Thesis advisor: Michael J. Graf / In this work I present a characterization of spin dynamics in LiY1-xHoxF4 over a wide region of frequency - temperature - magnetic field - concentration phase space to probe the onset of magnetic correlations. Specifically, measurements were made of the T = 1.8 K magnetic field and frequency dependence of AC susceptibility, and temperature and field dependence of the longitudinal field positive muon spin relaxation (μSR) for LiY1-xHoxF4 with x = 0.0017, 0.0085, 0.0408, and 0.0855. To determine the concentration range over which the spin dynamics are determined primarily by the Ho3+-μ interaction rather than by the F-μ interaction I characterize the dynamics associated with the formation of the (F-μ-F)−complex by comparing data with Monte Carlo simulations. Numerical simulations of the susceptibility for the x = 0.0017 and 0.0085 are fit to my data and show that Ho-Ho cross-relaxation processes become important at higher concentration, signaling the crossover from single-ion to correlated behavior. The muon spin depolarization is simulated using the parameters extracted from the susceptibility, and the simulations agree well with data for these two samples. It is found that the susceptibility and μSR data for samples with x = 0.0408 and 0.0855 cannot be described within a single-ion picture, possibly due to the onset of collective phenomena. An unusual peak is also discovered in the magnetic field dependence of the muon relaxation rate in the temperature interval 10 – 20 K, and ascribed to a modification of the Ho3+ fluctuation rate due to a field induced shift of the energy splitting between the ground and first excited doublet crystal field states relative to a peak in the phonon density of states centered near 63 cm-1. / Thesis (PhD) — Boston College, 2012. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.