Temperature Dependence of Ferromagnetic Anisotropy in Cubic Crystals

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Abstract
Two theories of the temperature dependence of ferromagnetic anisotropy in cubic crystals, the nearestneighbor quadrupole-quadrupole coupling theory of Van Vleck, and the more recent classical theory of Zener, seem to be contradictory. It is shown that these theories are, respectively, high- and low-temperature approximations to the same physical picture: namely, an anisotropy which decreases with rising temperature due to statistical fluctuations from alignment of anisotropically-coupled neighbor spins. Zener's low-temperature approximation shows that the anisotropy decreases as the tenth power of the magnetization, Van Vleck's high-temperature approximation yields a lower power law. It is argued that most of the anisotropy has vanished before sufficiently high temperatures are reached for Van Vleck's approximation to be appropriate. Van Vleck's nearest-neighbor dipole-dipole coupling theory, which has no classical analog and cannot be compared with Zener's theory, is discussed from a spin-wave picture.