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

摘要

We study the effective long-range Ising dipole model with a local exchangeinteraction 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 exchangeinteraction. Using a Monte Carlo method we calculate the phase boundary T_c(x)between the ferromagnetic and paramagnetic phases. We demonstrate that theexperimentally observed linear decrease in T_c with dilution is not the simplemean-field result, but a combination of the effects of fluctuations, theexchange interaction and the hyperfine coupling. Furthermore, we find acritical dilution x_c=0.21(2), below which there is no ordering. In agreementwith recent Monte Carlo simulations on a similar model, we find no evidence ofthe experimentally observed freezing of the glassy state in our calculation. Weapply the theory of Stephen and Aharony to LiHo_{x}Y_{1-x}F_4 and find that thetheory does predict a finite-temperature freezing of the spin glass. Reasonsfor the discrepancies are discussed.