Coupled Micromagnetic-Electromagnetic Solvers with Truncated Boundaries

Magnetization dynamics in nano- and micro-scale magnetic materials and devices is governed by the Landau-Lifshitz-Gilbert (LLG) equation. This equation links magnetization dynamics to torques arising from various physical interactions, including electromagnetic effects influenced by magnetic field time variations. At low frequencies, these effects are approximated by magnetostatics, but at higher frequencies and device sizes, electrodynamic effects, such as eddy currents, become significant. Dynamic magnetic fields are determined using dynamic Maxwell's equations. Methods to solve Maxwell's equations for eddy current issues include Finite Element Method (FEM) and integral equation-based techniques. Challenges in developing efficient solvers involve computational domain truncation, efficient time stepping, and coupling Maxwell's with LLG equations.