Ferromagnetic resonance investigation of magnetic anisotropy in ${\text{Ga}}_{1-x}{\text{Mn}}_x\text{As}$ synthesized by ion implantation and pulsed laser melting

A systematic investigation of ferromagnetic resonance (FMR) was carried out on ${\text{Ga}}_{1-x}{\text{Mn}}_x\text{As}$ layers synthesized by Mn ion implantation into GaAs followed by pulsed laser melting. Angular and temperature dependences of FMR were measured on layers prepared on GaAs (001), (110), and (311) surfaces. The observed angular dependence of FMR can be understood in terms of contributions from cubic anisotropy fields defined by the crystal symmetry of ${\text{Ga}}_{1-x}{\text{Mn}}_x\text{As}$ and uniaxial anisotropy fields perpendicular or parallel to the film plane. For completeness, the angular dependence of the FMR linewidth was also investigated and was found to be dominated by broadening ascribed to local inhomogeneities in magnetic anisotropy. Our results show that both the magnetic anisotropy and the FMR linewidth in (Ga,Mn)As prepared by ion implantation are similar to those observed on ${\text{Ga}}_{1-x}{\text{Mn}}_x\text{As}$ samples grown by low-temperature molecular beam epitaxy, indicating that the two very different growth methods lead to materials with fundamentally similar magnetic properties.

Figure 1

(Color online) Four experimental configurations used in the present study. For the (001) sample (sample A) the orientation of the dc magnetic field $\mathbf{H}$ can be varied in the $\left(\overline{1}10\right)$, (110), (010), and (001) planes (setups 1, 2, 3, and 4); for the (110) sample (sample B) the orientation of $\mathbf{H}$ can be varied in the $\left(1\overline{12}\right)$, $\left(1\overline{1}1\right)$, and (110) planes (setups 5, 6, and 7); and for the (311) sample [sample C] the $\mathbf{H}$ orientation can be varied in the $\left(0\overline{1}1\right)$, $\left(2\overline{3}3\right)$, and (311) planes (setups 8, 9, and 10). Crystal orientations for the (311)B sample (sample D) are as for setups 8, 9, and 10, but with Miller index signs in the horizontal plane reversed.

Figure 2

(Color online) Coordinate systems used in this paper. The orientation of the dc applied magnetic field $\mathbf{H}$ is described by ${\theta }_H$, ${\phi }_H$. The resulting equilibrium orientation of the magnetization $\mathbf{M}$ is given by $\left(\theta ,\phi \right)$. From left to right: the (001) sample (sample A); the (110) sample (sample B); and the (311)A sample (sample C).

Figure 3

(Color online) Selected FMR spectra for sample A taken at 4 K from ${\theta }_H=0°$ to $180°$, with $\mathbf{H}$ in the $\left(\overline{1}10\right)$ plane (setup 1).

Figure 4

(Color online) Angular dependence of the FMR field observed at 4 K for sample A grown on (001) plane, including all setups for that plane as shown in Fig. 1. Points are experimental; solid curves are theoretical fits.

Figure 5

(Color online) Temperature dependence of the cubic anisotropy field $H_4$ and uniaxial anisotropy fields $H_{eff}$ and $H_{2\parallel }$ for sample A.

Figure 6

(Color online) Selected FMR spectra for sample B taken at 4 K for ${\theta }_H$ from $0°$ to $180°$, with $\mathbf{H}$ in the $\left(1\overline{12}\right)$ plane (setup 5).

Figure 7

(Color online) Angular dependence of FMR for sample B at 4.0 K observed in setup 5 (field rotated in the $\left(1\overline{12}\right)$ plane), setup 6 (field rotated in the $\left(1\overline{11}\right)$ plane), and setup 7 [field in the (110) plane]. Points are experimental; solid curves are best theoretical fits; dotted curves represent theoretical fits with $H_{4\perp }=H_{4\parallel }$.

Figure 8

(Color online) Selected FMR spectra for samples C and D taken at 4 K for ${\theta }_H$ from $0°$ to $180°$, with $\mathbf{H}$ in the $\left(0\overline{1}1\right)$ plane (setup 8).

Figure 9

(Color online) Angular dependence of FMR for sample D observed at 4 K in setups 8, 9, and 10. Points are experimental; solid curves are theoretical fits.

Figure 10

(Color online) Temperature dependence of the cubic magnetic anisotropy field $H_4$ and the effective uniaxial magnetic anisotropy field $H_{eff}$ for samples C and D.

Figure 11

(Color online) Angular dependence of FMR linewidth for sample A at 4.0 K observed in four setups corresponding to the (001) plane geometry of this sample. Points are experimental; continuous curves are best theoretical fits for each setup obtained using Eq. (6).

Figure 12

(Color online) Angular dependence of FMR line width at 4.0 K for sample D observed in setups 8 to 10. Points are experimental; solid curves are guides for the eye.