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$LiHo_xY_{1-x}F_4$ is an insulating system where the magnetic Ho$^{3+}$ ionshave an Ising character, and interact mainly through magnetic dipolar fields.We used the muon spin relaxation technique to study the nature of the groundstate for samples with x=0.25, 0.12, 0.08, 0.045 and 0.018. In contrast withsome previous works, we have not found any signature of canonical spin glassbehavior down to $\approx$15mK. Instead, below $\approx$300mK we observeddynamic magnetism characterized by a single correlation time with a temperatureindependent fluctuation rate. We observed that this low temperature fluctuationrate increases with x up to 0.08, above which it levels off. The 300mK energyscale corresponds to the Ho3+ hyperfine interaction strength, suggesting thatthe hyperfine interaction may be intimately involved with the spin dynamics inthis system.

Study of the ground state properties of $LiHo_xY_{1-x}F_4$ using $\mu$SR