Dynamic domain model for magnetic thin films

A domain model for computing magnetization dynamics in small (≈100 μm) patterned, magnetically soft thin films is described. The magnetization distribution of the film is modeled by a dynamic grid of contiguous polygonal domains with uniform in-plane magnetization. Dynamic variables for this system include both the magnetization directions and the domain wall positions (i.e. domain vertex locations) of each domain. The formulation of the model is motivated in part by the analogy to a nonlinear system of coupled, viscously damped oscillators with geometrically constrained motion. The equations of motion for the magnetic system are obtained via methods of Lagrangian mechanics and solved numerically by computer. The model is demonstrated on the computation of the frequency-dependent permeability in narrow Permalloy stripes. Also included are results on flux propagation in film geometries resembling those typical of inductive thin-film head poles. Predictions obtained are compared with other experimental and theoretical results