Periodic phase diagrams in micromagnetics with an eigenvalue solver

TL;DR

This paper presents a novel eigenvalue solver-based method using Finite Element Analysis to compute periodic phase diagrams in micromagnetics, enabling detailed analysis of spin wave behavior in complex structures.

Contribution

It introduces a general eigenvalue-based approach for calculating periodic phase diagrams in 3D micromagnetic systems with various periodicities.

Findings

Allows calculation of dispersion diagrams for complex structures

Handles 1D, 2D, and 3D periodicities

Provides insights into spin wave propagation and resonances

Abstract

This work introduces an approach to compute periodic phase diagram of micromagnetic systems by solving a periodic linearized Landau-Lifshitz-Gilbert (LLG) equation using an eigenvalue solver with the Finite Element Method formalism. The linear operator in the eigenvalue problem is defined as a function of the periodic phase shift wave vector. The dispersion diagrams are obtained by solving the eigenvalue problem for complex eigen frequencies and corresponding eigen states for a range of prescribed wave vectors. The presented approach incorporates a calculation of the periodic effective field, including the exchange and magnetostatic field components. The approach is general in that it allows handling 3D problems with any 1D, 2D, and 3D periodicities. The ability to calculated periodic diagrams provides insights into the spin wave propagation and localized resonances in complex micromagnetic structures.