Assessment of the RE(OH)3 Ising-like Magnetic Materials as Possible Candidates for the Study of Transverse-Field-Induced Quantum Phase Transitions

The LiHo$_x$Y$_{1-x}$F$_4$ Ising magnetic material subject to a magnetic field, $B_x$, perpendicular to the Ho$^{3+}$ Ising direction has shown over the past twenty years to be a host of very interesting thermodynamic and magnetic phenomena. Unfortunately, the availability of other magnetic materials other than LiHo$_x$Y$_{1-x}$F$_4$ that may be described by a transverse field Ising model remains very much limited. It is in this context that we use here mean-field theory to investigate the suitability of the Ho(OH)$_{3}$, Dy(OH)$_{3}$ and Tb(OH)$_3$ insulating hexagonal dipolar Ising-like ferromagnets for the study of the quantum phase transition induced by a magnetic field, $B_x$, applied perpendicular to the Ising spin direction. From our calculations we estimate the critical transverse field, $B_{x}^{c}$, to destroy ferromagnetic order at zero temperature to be $B_{x}^{c}=$4.35 T, $B_{x}^{c}=$5.03 T and $B_{x}^{c}=$54.81 T for Ho(OH)$_{3}$, Dy(OH)$_{3}$ and Tb(OH)$_{3}$, respectively. We conclude from our calculations that Ho(OH)$_{3}$ and Dy(OH)$_{3}$, and their Y$^{3+}$ diamagnetically diluted variants, Ho$_{x}$Y$_{1-x}$(OH)$_{3}$ and Dy$_{x}$Y$_{1-x}$(OH)$_{3}$, are potentially interesting systems to study transverse-field induced quantum fluctuations effects in hard axis (Ising-like) magnetic materials.