We address the physical mechanism responsible for the emergence of magnetization plateaux in the Shastry-Sutherland model. By using a hierarchical mean-field approach, we demonstrate that a plateau is stabilized in a certain spin pattern, satisfying local commensurability conditions derived from our formalism. Our results provide evidence in favor of a robust local physics nature of the plateaux states and are in agreement with recent NMR experiments on ${\mathrm{SrCu}}_2({\mathrm{BO}}_3{)}_2$.

• Received 26 June 2009

DOI:https://doi.org/10.1103/PhysRevLett.103.177201