Assessment of the RE(OH)3 Ising magnetic materials as possible candidates for the study of transverse-field-induced quantum phase transitions

The LiHoxY1−xF4 Ising magnetic material subject to a magnetic field perpendicular to the Ho3+ Ising direction has shown over the past 20 years to be a host of very interesting thermodynamic and magnetic phenomena. Unfortunately, the availability of other magnetic materials other than LiHoxY1−xF4 that may be described by a transverse-field Ising model remains very much limited. It is in this context that we use here a mean-field theory to investigate the suitability of the Ho(OH)3, Dy(OH)3, and Tb(OH)3 insulating hexagonal dipolar Ising-type ferromagnets for the study of the quantum phase transition induced by a magnetic field, Bx, applied perpendicular to the Ising spin direction. Experimentally, the zero-field critical (Curie) temperatures are known to be Tc≈2.54, 3.48, and 3.72 K, for Ho(OH)3, Dy(OH)3, and Tb(OH)3, respectively. From our calculations we estimate the critical transverse field, Bxc, to destroy ferromagnetic order at zero temperature to be Bxc=4.35, 5.03, and 54.81 T for Ho(OH)3, Dy(OH)3, and Tb(OH)3, respectively. We find that Ho(OH)3, similarly to LiHoF4, can be quantitatively described by an effective S=1/2 transverse-field Ising model. This is not the case for Dy(OH)3 due to the strong admixing between the ground doublet and first excited doublet induced by the dipolar interactions. Furthermore, we find that the paramagnetic (PM) to ferromagnetic (FM) transition in Dy(OH)3 becomes first order for strong Bx and low temperatures. Hence, the PM to FM zero-temperature transition in Dy(OH)3 may be first order and not quantum critical. We investigate the effect of competing antiferromagnetic nearest-neighbor exchange and applied magnetic field, Bz, along the Ising spin direction ẑ on the first-order transition in Dy(OH)3. We conclude from these preliminary calculations that Ho(OH)3 and Dy(OH)3 and their Y3+ diamagnetically diluted variants, HoxY1−x(OH)3 and DyxY1−x(OH)3, are potentially interesting systems to study transverse-field-induced quantum fluctuations effects in hard axis (Ising-type) magnetic materials.

Induced random fields in the LiHoxY1-xF4 quantum ising magnet in a transverse magnetic field

The LiHoxY1-xF4 magnetic material in a transverse magnetic field Bxx̂ perpendicular to the Ising spin direction has long been used to study tunable quantum phase transitions in a random disordered system. We show that the Bx-induced magnetization along the x̂ direction, combined with the local random dilution-induced destruction of crystalline symmetries, generates, via the predominant dipolar interactions between Ho3+ ions, random fields along the Ising ẑ direction. This identifies LiHoxY1-xF4 in Bx as a new random field Ising system. The random fields explain the rapid decrease of the critical temperature in the diluted ferromagnetic regime and the smearing of the nonlinear susceptibility at the spin-glass transition with increasing Bx and render the Bx-induced quantum criticality in LiHoxY1-xF4 likely inaccessible.