Spin wave resonance in Ga1−xMnxAs

We report ferromagnetic resonance experiments on ${\mathrm{Ga}}_{\text{1−x}}{\mathrm{Mn}}_x\mathrm{As}$ thin films. For the dc magnetic field perpendicular to the sample plane, we observe up to eight distinct resonances, which we attribute to spin wave modes. To account for the spacing of the resonances, we infer a linear gradient in the magnetic properties, which is ascribed to a linear variation of the uniaxial magnetic anisotropy with film thickness. Values of ${\text{D=(1±0.4)×10}}^{\text{−9}}\hspace{0.17em}{\mathrm{Oe cm}}^2$ for the spin stiffness and $J_{\mathrm{MnMn}}\text{≈1\hspace{0.17em}}\mathrm{meV}$ for the exchange integral between Mn spins are obtained.