Ferromagnetic resonance in thin films studied via cross-validation of numerical solutions of the Smit-Beljers equation: Application to (Ga,Mn)As

The 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 widespread conviction in the literature that only the 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 the SB-CV approach.