Spin-wave resonance as a tool for probing surface anisotropies in ferromagnetic thin films: Application to the study of (Ga,Mn)As

In this paper we provide a concise review of present achievements in the study of spin-wave resonance (SWR) in ferromagnetic semiconductor (Ga,Mn)As thin films. The theoretical treatment of the experimental SWR data obtained so far concentrates specifically on the spherical surface pinning (SSP) model, in which the surface spin pinning energy is expressed by configuration angles (the out-of-plane polar angle $\vartheta$ and the in-plane azimuthal angle $\phi$) defining the direction of surface magnetization in the considered thin film. The model is based on a series expansion of the surface spin pinning energy; the terms in the series represent the respective pinning contributions from the cubic anisotropy as well as uniaxial anisotropies. Comparing theory with the reported experimental studies of SWR in thin films of the ferromagnetic semiconductor (Ga,Mn)As, we find that besides the first-order cubic anisotropy, higher-order cubic anisotropies (in the second and third orders) as well as uniaxial anisotropies (perpendicular in the first and second orders, and in-plane diagonal) occur on the surface of this material. We use our results to plot a 3D hypersurface visualizing the angle dependence of the surface spin pinning energy in configurational space. An advantage of this spatial representation is that the shape of the obtained hypersurface allows us to predict new SWR effects that have not yet been observed experimentally. Prospective experimental studies for the verification of this surface pinning model would bring new insight into the surface anisotropy phenomenon in (Ga,Mn)As thin films and help complete the knowledge in this field, the shortage of which in the literature available to date is becoming bothersome.