Magnetization plateau in a two-dimensional multiple-spin exchange model

Abstract

We study a multiple-spin exchange model on a triangular lattice, which is a possible model for low-density solid ${}^{3}\mathrm{He}$ films. Due to strong competitions between ferromagnetic three-spin exchange and the antiferromagnetic four-spin one, the ground states are highly degenerate in the classical limit. At least ${2}^{L/2}$-fold degeneracy exists on the $L\ifmmode\times\else\texttimes\fi{}L$ triangular lattice except for the SO(3) symmetry. In the magnetization process, we found a plateau at ${m/m}_{\mathrm{sat}}=\frac{1}{2},$ in which the ground state is uuud state (a collinear state with four sublattices). The $\frac{1}{2}$ plateau appears due to the strong four-spin exchange interaction. This plateau survives against both quantum and thermal fluctuations. Under a magnetic field which realizes the uuud ordered state, a phase transition occurs at a finite temperature due to the breakdown of translational symmetry. We predict that low-density solid ${}^{3}\mathrm{He}$ thin films may show the $\frac{1}{2}$ plateau in the magnetization process. Experimental observation of the plateau will verify the strength of the four-spin exchange. It is also discussed that this magnetization plateau can be understood as an insulating-conducting transition in a particle picture.