Evolution of spin relaxation processes in LiY1−xHoxF4studied via ac-susceptibility and muon spin relaxation

Abstract

We present measurements of magnetic field and frequency dependence of the low-temperature ($T$ = 1.8 K) ac-susceptibility and temperature and field dependence of the longitudinal field positive muon spin relaxation (\ensuremath{\mu}SR) for LiY${}_{1\ensuremath{-}x}$Ho${}_{x}$F${}_{4}$ with $x$ = 0.0017, 0.0085, 0.0408, and 0.0855. The fits of numerical simulations to the susceptibility data for the $x$ = 0.0017, 0.0085, and 0.0408 show that Ho-Ho cross-relaxation processes become more important at higher concentrations, signaling the crossover from single-ion to correlated behavior. We simulate the muon spin depolarization using the parameters extracted from the susceptibility, and the simulations agree well with our data for samples with $x$ = 0.0017 and 0.0085. The \ensuremath{\mu}SR data for samples with $x$ = 0.0408 and 0.0855 at low temperatures ($T$ 10 K) cannot be described within a single-ion picture of magnetic field fluctuations and give evidence for additional mechanisms of depolarization due to Ho${}^{3+}$ correlations. We also observe an unusual peak in the magnetic field dependence of the muon relaxation rate in the temperature interval 10--20 K that we ascribe to a modification of the Ho${}^{3+}$ fluctuation rate due to a field induced shift of the energy gap between the ground and the first excited doublet crystal field states relative to a peak in the phonon density of states centered near 63 cm${}^{\ensuremath{-}1}$.