Fractional magnetization plateaus in the extended Ising model on the Shastry-Sutherland lattice: Application to rare-earth metal tetraborides

Abstract

The classical Monte Carlo method is used to examine possibilities of formation of magnetization plateaus in the extended Ising model with the first , second , third , and fourth nearest-neighbour spin couplings on the Shastry–Sutherland lattice. It is shown that in the limit of ferromagnetic interaction the combined effects of and lead to the stabilization of the magnetization plateau against the standard Ising plateau (where is the saturation magnetization). At some critical values of and interactions the plateau phase is fully removed from the ground-state phase diagram providing a possible explanation of the fact that in some rare-earth tetraborides this phase is present and in some completely absent. In the opposite limit of antiferromagnetic interaction the model provides a reach spectrum of magnetic solutions, where in addition to the standard magnetization plateau one can find the following sequence of plateaus with the fractional magnetization: =1/10, 1/9, 1/6, 1/5, 2/5, 4/9, 7/15, and 5/9. The results obtained are consistent with experimental measurements of magnetization curves in selected rare-earth tetraborides.