Magnetic Anisotropy, Spin Pinning and Exchange Constants of (Ga,Mn)As films

We present a detailed investigation of exchange-dominated nonpropagating spin-wave modes in a series of 100 nm Ga$_{1 - x}$Mn$_{x}$As films with Mn concentrations $x$ ranging from 0.02 to 0.08. The angular and Mn concentration dependences of spin wave resonance modes have been studied for both as-grown and annealed samples. Our results indicate that the magnetic anisotropy terms of Ga$_{1 - x}$Mn$_{x}$As depend on the Mn concentration $x$, but are also strongly affected by sample growth conditions; moreover, the magnetic anisotropy of Ga$_{1 - x}$Mn$_{x}$As films is found to be clearly linked to the Curie temperature. The spin wave resonance spectra consist of a series of well resolved standing spin-wave modes. The observed mode patterns are consistent with the Portis volume-inhomogeneity model, in which a spatially nonuniform anisotropy field acts on the Mn spins. The analysis of these exchange-dominated spin wave modes, including their angular dependences, allows us to establish the exchange stiffness constants for Ga$_{1 - x}$Mn$_{x}$As films.