Competition of Multiple Spin Exchanges in Submonolayer Solid3He

We have made NMR measurements of the first layer of solid ${}^3\mathrm{He}$ adsorbed on graphite down to $120\mu \mathrm{K}$. Magnetization varies from antiferro- to ferromagnetic on increasing the coverage except for the region around the $\sqrt{3}\times \sqrt{3}$ commensurate phase. This behavior is very similar to that of the second layer and is understood as due to the competition among various multiple spin exchanges. The $\sqrt{3}\times \sqrt{3}$ phase exhibits a ferromagnetic behavior which is not expected from a simple coverage dependence of the multiple exchange energies.