Exact ground state of the Shastry-Sutherland lattice with classical Heisenberg spins

TL;DR

This paper provides an exact analytical solution for the ground state of the classical Heisenberg model on the Shastry-Sutherland lattice, revealing phase behavior and magnetization features relevant to rare earth tetraborides.

Contribution

It presents the first exact ground state solution for the classical Heisenberg model on this lattice, including phase diagram and magnetization properties, with implications for real materials.

Findings

Exact ground state solution for arbitrary J2/J1 ratio.

Identification of spin-flop, spin-flip, and umbrella phases.

Explanation of the 1/3 magnetization plateau in RB4 compounds.

Abstract

An exact analytical solution of the ground state problem of the isotropic classical Heisenberg model on the Shastry-Sutherland lattice in external magnetic field $H$ is found for arbitrary ratio of diagonal to edge exchange constants $J_2/J_1$. The phase diagram of this model in the ($J_2/J_1, H/J_1$) plane is presented. It includes spin-flop, spin-flip and umbrella phases. The magnetization curves are found to be linear until saturation. It is shown numerically that the inclusion of the easy-axis anisotropy into the model leads to the appearance of the 1/3 magnetization plateau, corresponding to the collinear up-up-down spin structure. This explains the appearance of the 1/3 magnetization plateau in rare earth tetraborides RB$_4$. In particular, magnetization curve of the compound HoB$_4$ is explained.