Dirty spin ice: The effect of dilution on spin freezing inDy2Ti2O7

We have studied spin freezing in the diluted spin ice compound ${\mathrm{Dy}}_{2-x}{\mathrm{Y}}_x{\mathrm{Ti}}_2{\mathrm{O}}_7$ where the nonmagnetic Y ions replace the magnetic Dy ions on the frustrated pyrochlore lattice. Magnetic ac and dc susceptibility data are presented with an analysis of relaxation times for dilutions of $x=0,$ 0.1, 0.2, and 0.4. Site dilution apparently decreases the relative number of spins participating in the icelike freezing near 16 K while leaving the freezing temperature unchanged. Correspondingly the distribution of relaxation times associated with the freezing is broadened only slightly with increasing dilution, suggesting that the freezing process observed near $T=16\mathrm{}\mathrm{K}$ involves the development of local correlations among the spins.