Finite-temperature phase transition to them=12plateau phase in the spin-12XXZmodel on the Shastry-Sutherland lattices

We study the finite-temperature transition to the $m=1/2$ magnetization plateau in a model of interacting $S=1/2$ spins with longer-range interactions and strong exchange anisotropy on the geometrically frustrated Shastry-Sutherland lattice. This model was shown to capture the qualitative features of the field-induced magnetization plateaus in the rare-earth tetraboride, ${\text{TmB}}_{4}$. Our results show that the transition to the plateau state occurs via two successive transitions with the two-dimensional Ising universality class, when the quantum exchange interactions are finite, whereas a single phase transition takes place in the purely Ising limit. To better understand these behaviors, we perform Monte Carlo simulations of the classical generalized four-state chiral clock model and compare the phase diagrams of the two models. Finally, we estimate a parameter set that can explain the magnetization curves observed in ${\text{TmB}}_{4}$. The magnetic properties and critical behavior of the finite-temperature transition to the $m=1/2$ plateau state are also discussed.