Multiple-Spin Exchange on a Triangular Lattice: A Quantitative Interpretation of Thermodynamic Properties of Two-Dimensional SolidH3e

Abstract

We apply exact high-temperature series expansions of the multiple-spin-exchange Hamiltonian for a triangular lattice to describe high precision NMR measurements of the nuclear magnetic susceptibility of ${}^3\mathrm{He}$ films adsorbed on graphite, reported here, as well as all available specific heat data. A consistent quantitative description of the unusual thermodynamic properties of the second layer solid, which provides canonical examples of two-dimensional magnets, is obtained as a function of temperature and areal density. We prove that cyclic multiple-spin exchange processes are responsible for the large degree of frustration found in the antiferromagnetic phase and that they remain significant in the ferromagnetic phase.