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A complete solution of the ground-state problem for an Ising model on theShastry-Sutherland lattice with an additional interaction along the diagonalsof "empty" squares in an applied magnetic field is presented. A rigorous proofis given that this interaction gives rise to a plateau at one-half of thesaturation magnetization. Such a fractional plateau has been observed in somerare-earth-metal tetraborides, in particular, in strong Ising magnets ErB4(where it is the only one) and TmB4 (where it is the broadest one), but itsorigin has remained unclear. Our study sheds new light on the solution of thisproblem.

Ground states of an Ising model on an extended Shastry-Sutherland lattice and the 1/2-magnetization plateau in some rare-earth-metal tetraborides