Dynamics of the fcc Heisenberg antiferromagnet with nearest-neighbor interactions. II. Dilute arrays

We report the results of a study of the dynamics of the site-dilute face-centered-cubic Heisenberg antiferromagnet with nearest-neighbor interactions. Numerical techniques are used to obtain information about the effect of dilution on the distributions of local fields in the various equilibrium spin configurations. Spin excitations are studied within the framework of a linearized magnon theory. The density of magnon modes is determined for 50% dilution and compared with the corresponding results for the fully occupied lattice and an antiferromagnet with type-III long-range order. The equations of motion for the spins are integrated to obtain the dynamic structure factor. The peaks in the dynamic structure factor indicate the existence of damped spin waves which mirror the short-range-order characteristic of the fully occupied lattice. We find no evidence for weakly damped, long-wavelength hydrodynamic spin waves. The relation of the work to experimental studies of the dilute semiconductors ${\mathrm{Cd}}_{1-c}{\mathrm{Mn}}_c\mathrm{Te}$, ${\mathrm{Hg}}_{1-c}{\mathrm{Mn}}_c\mathrm{Te}$, and ${\mathrm{Zn}}_{1-c}{\mathrm{Mn}}_c\mathrm{Te}$ is commented on.