$LiHo_xY_{1-x}F_4$ is an insulating system where the magnetic Ho$^{3+}$ ions have an Ising character, and interact mainly through magnetic dipolar fields. We used the muon spin relaxation technique to study the nature of the ground state for samples
with x=0.25, 0.12, 0.08, 0.045 and 0.018. In contrast with some previous works, we have not found any signature of canonical spin glass behavior down to $approx$15mK. Instead, below $approx$300mK we observed dynamic magnetism characterized by a single correlation time with a temperature independent fluctuation rate. We observed that this low temperature fluctuation rate increases with x up to 0.08, above which it levels off. The 300mK energy scale corresponds to the Ho3+ hyperfine interaction strength, suggesting that the hyperfine interaction may be intimately involved with the spin dynamics in this system.
We have performed zero-field muon spin rotation measurements on single crystals of La_{2-x}Sr_{x}CuO_{4} to search for spontaneous currents in the pseudo-gap state. By comparing measurements on materials across the phase diagram, we put strict upper
limits on any possible time-reversal symmetry breaking fields that could be associated with the pseudo-gap. Comparison between experimental limits and proposed circulating current states effectively eliminates the possibility that such states exist in this family of materials.
Muon spin relaxation (MuSR) measurements in iron oxy-pnictide systems have revealed: (1) commensurate long-range order in undoped LaOFeAs; (2) Bessel function line shape in La(O0.97F0.03)FeAs which indicates possible incommensurate or stripe magnetis
m; (3) anomalous weak magnetism existing in superconducting LaOFeP, Ce(O0.84F0.16)FeAs, and Nd(O0.88F0.12)FeAs but absent in superconducting La(O0.92F0.08)FeAs; and (4) scaling of superfluid density and Tc in the Ce, La, and Nd-FeAs superconductors following a nearly linear relationship found in cuprates.
