Simulating micromagnetism

Abstract

We present an introductory review of concepts behind micromagnetic simulations, in which magnetic moments representing collections of atomic spins within a material evolve according to the Landau-Lifshitz-Gilbert equation, a generalized torque equation. This evolution is determined by a variety of interactions, including those arising from external fields, magnetostatic and exchange effects, and magnetic anisotropy. Anisotropy is a key ingredient in the Stoner-Wohlfarth model, which provides a quantitative basis for understanding magnetic hysteresis. In turn, hysteresis loops provide a basis for comparing simulations and experiments, and are important, for example, in quantifying the heating response of a sample to an oscillating external magnetic field. Micromagnetic simulations bear conceptual similarity to molecular dynamics (MD) simulations, but whereas in MD classical potentials are used to naturally model interactions between atoms and/or molecules, the choice of modelling length scale in micromagnetics is less obvious. If effective interactions are determined for, say, two crystallographic unit cells of a material, how interaction parameters should scale with micromagnetic simulation cell size, particularly at finite temperature, is still an area of research. Finally, we discuss the coupling of magnetic and mechanical degrees of freedom in simulating atomic and nanoparticle systems. This review is based, in part, on our own experience in modelling hysteretic heating of magnetite nanoparticles.

Keywords

• Micromagnetic simulations
• Landau-Lifshitz-Gilbert equation
• magnetic hysteresis
• magnetic nanoparticles