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

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.