The ferromagnetic transition and domain structure in LiHoF4

TL;DR

This study uses advanced Monte Carlo simulations to confirm LiHoF4 as a dipolar Ising model, accurately reproduces experimental thermodynamic data, and provides new insights into domain structures and finite-size effects in ferromagnetic materials.

Contribution

It offers the first detailed simulation-based analysis of LiHoF4's magnetic properties, including domain structures and finite-size corrections, with strong evidence for logarithmic renormalization effects.

Findings

Quantitative agreement with experimental magnetization, heat capacity, and susceptibility data.

Evidence of logarithmic corrections predicted by renormalization group theory.

Prediction of domain structures consisting of thin parallel sheets in finite samples.

Abstract

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.