Ferromagnetic resonance in thin films - cross-validation analysis of numerical solutions of Smit-Beljers equation. Application to GaMnAs

TL;DR

This paper introduces a numerical analysis method for ferromagnetic resonance spectra in thin films, applying cross-validation to interpret experimental data and determine higher-order anisotropy constants in GaMnAs, challenging previous assumptions.

Contribution

It develops a novel numerical and statistical approach combining Smit-Beljers solutions with cross-validation to analyze FMR spectra in thin films, revealing the importance of higher-order anisotropy terms.

Findings

Higher-order cubic anisotropy terms are necessary for accurate FMR modeling.

Numerical values of higher-order anisotropy constants are provided.

Contradicts previous literature by emphasizing the significance of fourth-order terms.

Abstract

(Dated: August 3, 2018) The new method of numerical analysis of experimental ferromagnetic resonance (FMR) spectra in thin films is developed and applied to (Ga,Mn)As thin films. Specifically, it starts with the finding of numerical solutions of Smit-Beljers (SB) equation and continues with their subsequent statistical analysis within the cross-validation (CV) approach taken from machine learning techniques. As a result of this treatment, we are able to reinterpret the available FMR experimental results in diluted ferromagnetic semiconductor (Ga,Mn)As thin films with the resulting determination of magnetocrystalline anisotropy constants. The outcome of CV analysis points out that it is necessary to take into account terms describing the bulk cubic anisotropy up to the fourth order to reproduce FMR experimental results for (Ga,Mn)As correctly. This finding contradicts the wide-spread conviction in the literature that only first order cubic anisotropy term is important in this material. We also provide numerical values of these higher order cubic anisotropy constants for (Ga,Mn)As thin films resulting from SB-CV approach.