Heat Capacity Study of the Quantum Antiferromagnetism of a ${}^3$He Monolayer

We have measured the heat capacity of the second layer solid in a ${}^3\mathrm{He}$ film adsorbed on the surface of graphite to temperatures below 1 mK, in the regime where the nuclear exchange interaction is antiferromagnetic. The temperature dependence of the data is described by high temperature series expansions for a 2D Heisenberg antiferromagnet on a triangular lattice. There is no evidence for a phase transition down to $J/3$. Comparison with $J$ inferred from the magnetization provides a measure of the frustration due to competing antiferromagnetic and ferromagnetic cyclic exchanges.