Magnetization plateaus of the Shastry-Sutherland model for ${\mathrm{SrCu}}_2({\mathrm{BO}}_3{)}_2:$ Spin-density wave, supersolid, and bound states

We study the Heisenberg antiferromagnet on the Shastry-Sutherland lattice under magnetic fields to clarify the magnetic properties of ${\mathrm{SrCu}}_2({\mathrm{BO}}_3{)}_2.$ Treating magnetic excitations promoted by the field as Bose particles and using strong-coupling expansion, we derive an effective Hamiltonian for the effective magnetic particles. Anisotropic repulsive interactions between effective particles induce “insulating” states with a stripe spin-density wave (SDW) structure at magnetization ${m/m}_{\mathrm{sat}}=1/3\mathrm{}$ and a checkerboard structure at 1/2, and thereby form magnetization plateaus. Supersolid phases appear around insulating SDW phases by changing the magnetic field. The nature of these supersolid phases is discussed in detail. We also demonstrate how the geometry of the Shastry-Sutherland lattice affects dynamical properties of magnetic excitations significantly and makes quintuplet $\mathrm{}(S=2\mathrm{})\mathrm{}$ bound states condense for very small magnetization.