Theory of the Magnetic phase diagram of LiHoF$_4$

TL;DR

This paper advances the understanding of LiHoF$_4$ by calculating its magnetic phase diagram beyond mean-field theory using quantum Monte Carlo, incorporating domain structures and hyperfine interactions.

Contribution

It introduces a non-perturbative projection for the Ising model in a transverse field and explicitly accounts for domain structures and hyperfine effects.

Findings

Phase diagram calculated with quantum Monte Carlo

Explicit inclusion of domain structures

Proposal for spectroscopy experiment to measure key parameters

Abstract

The properties of LiHoF$_4$ are believed to be well described by a long-range dipolar Ising model. We go beyond mean-field theory and calculate the phase diagram of the Ising model in a transverse field using a quantum Monte Carlo method. The relevant Ising degrees of freedom are obtained using a non-perturbative projection onto the low-lying crystal field eigenstates. We explicitly take the domain structure into account, and the strength of the near-neighbor exchange interaction is obtained as a fitting parameter. The on-site hyperfine interaction is approximately taken into account through a renormalization of the transverse applied magnetic field. Finally, we propose a spectroscopy experiment to precisely measure the most important parameter controlling the location of the phase boundary.