Exchange narrowing of NMR line shapes in randomly diluted magnetic systems

An analysis of ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$ NMR linewidths in the randomly diluted magnetic system ${\mathrm{KMn}}_{\mathrm{x}}$ ${\mathrm{Mg}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{F}}_3$ is presented. It is shown that good agreement with measured linewidths can be obtained if in the usual asymptotic spin-diffusion assumption for the spin autocorrelation function &(0)${\mathrm{〉}}_{\mathrm{av}}$ α${\mathrm{\tau }}^{\mathrm{-}\mathrm{d}\left(\mathrm{x}\right)/2\mathrm{}}$, d(x) is taken to be independent of x above the percolation concentration. Experimental results in the system ${\mathrm{KNi}}_{\mathrm{x}}$ ${\mathrm{Mg}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{F}}_3$ are also presented. These data exhibit striking differences with the behavior of isostructural ${\mathrm{KMn}}_{\mathrm{x}}$ ${\mathrm{Mg}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{F}}_3$ whose origin is discussed.