Breathing Fermi surface model for noncollinear magnetization:: A generalization of the Gilbert equation

The breathing Fermi surface model which has been developed to describe the dissipative magnetization dynamics of collinear magnetization configurations is generalized to the case of noncollinear configurations. The theory is valid for small relative cantings of the atomic magnetic moments, and it is based on a phenomenological expansion of the ab initio density functional electron theory in atomic-sphere approximation for the spin direction. An equation of motion is obtained which looks like a Gilbert equation, with the important difference that Gilbert's damping constant is replaced by a damping matrix alpha_(R)({M-R}) which in general is different for the different atomic sites R and which depends on the momentary magnetization configuration {M-R} of the whole system, i.e., it is a strongly nonlocal equation.