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

TL;DR

This paper models the phase diagram of dilute LiHo_xY_{1-x}F_4 using Monte Carlo simulations, revealing the effects of fluctuations and interactions on the critical temperature and identifying a critical dilution point.

Contribution

It provides a detailed Monte Carlo analysis of the phase boundary and critical dilution in LiHo_xY_{1-x}F_4, highlighting deviations from mean-field predictions.

Findings

Critical temperature T_c decreases linearly with dilution.

Critical dilution x_c is approximately 0.21.

No evidence of glassy state freezing in simulations.

Abstract

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.