Nuclear Magnetism in Two-Dimensional Solid Helium Three on Graphite

Abstract

Recent studies of nuclear magnetism of monolayer helium three (³He) adsorbed on graphite are reviewed. This system provides us a fascinating testing ground for physics of highly frustrated quantum spins of two dimensions (2D) such as spin liquids. Particular emphasis is devoted to the gapless spin liquid state observed in the low-density commensurate phase (4/7 phase) in the second layer. Existing experiments on heat capacity in zero magnetic field and magnetization in low fields of this phase show unambiguously the gapless excitations down to three orders of magnitude lower temperatures than the relevant exchange interactions (≈1 mK). This is a new class of spin liquid, and recently electronic counterparts are found in quasi-1D and -2D conductors. On the other hand, measured magnetic properties of the incommensurate phase at much higher densities can be described as a nearly ideal 2D S=1⁄2 ferromagnet on a triangular lattice. We propose the existence of a new ferromagnetic commensurate phase at a density in between the 4/7 and incommensurate phases based on new heat capacity data. None of these phases show signatures of finite temperature phase transitions being consistent with the Mermin–Wagner theorem. The exchange interactions among ³He nuclear spins originate from atom-atom tunnel exchanges due to the large zero-point motions. Because of the steric hindrance, higher order exchanges like three-, four-, five-, and six-spin ring exchanges are expected to compete each other in similar strengths (MSE model). The applicability of the MSE model to the experimental magnetic properties of this system including its density variation is discussed. It is satisfactory except the fact that the model does not reproduce the gapless nature of the 4/7 phase, which recently stimulates different theoretical approaches such as the Hubbard model.