Frustration by Multiple Spin Exchange in 2D Solid ${}^3\mathrm{He}$ Films

Measurements of the magnetization and heat capacity of the second layer of ${}^3\mathrm{He}$ films adsorbed on graphite indicate that the evolution of the exchange from antiferromagnetic to ferromagnetic arises from a tuning of the competing exchange processes. At certain coverages the coexistence of an antiferromagnetic heat capacity with a ferromagnetic magnetization is a clear manifestation, predicted by theory, of frustration. At the ferromagnetic anomaly the system is well described by series expansions for a 2D Heisenberg ferromagnet on a triangular lattice.