The competing spin orders and fractional magnetization plateaus of classical Heisenberg model on Shastry-Sutherland lattice: Consequence of long-range interactions

TL;DR

This study uses Monte Carlo simulations and mean-field theory to explore how long-range interactions influence spin orderings and magnetization plateaus in the classical Heisenberg model on a Shastry-Sutherland lattice, explaining experimental phenomena in rare-earth tetraborides.

Contribution

It demonstrates the role of long-range interactions in stabilizing the 1/2 magnetization plateau and provides a comprehensive analysis of phase transitions in the model.

Findings

Reproduces the 1/2 magnetization plateau observed experimentally.

Shows local long-range interactions favor the 1/2 plateau over the 1/3 plateau.

Identifies conditions favoring Neel state stabilization at finite temperatures.

Abstract

The competing spin orders and fractional magnetization plateaus of classical Heisenberg model with long-range interactions on a Shastry-Sutherland lattice are investigated using Monte Carlo simulations, in order to understand the fascinating spin ordering sequence observed in TmB4 and other rare-earth tetraborides. The simulation reproduces the experimental 1/2 magnetization plateau at low temperature by considering multifold long range interactions. It is found that more local long range interactions can be satisfied in the 1/2 plateau state than those in the 1/3 plateau state, leading to the stabilization of the extended 1/2 plateau. A mean-field theory on the spin ground states in response to magnetic field is proposed, demonstrating the simulation results. When the energies of the Neel state and the collinear state are degenerated, the former state is more likely to be stabilized due to the competitions among the local collinear spin orders. The present work provides a comprehensive proof of the phase transitions to the Neel state at nonzero temperature, in complimentary to the earlier predictions for the Fe-based superconductors.