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

In this paper, 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 (SWR) 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 SWR 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