VALIDITY OF THE FORCE THEOREM FOR MAGNETOCRYSTALLINE ANISOTROPY

The validity of the so-called force theorem is critical for the comput ational/theoretical determination of the magnetocrystalline anisotropy (MCA) in the framework of local density theory. This theorem states t hat the spin-orbit coupling induced MCA energy is given by the differe nce in the fully relativistic band energies between two magnetization directions calculated with the same self-consistent scalar-relativisti c potential. We show that the charge- and spin-density variations caus ed by spin-orbit coupling vanish to first order in the spin-orbit coup ling strength. By the stationary property of the total energy function al, we establish rigorously the validity of the force theorem for surf ace/interface MCA. We show that our arguments also apply to a variant of the MCA force theorem and discuss problems of applying the force th eorem for MCA in bulk systems with cubic crystalline symmetry.