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We study the finite-temperature transition to the $m=1/2$ magnetizationplateau in a model of interacting $S=1/2$ spins with longer range interactionsand strong exchange anisotropy on the geometrically frustratedShastry-Sutherland lattice. This model was shown to capture the qualitativefeatures of the field-induced magnetization plateaus in the rare-earthtetraboride, ${\rm TmB_4}$. Our results show that the transition to the plateaustate occurs via two successive transitions with the two-dimensional Isinguniversality class, when the quantum exchange interactions are finite, whereasa single phase transition takes place in the purely Ising limit. To betterunderstand these behaviors, we perform Monte Carlo simulations of the classicalgeneralized four-state chiral clock model and compare the phase diagrams of thetwo models. Finally, we estimate a parameter set that can explain themagnetization curves observed in ${\rm TmB_4}$. The magnetic properties andcritical behavior of the finite-temperature transition to the $m=1/2$ plateaustate are also discussed.

Finite-temperature phase transition to $m=1/2$ plateau phase in a S=1/2 XXZ model on Shastry-Sutherland Lattices