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

$\mathrm{LiHoF_{4}}$ is a magnetic material known for its Ising-type anisotropy, making it a model system for studying quantum magnetism. However, the theoretical description of $\mathrm{LiHoF_{4}}$ 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 $\mathrm{LiHoF_{4}}$, previously neglected, in determining its properties. We analytically derive the low-energy effective Hamiltonian of $\mathrm{LiHoF_{4}}$, 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 $\mathrm{Fe_{8}}$ system.Comment: 7+12 pages, 2+4 figure

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

LiHoF$_{4}$ is a magnetic material known for its Ising-type anisotropy, making it a model system for studying quantum magnetism. However, the theoretical description of LiHoF$_{4}$ 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 LiHoF$_{4}$, previously neglected, in determining its properties. We analytically derive the low-energy effective Hamiltonian of LiHoF$_{4}$, including the off-diagonal dipolar terms perturbatively, both in the absence and presence of a transverse field. Our results encompass the full \boldmath{$B_{x}-T$} 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 Fe$_{8}$ system

The Effect of Intrinsic Quantum Fluctuations on the Phase Diagram of Anisotropic Dipolar Magnets

The rare-earth material $\mathrm{LiHoF_4}$ is believed to be an experimental realization of the celebrated (dipolar) Ising model, and upon the inclusion of a transverse field $B_x$, an archetypal quantum Ising model. Moreover, by substituting the magnetic Ho ions by non-magnetic Y ions, disorder can be introduced into the system giving rise to a dipolar disordered magnet and at high disorders to a spin-glass. Indeed, this material has been scrutinized experimentally, numerically and theoretically over many decades with the aim of understanding various collective magnetic phenomena. One of the to-date open questions is the discrepancy between the experimental and theoretical $B_x -T$ phase diagram at low-fields and high temperatures. Here we propose a mechanism, backed by numerical results, that highlights the importance of quantum fluctuations induced by the off-diagonal dipolar terms, in determining the critical temperature of anisotropic dipolar magnets in the presence and in the absence of a transverse field. We thus show that the description as a simple Ising system is insufficient to quantitatively describe the full phase diagram of $\mathrm{LiHoF_4}$, for the pure as well as for the dilute system.Comment: 5+8 pages, 5+5 figures; added argument to results section, corrected typo