Effective models for the magnetization behavior of Shastry-Sutherland model

TL;DR

This paper derives effective models for the magnetization behavior of the Shastry-Sutherland model, explaining observed plateaus and asymmetries through Ising and XXZ models with Dzyaloshinsky-Moriya interactions.

Contribution

It introduces a minimal effective Ising model for magnetization plateaus below 1/2 and an XXZ model above 1/2, clarifying the role of DM interactions and particle-hole symmetry.

Findings

Identifies magnetization plateaus at 1/8, 1/6, 1/4, 1/3, and 3/8.

Explains asymmetry in magnetization using inhomogeneous transverse fields.

Shows the effective models reproduce key experimental features.

Abstract

The minimal effective model for the magnetisation plateaus below 1/2 in the Shastry-Sutherland model is derived to be an Ising model of certain unit-cell hard-core bosons with anisotropic repulsive interactions on isosceles triangular 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 an inhomogeneous transverse field that also causes p-h asymmetry due to an in-plane component of the inter-dimer DM vector. This explains the asymmetry between the magnetisation below and above 1/4 in SrCu$_2$(BO$_3$)$_2$. The effective model above 1/2 plateau is an XXZ model with stronger XY parts. It gives no magnetisation plateaus, but exhibits chiral order.