The melting pressure of helium-3 at very low temperatures

Abstract

The melting pressure of3 He at very low temperatures was shown earlier to be determined overwhelmingly by the solid phase. Using an extended solid3He model based on isotropic effective first-neighbor-pair antiferromagnetic and second-neighbor-pair ferromagnetic exchange interactions, the melting process is reinvestigated here. One of its motivating aspects may be said to be tied to its possible use, suggested by us earlier, for the establishment of a thermodynamic temperature scale at very low temperatures. As a consequence of the assumed multineighbor interactions, spin ordering is accelerated and, at the same temperature, the extended-model solid entropy falls below that of the simpler nearest-neighbor-pair interaction model. Equivalently, the spinordering critical transition temperature is raised over that associated with the simpler interaction scheme. The overall result is a decrease in the melting pressure variations at very low temperatures below those arising from the simple solid model. In the absence of a reliable experimental temperature scale at very low temperatures, only a qualified and cursory comparison is justified with recent experimentally estimated melting pressures. Discrepancies arise between theory and preliminary data on the temperature derivatives of the melting pressure or the entropy of the solid at melting. They might be due in part to the tentative experimental temperatures, which appear shifted toward too low temperatures when compared with the theoretical temperature scale implicit in the treatment of the generalized solid model. However, from the viewpoint which accepts the rather preliminary, scarce, very low temperature melting pressure data at face value, failure of the extended exchange model of solid3He at those temperatures must be kept in mind.