Micromagnetic frequency-domain simulation methods for magnonic systems

TL;DR

This paper introduces efficient numerical methods for simulating magnetization oscillations in 3D micromagnetic systems, enabling large-scale analysis of magnonic devices with high computational efficiency.

Contribution

The paper develops novel frequency-domain algorithms for micromagnetic simulations, including eigenmode computation and response analysis, applicable to complex nanomagnet geometries.

Findings

Effective algorithms for eigenmode calculation demonstrated.

Fast frequency response evaluation techniques introduced.

Applicability to large-scale magnonic systems shown.

Abstract

We present efficient numerical methods for the simulation of small magnetization oscillations in three-dimensional micromagnetic systems. Magnetization dynamics is described by the Landau-Lifshitz-Gilbert (LLG) equation, linearized in the frequency domain around a generic equilibrium configuration, and formulated in a special operator form that allows leveraging large-scale techniques commonly used to evaluate the effective field in time-domain micromagnetic simulations. By using this formulation, we derive numerical algorithms to compute the free magnetization oscillations (i.e., spin wave eigenmodes) as well as magnetization oscillations driven by ac radio-frequency fields for arbitrarily shaped nanomagnets. Moreover, semi-analytical perturbation techniques based on the computation of a reduced set of eigenmodes are provided for fast evaluation of magnetization frequency response and absorption spectra as a function of damping and ac field. We present both finite difference and finite element implementations and demonstrate their effectiveness on a test case. These techniques open the possibility to study generic magnonic systems discretized with several hundred thousand (or even millions) of computational cells in a reasonably short time.