}^{*}$ remains finite with an estimate of $\sim {\left(\frac{T_A}{T_N}\right)}^{\frac{1}{2}}$ times the powder susceptibility at ${T_N}^{*}$. The theoretical results are in good agreement with the experiments made by Stout et al. The other short-range order effects are also discussed. Especially, the theory predicts that the peak of the powder susceptibility appears above $T_N$, in agreement with the measment. In the course of the treatment, $\varphi \mathrm{}\left(x\right)=\frac{1}{{\left(2\mathrm{}\pi \right)}^3}\int \stackrel{\pi }{-\pi }\frac{d{k}_{1}d{k}_{2}d{k}_3}{1-x{cos}^2\left(\frac{k_1}{2}\right){cos}^2\left(\frac{k_2}{2}\right){cos}^2\left(\frac{k_3}{2}\right)}$ and its derivative, which play an important role in the present theory, are plotted for $0\leqq x\leqq 1$.