Multiscale method for Heisenberg spin simulations

A multiscale method that couples classical Heisenberg model to micromagnetics in a unified formalism is presented. It is based on a multiresolution adaptive finite difference mesh, which ensures significant reduction of the number of variables and computation time with respect to either atomistic or micromagnetic simulations, together with a precise description of the modeled system where necessary. The hierarchical structure of the mesh is used to compute efficiently the dipolar field by means of a fast multipole method. The underlying atomistic approach is particularly useful to handle magnetic singularities and describe structural defects. The method is applied here to the case of a magnetic vortex and a thin layer of FePt with a microtwin. Results are compared to fully atomistic and micromagnetic simulations when possible.