Spin-wave resonances and surface spin pinning in ${\text{Ga}}_{1-x}{\text{Mn}}_x\text{As}$ thin films

We investigate the dependence of the spin-wave resonance (SWR) spectra of ${\text{Ga}}_{0.95}{\text{Mn}}_{0.05}\text{As}$ thin films on the sample treatment. We find that for the external magnetic field perpendicular to the film plane, the SWR spectrum of the as-grown thin films and the changes upon etching and short-term hydrogenation can be quantitatively explained via a linear gradient in the uniaxial magnetic anisotropy field in growth direction. The model also qualitatively explains the SWR spectra observed for the in-plane easy-axis orientation of the external magnetic field. Furthermore, we observe a change in the effective surface spin pinning of the partially hydrogenated sample, which results from the tail in the hydrogen-diffusion profile. The latter leads to a rapidly changing hole concentration/magnetic anisotropy profile acting as a barrier for the spin-wave excitations. Therefore, short-term hydrogenation constitutes a simple method to efficiently manipulate the surface spin pinning.

Figure 1

FMR spectra at 5 K with the external magnetic field oriented perpendicular to the film plane of ${\text{Ga}}_{0.95}{\text{Mn}}_{0.05}\text{As}$ thin films etched to different thicknesses in a 38:1:1 by volume solution of ${\text{H}}_2\text{O}$, ${\text{H}}_2{\text{O}}_2$, and ${\text{H}}_3{\text{PO}}_4$. For clarity, the individual spectra are shifted vertically.

Figure 2

(a) Uniform resonance field profile ${\mu }_0{H}_{\text{un}}^{001}\left(z\right)$ used for the simulation of the SWR spectrum of the partially hydrogenated sample. The profile is subdivided into several regions: (0) $0<z<z_0$, fully passivated, ferromagnetism suppressed; (i) $z_0<z<z_{\text{I}}$, partially passivated, ${\mu }_0{H}_{\text{un}}^{001}\left(z\right)={\mu }_0{H}_{\text{un},\text{I}}^{001}$, (II) $z_{\text{I}}<z<z_{\text{II}}$, linear gradient ${\mu }_0{H}_{\text{un}}^{001}\left(z\right)=\omega /\gamma -\left[G\left(z-z_{\text{I}}\right)+C\right]$; and (III) $z_{\text{II}}<z<z_{\text{III}}$, ${\mu }_0{H}_{\text{un}}^{001}\left(z\right)={\mu }_0{H}_{\text{un},\text{III}}^{001}$. In the case of an etched sample the thickness of region 0 corresponds to the etch depth and the thickness of region I, $L_{\text{I}}=0$. (b) Schematic hydrogenation profile used to account for the profile of the uniform resonance field in (a).

Figure 3

(Color online) Experimental (full curves) and simulated (dashed curves) SWR spectra for $\vec{H}\parallel \left[001\right]$ perpendicular to the film plane of (a) the as-grown, (d) the etched, and (g) the partially hydrogenated samples. In (b), (e), and (h) the pairs of effective wave vectors $\left\{l^2{k}_{n,\text{II}}^2\left(z_{\text{I}}\right),l^2{k}_{n,\text{II}}^2\left(z_{\text{II}}\right)\right\}$ fulfilling the boundary condition of natural freedom for the ${\mu }_0{H}_{\text{un}}^{001}\left(z\right)$ profiles displayed as thick solid black lines in (c), (f), and (i), respectively, are represented by the set of curves $A_n$. The straight diagonal line in (b), (e), and (h) represents restriction (23) additionally imposed by the linear gradient in $H_{\text{aniso}}^{001}\left(z\right)$. From the intersection points the solutions of the spin wave equation [Eq. (6)] are derived with the spin-wave excitations ${\tilde{m}}_n\left(z\right)$ plotted at the positions of the corresponding resonance field ${\mu }_0{H}_{\text{res},n}$ indicated by thin dashed lines in (c), (f), and (i).

Figure 4

(Color online) Experimental (full curves) and simulated (dashed curves) SWR spectra for $\vec{H}\parallel \left[010\right]$ within the film plane of (a) the as-grown, (d) the etched, and (g) the partially hydrogenated samples. The straight vertical lines point out the SWR spacing of the simulated spectra. For better comparison with the experimental data they are also shown shifted horizontally. In (b), (e), and (h) the pairs of effective wave vectors $\left\{l^2{k}_{n,\text{II}}^2\left(z_{\text{I}}\right),l^2{k}_{n,\text{II}}^2\left(z_{\text{II}}\right)\right\}$ fulfilling the boundary condition of natural freedom for the ${\mu }_0{H}_{\text{un}}^{001}\left(z\right)$ profiles displayed as thick solid black lines in (c), (f), and (i), respectively, are represented by the set of curves $A_n$. The straight vertical line in (b), (e), and (h) represents restriction (23) additionally imposed by the linear gradient in $H_{\text{aniso}}^{001}\left(z\right)$. From the intersection points the solutions of the spin wave equation [Eq. (28)] are derived with the spin-wave excitations ${\tilde{m}}_n\left(z\right)$ plotted at the positions of the corresponding resonance field ${\mu }_0{H}_{\text{res},n}$ indicated by thin dashed lines in (c), (f), and (i).

Figure 5

(a) In-plane SWR spectra for $\vec{H}\parallel \left[0\overline{1}1\right]$ and (b) $\vec{H}\parallel \left[010\right]$. Both upon etching and hydrogenation the main resonance shifts to higher (lower) fields for $\vec{H}\parallel \left[0\overline{1}1\right]$ $\left(\vec{H}\parallel \left[010\right]\right)$, indicating an increase in the in-plane cubic anisotropy field ${\mu }_0{H}_{c1}^{\parallel }\left(z\right)$ from the surface to the film-substrate interface.