Magnetization plateaus as insulator-superfluid transitions in quantum spin systems

We study the magnetization process in two-dimensional $S=1/2\mathrm{}$ spin systems, to discuss the appearance of a plateau structure. The following three cases are considered: (1) the Heisenberg antiferromagnet and multiple-spin exchange model on the triangular lattice, (2) the Shastry-Sutherland-type lattice [which is a possible model for ${\mathrm{SrCu}}_2\left({\mathrm{BO}}_3{)}_2\right],$ (3) the 1/5-depleted lattice (for ${\mathrm{CaV}}_4{\mathrm{O}}_9).\mathrm{}$ We find in these systems that magnetization plateaus can appear owing to a transition from superfluid to a Mott insulator of magnetic excitations. The plateau states have charge-density-wave order of the excitations. The magnetizations of the plateaus depend on components of the magnetic excitations, the range of the repulsive interaction, and the geometry of the lattice.