We present measurements of magnetic field and frequency dependences of the low temperature (T = 1.8 K) AC-susceptibility, and temperature and field dependences of the longitudinal field positive muon spin relaxation ({mu}SR) for LiY$_{1-x}$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 {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$^{-1}$.
Magnetic and magnetoelastic properties of terbium titanate pyrochlore in paramagnetic phase are simulated. The magnetic field and temperature dependences of magnetization and forced magnetostriction in Tb2Ti2O7 single crystals and polycrystalline sam
ples are calculated in the framework of exchange charge model of crystal field theory and a mean field approximation. The set of electron-deformation coupling constants has been determined. Variations of elastic constants with temperature and applied magnetic field are discussed. Additional strong softening of the crystal lattice at liquid helium temperatures in the magnetic field directed along the rhombic symmetry axis is predicted.
Temperature and magnetic field dependences of the 19F nuclear spin-lattice relaxation in a single crystal of LiYF4 doped with holmium are described by an approach based on a detailed consideration of the magnetic dipole-dipole interactions between nu
clei and impurity paramagnetic ions and nuclear spin diffusion processes. The observed non-exponential long time recovery of the nuclear magnetization after saturation at intermediate temperatures is in agreement with predictions of the spin-diffusion theory in a case of the diffusion limited relaxation. At avoided level crossings in the spectrum of electron-nuclear states of the Ho3+ ion, rates of nuclear spin-lattice relaxation increase due to quasi-resonant energy exchange between nuclei and paramagnetic ions, in contrast to the predominant role played by electronic cross-relaxation processes in the low-frequency ac-susceptibility.
