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The minimal effective model for the magnetisation plateaus below 1/2 in theShastry-Sutherland model is derived to be an Ising model of certain unit-cellhard-core bosons with anisotropic repulsive interactions on isoscelestriangular lattice. It unambiguously gives the prominent plateaus at 1/8, 1/6,1/4, 1/3 and an additional one at 3/8, related through a particle-hole (p-h)transformation. The Dzyaloshinsky-Moriya (DM) interaction dresses it up with aninhomogeneous transverse field that also causes p-h asymmetry due to anin-plane component of the inter-dimer DM vector. This explains the asymmetrybetween the magnetisation below and above 1/4 in SrCu$_2$(BO$_3$)$_2$. Theeffective model above 1/2 plateau is an XXZ model with stronger XY parts. Itgives no magnetisation plateaus, but exhibits chiral order.

Effective models for the magnetization behavior of Shastry-Sutherland model