Anomalous behavior of spin-wave resonances in ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{As}$ thin films

We report ferromagnetic and spin-wave resonance absorption measurements on high quality epitaxially grown ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{As}$ thin films. We find that these films exhibit robust ferromagnetic long-range order, based on the fact that up to seven resonances are detected at low temperatures, and the resonance structure survives to temperatures close to the ferromagnetic transition. On the other hand, we observe a spin-wave dispersion, which is linear in mode number, in qualitative contrast with the quadratic dispersion expected for homogeneous samples. We perform a detailed numerical analysis of the experimental data and provide analytical calculations to demonstrate that such a linear dispersion is incompatible with uniform magnetic parameters. Our theoretical analysis of the ferromagnetic resonance data, combined with the knowledge that strain-induced anisotropy is definitely present in these films, suggests that a spatially dependent magnetic anisotropy is the most likely reason behind the anomalous behavior observed.