Pseudodipolar Anisotropy in Cubic Ferromagnets at Low Temperatures

The first order anisotropy constant, $K_1$, of a cubic ferromagnet with spin ½ per atom is calculated as a function of temperature at low temperatures. The source of this anisotropy is taken to be the nearest neighbor pseudodipolar spin-spin interaction and the spin-wave approach of Dyson is used. It is shown that $K_1$ varies as the tenth power of the magnetization, itself a function of the temperature. In order to explain the experimental value of $K_1$ for nickel at $T=0\mathrm{}$ the strength of the dipolar interaction must be ∼300 times the classical value. Previous calculations by Van Vleck, Van Peipe, and Tessman are compared with the present work on the ground state. Only the work of Van Peipe accounts properly for the exchange and is in complete agreement with the present investigation. The perturbation scheme of Van Peipe is shown to be rigorously correct, the wave function converging to an exponential form.