On the existence conditions of surface spin wave modes in (Ga,Mn)As thin films

Spin-wave resonance (SWR) is a newly emerged method for studying surface magnetic anisotropy and surface spin-wave modes (SSWMs) in (Ga,Mn)As thin films. The existence of SSWMs in (Ga,Mn)As thin films has recently been reported in the literature; SSWMs have been observed in the in-plane configuration (with variable azimuth angle ${\varphi }_M$ between the in-plane magnetization of the film and the surface [100] crystal axis), in the azimuth angle range between two in-plane critical angles ${\varphi }_{c1}$ and ${\varphi }_{c2}$. We show here that cubic surface anisotropy is an essential factor determining the existence conditions of the above-mentioned SSWMs: conditions favorable for the occurrence of surface spin-wave modes in a (Ga,Mn)As thin film in the in-plane configuration are fulfilled for those azimuth orientations of the magnetization of the sample that lie around the hard axes of cubic magnetic anisotropy. This implies that a hard cubic anisotropy axis can be regarded in (Ga,Mn)As thin films as an easy axis for surface spin pinning.