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

TL;DR

This paper investigates the finite-temperature phase transition to the half-magnetization plateau in a frustrated S=1/2 XXZ model on the Shastry-Sutherland lattice, revealing a two-step transition with Ising universality and comparing classical and quantum models.

Contribution

It demonstrates the nature of the phase transition to the magnetization plateau and compares quantum and classical models to understand the critical behavior.

Findings

Transition occurs via two successive Ising-like transitions with finite quantum interactions.

Single phase transition occurs in the purely Ising limit.

Parameter estimation aligns the model with experimental magnetization curves in TmB4.

Abstract

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, ${\rm TmB_4}$. 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 ${\rm TmB_4}$. The magnetic properties and critical behavior of the finite-temperature transition to the $m=1/2$ plateau state are also discussed.