Tensorial character of magnetization diffusion in periodic lattices

Averaged Bloch equations for magnetization evolution in a biphasic heterogeneous material with periodic structures are derived using a two-scale asymptotic expansion. Upscaling of the partial differential equations with microscopic boundary conditions results in equations of motion for the magnetization vector that are functionally similar to the Bloch equations, but without microscopic boundaries, and with a tensorial term describing effective diffusion behavior. In the process we obtain a prescription for calculating individual components of the diffusion tensor by solving an auxiliary boundary-valued problem on the microscopic unit cell. This allows, in particular, numerical calculations of the diffusion tensor for arbitrary geometries of the unit cellin a reasonable computing time.