Magnetic anisotropy of transition-metal impurities in metallic hosts

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Abstract
We show that transition-metal impurities in metallic hosts, which have a high crystalline symmetry, can have appreciable anisotropic magnetic moments and the anisotropy may change sign on varying the transition-metal impurity. Our basic model is a spherically symmetric Friedel-Anderson model, with orbital degeneracy and Hund's-rule couplings. We treat this model in a way which is appropriate to the situation in which an appreciable mixture of ionic configurations exists in the ground state of the impurity. We calculate, in the Hartree-Fock approximation, the effect of the crystalline field and the spin-orbit coupling. The crystalline field acts, in a manner, to quench any orbital magnetic moment present. The spin-orbit interaction is responsible for the reappearance of the orbital magnetic moment, and is, thus, the source of the anisotropic magnetization. We calculate the orbital magnetization induced by the spin-orbit coupling, and the anisotropy energy is calculated to second order in the spin-orbit coupling. We show that the model is capable of generating changes in the sign of the anisotropy energy, as has been observed by the low-field-magnetization measurements on very dilute ZnMn and ZnCr alloys.