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

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.

Submitted to Phys. Rev. B

References in corpus (5)

• Fractional magnetization plateaus and magnetic order in the Shastry Sutherland magnet TmB4
• Ground States of the Ising Model on the Shastry-Sutherland Lattice and the Origin of the Fractional Magnetization Plateaus in Rare-Earth Tetraborides
• Magnetization Plateau of Classical Ising Model on Shastry-Sutherland Lattice
• Magnetization Process of the Classical Heisenberg Model on the Shastry-Sutherland Lattice
• The competing spin orders and fractional magnetization plateaus of classical Heisenberg model on Shastry-Sutherland lattice: Consequence of long-range interactions

Cited by in corpus (6)

• Field Induced Magnetic States in Holmium Tetraboride
• Mott transition and Antiferromagnetic Metal on Shastry-Sutherland Lattice
• Possible stripe phases in the multiple magnetization plateaus in TbB${}_4$ derived from single-crystal neutron diffraction under pulsed high magnetic fields
• Phase Diagram of the Shastry-Sutherland Kondo Lattice Model with Classical Localized Spins: A Variational Calculation Study
• Topological Hall effect in the Shastry-Sutherland lattice
• The ground state structure of electron's ensemble on one-dimension disordered lattice