Accurate finite-difference micromagnetics of magnets including RKKY interaction -- analytical solution and comparison to standard micromagnetic codes

TL;DR

This paper emphasizes the importance of precise RKKY interaction implementations in micromagnetics, introduces a benchmark with an analytical solution, and demonstrates that higher-order finite-difference methods significantly improve accuracy over standard codes.

Contribution

It develops a benchmark problem with an analytical solution for RKKY interactions and introduces higher-order finite-difference methods that greatly enhance accuracy in micromagnetic simulations.

Findings

Standard implementations have over 20% error in saturation field at 2 nm mesh size.

Higher-order finite-difference methods reduce error to about 2%.

Benchmark results highlight the need for improved numerical schemes.

Abstract

Within this paper we show the importance of accurate implementations of the RKKY interactions for antiferromagnetically coupled ferromagnetic layers with thicknesses exceeding the exchange length. In order to evaluate the performance of different implementations of RKKY interaction, we develop a benchmark problem by deriving the analytical formula for the saturation field of two infinitely thick magnetic layers that are antiparallelly coupled. This benchmark problem shows that state-of-the-art implementations in commonly used finite-difference codes lead to errors of the saturation field that amount to more than 20% for mesh sizes of 2 nm which is well below the exchange length of the material. In order to improve the accuracy, we develop higher order cell based and nodal based finite-difference codes that significantly reduce the error compared to state-of-the-art implementations. For the second order cell based and first order nodal based finite element approach the error of the saturation field is reduced by about a factor of 10 (2% error) for the same mesh size of 2 nm.