Theory of Ferromagnetic Anisotropy

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Abstract
By means of a virial theorem and perturbation theory, the anisotropy energy of a ferromagnetic crystal is expressed in terms of the Coulomb energy alone. This latter energy is approximated by a multipole expansion and the anisotropy constants are given in terms of electric multipole moments and crystallinepotential constants. The multipole moments, which arise from the orbital angular momentum induced by spin-orbit coupling, have been estimated from the known values of angular momentum. The method avoids explicitly carrying out high-order perturbations, and furnishes a physical interpretation of the anisotropy mechanism without the use of phenomenological couplings. In most cases, the principal mechanism leading to anisotropy is found to be different from those considered by Van Vleck.