The classical phase transition in LiHoF4: Results from mean field theory and Monte Carlo simulations

We show that mean field theory for the dipole compled Ising model for the specific lattice of LiHoF4 predicts a ferromagnetic critical temperature Tc=2.29 K, which is about 50% above the experimental value Tc=1.53 K. The inclusion of antiferromagnetic exchange interactions lowers the mean field Tc. We show however that to reach the experimental value, the antiferromagnetic interactions would need to have a strength greater than the ferromagnetic interactions. Hence it can be concluded that mean field theory is not well suited for predicting the correct ordering of LiHoF4. Including thermal fluctuations we resolve the discrepancy and predict from Monte Carlo simulations that a pair of parallel nearest neighbor Ho-ions have an antiferromagnetic exchange energy E/kB=(0.14±0.01) K. This is consistent with ferromagnetic ordering. The Monte Carlo results also clearly show that needle-shaped domains form in this system, the extended direction being along the crystal c-axis.