Nuclear relaxation in a randomly diluted Heisenberg paramagnet

The high (room)-temperature relaxation rates of those ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$ nuclei which are not transfer hyperfine coupled to Mn spins in $\mathrm{K}{\mathrm{Mn}}_x{\mathrm{Mg}}_{1-x}{\mathrm{F}}_3$ are calculated as a function of Mn concentration. Good agreement with experiment is found for the theoretical results, which have been obtained in the concentration range $0.02<~x<\mathrm{}1\mathrm{}$ (excluding values near the critical percolation concentration $x_c=0.31\mathrm{}$). The time dependence of the nuclear-spin decay is found to be well represented by $\exp [-{\left(\frac{t}{\tau }\right)}^n]$, with $n$ varying smoothly from $n=1\mathrm{}$ at $x=1\mathrm{}$ to $n\approx 0.5$ for $x\ll 1$. The secondneighbor exchange constant between Mn spins needed for agreement with experiment is found to be smaller than an independently, but also indirectly, measured value.