The ferromagnetic transition and domain structure in LiHoF₄

Department of Theoretical Physics, Royal Institute of Technology - SE-106 91 Stockholm, Sweden, EU

Corresponding author: henelius@kth.se

Received: 17 March 2009
Accepted: 7 July 2009

Abstract

Using Monte Carlo simulations we verify 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 0.5–3 kelvin 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 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 consider surface corrections to Griffiths's theorem, which arise in finite macroscopic samples and lead to a theory of magnetic domains. We find a domain wall energy of 0.059 erg/cm² and predict that the ground-state domain structure for cylinders with a demagnetization factor consists of thin parallel sheets of opposite magnetization, with a width depending on the demagnetization factor.