Phase diagram of the dilute magnet LiHo_xY_{1-x}F_4

We study the effective long-range Ising dipole model with a local exchange interaction appropriate for the dilute magnetic compound LiHo_{x}Y_{1-x}F_4. Our calculations yield a value of 0.12 K for the nearest neighbor exchange interaction. Using a Monte Carlo method we calculate the phase boundary T_c(x) between the ferromagnetic and paramagnetic phases. We demonstrate that the experimentally observed linear decrease in T_c with dilution is not the simple mean-field result, but a combination of the effects of fluctuations, the exchange interaction and the hyperfine coupling. Furthermore, we find a critical dilution x_c=0.21(2), below which there is no ordering. In agreement with recent Monte Carlo simulations on a similar model, we find no evidence of the experimentally observed freezing of the glassy state in our calculation. We apply the theory of Stephen and Aharony to LiHo_{x}Y_{1-x}F_4 and find that the theory does predict a finite-temperature freezing of the spin glass. Reasons for the discrepancies are discussed.Comment: 5 pages, 4 figure

Low-temperature properties of the dilute dipolar magnet LiHo_xY_(1-x)F_4

We analyze recent experiments on the dilute rare-earth compound LiHo_xY_(1-x)F_4 in the context of an effective Ising dipolar model. Using a Monte Carlo method we calculate the low-temperature behavior of the specific heat and linear susceptibility, and compare our results to measurements. In our model the susceptibility follows a Curie-Weiss law at high temperature, chi ~ 1/(T-T_cw), with a Curie-Weiss temperature that scales with dilution, T_cw ~ x, consistent with early experiments. We also find that the peak in the specific heat scales linearly with dilution, C_max(T) ~ x, in disagreement with recent experiments. Experimental studies do not reach a consensus on the functional form of these quantities, and in particular we do not see reported scalings of the form chi ~ T^-0.75 and chi ~ exp(-T/T_0). Furthermore we calculate the ground state magnetization as a function of dilution, and re-examine the phase diagram around the critical dilution x_c=0.24(3). We find that the spin glass susceptibility for the Ising model does not diverge below x_c, while recent experiments give strong evidence for a stable spin-glass phase in LiHo_0.167Y_0.833F_4.Comment: 6 pages, 9 figure

The ferromagnetic transition and domain structure in LiHoF4

Using Monte Carlo simulations we confirm that the rare-earth compound LiHoF4 is a very good realization of a dipolar Ising model. With only one free parameter our calculations for the magnetization, specific heat and inverse susceptibility match experimental data at a quantitative level in the single Kelvin temperature range, including the ferromagnetic transition at 1.53 K. Using parallel tempering methods and reaching system sizes up to 32000 dipoles with periodic boundary conditions we are able to give strong direct evidence of the logarithmic corrections predicted in renormalization group theory. Due to the long range and angular dependence of the dipolar model sample shape and domains play a crucial role in the ordered state. We go beyond Griffiths's theorem and consider surface corrections arising in finite macroscopic samples leading to a theory of magnetic domains. We predict that the ground-state domain structure for cylinders with a demagnetization factor N>0 consists of thin parallel sheets of opposite magnetization, with a width depending on the demagnetization factor.Comment: 5 pages, 9 figure