Periodic Phase Diagrams in Micromagnetics With an Eigenvalue Solver

This work introduces an approach to compute the 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 (FEM) 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 eigenfrequencies and corresponding eigenstates 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 3-D problems to be handled with any 1-D, 2-D, and 3-D periodicities. The ability to calculate periodic diagrams provides insights into the spin wave propagation and localized resonances in complex micromagnetic structures.