Mapping Surface Anisotropies In Ferromagnetic (Ga,Mn) As Films

Ferromagnetic semiconductor (Ga,Mn)As has emerged as the most thoroughly studied material for spintronic applications [1]. An important property of this ferromagnetic material is its magnetic anisotropy [2]. However, the origins of this anisotropy have not yet been entirely explained. Full understanding of magnetic anisotropy in (Ga,Mn)As is especially important for its use in prospective applications as memory devices, and is being intensively investigated by various experimental techniques, such as ferromagnetic resonance (FMR) and spin-wave resonance (SWR) [3]. Most of these methods have been used to obtain information on volume characteristics of this material, such as bulk anisotropy fields and exchange constants. Recently, it has also been proposed [4] that one can employ the full potential of SWR to probe information on magnetic characteristics of the surface, such as surface anisotropy and surface pinning energy, and their dependence on the orientation of magnetization in the material. Our early attempts [5] have successfully determined the surface pinning parameters of (Ga,Mn)As from SWR spectra using the surface inhomogeneity model [6, 7] obtained for different angular configurations $( theta_{H}, varphi _{H})$ of the external static magnetic field $mathrm{H}_{dc}$ with respect to the surface of the studied (Ga,Mn)As thin film. Although the obtained surface pinning parameter $A$ as a function of the field (or magnetization) polar and azimuthal angles was obtained in only limited ranges of both angles, these results have stimulated fruitful theoretical discussion and insight [8, 9]. Recent theoretical development in this area [4] focuses 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 $theta$ and the in-plane azimuthal angle $varphi )$. The model is based on a series expansion of the surface spin pinning energy, where the terms in the series represent respective pinning contributions from the cubic as well as the uniaxial anisotropies. In particular, the model has predicted the existence of double critical polar angle phenomenon in SWR measurements performed in specific out-of-plane configurations, not been observed in earlier studies. Stimulated by these predictions, we have conducted detailed SWR measurements on a 120 nm thick annealed Ga 0.92 Mn 0.08 As film. SWR measurements were carried out using three basic geometries. In Geometry 1, the [110] edge of the specimen was oriented vertically. This configuration allows measurements with the dc field in any arbitrary direction in the (110) crystal plane, from,[110] to [001]. In Geometry 2, the sample was mounted with the [1–10] edge of the specimen oriented vertically. This configuration allows measurements with the dc field in any arbitrary direction in the (1–10) plane, from [001] to [110]. In Geometry 3, the sample was mounted with the [010] edge of the film oriented vertically. This configuration allows measurements with the dc field in any arbitrary direction in the (010) plane, from [100] to [001]. In Fig. 1, the spectrum clearly evolves as the applied field $mathrm{H}_{dc}$ is rotated from the out-of-plane orientation $( theta _{H} quad = 0 ^{circ})$ to the in-plane orientation $( theta _{H} quad = 90 ^{circ}, varphi_{H} quad = - 45 ^{circ})$. In particular, for $mathrm{H}vert vert $ [001] a resonance spectrum consists of at least five well resolved Portis-type SWR lines. As one rotates H away from the perpendicular orientation, the SWR modes successively disappear, and eventually -- at some critical angle $theta _{c}( 24 ^{circ}$ in Fig. 1) - the multi-SW spectrum vanishes except for a single narrow resonance line, which corresponds to the uniform FMR mode. For angles $theta _{H} u003e theta _{c}$, the multi-mode nature of the SW spectrum re-emerges, generally containing two or three broad resonances. The spectra obtained in Geometry 2 are similar to those shown in Fig. 1. As predicted in Ref. [4], the spectra obtained in Geometry 3 show a new phenomenon: here we observe two critical angles $( 20 ^{circ}$ and 38° in Fig. 2). Specifically, as one rotates H away from the perpendicular orientation, the SWR modes disappear at the first critical angle $theta _{c1}$. As $theta _{H}$ increases, the multi-mode nature of the SW spectrum re-emerges; the peak on the highfield side is identified as an exchange-dominated non-propagating surface mode. However, at the second critical angle $theta _{c2}$, the multi-SW spectrum again vanishes, collapsing to a single narrow resonance line. For angles $theta _{H} u003e theta _{c} ( i.e.,$ as one approaches the easy axis, $mathrm{H}vert vert$ [100]), the spectrum consists of at least three SWR lines, which are believed to be bulk modes. In summary, we have observed the double polar critical angle phenomenon in SWR, as predicted from the recent theoretical model for specific experimental configurations. This observation verifies the surface pinning model of SWR, thus bringing new insights to surface anisotropy phenomena in (Ga,Mn)As thin films, and providing new information relevant to spintronic applications.