LiHoF4 as a spin-half non-standard quantum Ising system

LiHoF₄ is a magnetic material known for its Ising-type anisotropy, making it a model system for studying quantum magnetism. However, the theoretical description of LiHoF₄ using the quantum Ising model has shown discrepancies in its phase diagram, particularly in the regime dominated by thermal fluctuations. In this study, we investigate the role of off-diagonal dipolar terms in LiHoF₄, previously neglected, in determining its properties. We analytically derive the low-energy effective Hamiltonian of LiHoF₄, including the off-diagonal dipolar terms perturbatively, both in the absence and presence of a transverse field. Our results encompass the full B_x − T phase diagram, confirming the significance of the off-diagonal dipolar terms in reducing the zero-field critical temperature and determining the critical temperature’s dependence on the transverse field. We also highlight the sensitivity of this mechanism to the crystal structure by comparing our calculations with the Fe₈ system.