Full-spin-wave-scaled stochastic micromagnetism for mesh-independent simulations of ferromagnetic resonance and reversal

Harald Oezelt,Roy Chantrell,Luman Qu,Gergely T Zimanyi,Markus Gusenbauer,Alexander Kovacs,Dirk Praetorius,Masao Yano,Johann Fischbacher,Thomas Schrefl,Michael Winklhofer,Tetsuya Shoji,Roman Beigelbeck,Akira Kato

doi:10.1038/s41524-022-00719-5

Abstract

In this paper, we address the problem that standard stochastic Landau-Lifshitz-Gilbert (sLLG) simulations typically produce results that show unphysical mesh-size dependence. The root cause of this problem is that the effects of spin-wave fluctuations are ignored in sLLG. We propose to represent the effect of these fluctuations by a full-spin-wave-scaled stochastic LLG, or FUSSS LLG method. In FUSSS LLG, the intrinsic parameters of the sLLG simulations are first scaled by scaling factors that integrate out the spin-wave fluctuations up to the mesh size, and the sLLG simulation is then performed with these scaled parameters. We developed FUSSS LLG by studying the Ferromagnetic Resonance (FMR) in Nd2Fe14B cubes. The nominal scaling greatly reduced the mesh size dependence relative to sLLG. We then performed three tests and validations of our FUSSS LLG with this modified scaling. (1) We studied the same FMR but with magnetostatic fields included. (2) We simulated the total magnetization of the Nd2Fe14B cube. (3) We studied the effective, temperature- and sweeping rate-dependent coercive field of the cubes. In all three cases, we found that FUSSS LLG delivered essentially mesh-size-independent results, which tracked the theoretical expectations better than unscaled sLLG. Motivated by these successful validations, we propose that FUSSS LLG provides marked, qualitative progress towards accurate, high precision modeling of micromagnetics in hard, permanent magnets.

Highlights

Finite element micromagnetic modeling has been proven to be a reliable tool to describe many magnetic phenomena at finite temperatures
We carry out ferromagnetic resonance (FMR) simulations to critically test the developed full-spin-wave-scaled stochastic Landau–Lifshitz–Gilbert (sLLG) theory by checking whether it delivers results independent of the finite element mesh size
We addressed the problem that standard stochastic Landau–Lifshitz–Gilbert simulations typically produce results that show unphysical mesh-size dependence

Summary

Introduction

Finite element micromagnetic modeling has been proven to be a reliable tool to describe many magnetic phenomena at finite temperatures. The micromagnetic model utilizes a form of the Landau–Lifshitz–Gilbert (LLG) equation. The most popular approach to deal with thermal excitations in micromagnetics is to use a Landau–Lifshitz–Bloch (LLB) based equation[1,2] which combines the LLG equations for low temperatures and the Bloch equations for high temperatures. The magnetization reverses linearly by changing its length and orientation, a process which can be perfectly described using the LLB equation[3]. Constructing these parameters involves a considerable amount of effort, though, as it requires a multi-scale simulation approach including ab initio methods and atomistic simulations, typically necessitating additional assumptions and phenomenologies[4,5]

Methods

Results

Conclusion