Theory of magnetization plateaux in the Shastry-Sutherland model

TL;DR

This paper investigates the magnetization plateaux in the Shastry-Sutherland model using perturbative continuous unitary transformations, revealing new plateau structures and their implications for the compound SrCu$_2$(BO$_3$)$_2$.

Contribution

It introduces a detailed analysis of long-range interactions and predicts new magnetization plateaux, enhancing understanding of the model's low-magnetization behavior.

Findings

Plateaux at 2/9, 1/6, 1/9, and 2/15 identified

Reproduction of NMR magnetization profile around triplets

Prediction of a 1/6 plateau and residual interactions' effects

Abstract

Using perturbative continuous unitary transformations, we determine the long-range interactions between triplets in the Shastry-Sutherland model, and we show that an unexpected structure develops at low magnetization with plateaux progressively appearing at 2/9, 1/6, 1/9 and 2/15 upon increasing the inter-dimer coupling. A critical comparison with previous approaches is included. Implications for the compound SrCu$_2$(BO$_3$)$_2$ are also discussed: we reproduce the magnetization profile around localized triplets revealed by NMR, we predict the presence of a 1/6 plateau, and we suggest that residual interactions beyond the Shastry-Sutherland model are responsible for the other plateaux below 1/3.