Full-Spin-Wave-Scaled Finite Element Stochastic Micromagnetism: Mesh-Independent FUSSS LLG Simulations of Ferromagnetic Resonance and Reversal

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-Spinwave-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 Nd$_2$Fe$_{14}$B cubes. The nominal scaling greatly reduced the mesh size dependence relative to sLLG. We further discovered that adjusting one scaling exponent by less than 10% delivered fully mesh-size-independent results for the FMR peak. 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 Nd$_2$Fe$_{14}$B 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.