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Experimental Phase Diagram and Dynamics of a Dilute Dipolar-Coupled Ising System

We present ac susceptibility and specific heat measurements taken on samples of LiHo$_x$Y$_{1-x}$F$_4$ in the dilute limit: x = 0.018, 0.045, 0.080 and 0.12. Susceptibility measurements show glassy behavior including wide absorption spectra that continually broaden with decreasing temperature. Dynamical scaling analyses show evidence of finite-temperature spin-glass transitions, the temperatures of which match those of recent theoretical work. A surprisingly long intrinsic time constant is observed in these samples and is found to be inversely correlated with the concentration of magnetic moments, x. Our results support the picture that this behavior is largely a single-ion effect, related to the random transverse fields generated by the off-diagonal component of the dipolar interaction and significantly slowed by the important nuclear hyperfine interaction. Specific heat measurements show broad features due to the electronic spins on top of a large Schottky-like nuclear contribution. Unusually, the peak position of the electronic component is found to be largely concentration independent, unlike the glass transition temperature.