12-12U

A complete solution of the ground-state problem for an Ising model on a Shastry–Sutherland lattice with an additional interaction along the diagonals of ``empty'' squares in an applied magnetic field is presented. It is rigorously proven that this interaction gives rise to a plateau at the half-saturated magnetization. Such a fractional plateau has been observed in some rare-earth-metal tetraborides, in particular, in strong Ising magnets ErB$_4$ (where it is a single one) and TmB$_4$ (where it is a major one), but its origin remains unclear. Our study sheds new light on this problem.