Coarse-graining Landau-Lifshitz damping

High speed switching in magnetic materials is usually studied with the Landau-Lifshitz (LL) equation, which describes damping through a phenomenological coefficient. The results of micromagnetic calculations based on the LL equation have been observed to depend strongly on the cell size. We take a coarse-graining or renormalization-group approach to this cell size dependence: from a simulation using cell size L, we look at the dynamics of a cell of size 2L and determine an effective damping coefficient that describes the larger-scale dynamics. This can be thought of as a Green-Kubo calculation of the effective damping coefficient. In principle, this makes it possible to coarse grain from the atomic scale to determine the micromagnetic damping coefficient. (C) 2001 American Institute of Physics.