Crystalline Transformation of Helium Three

Abstract

The main thermal characteristics of the structural change at low temperatures of solid ${\mathrm{He}}^3$, from the cubic to the hexagonal form, are expected to be governed by the dominant spin excitations. The spin-dependent interactions in these structures are assumed to be proportional to the scalar product of the nuclear spin vectors on nearest-neighbor atoms. With the currently available, if scarce, empirical interaction strengths, the transformation is probably anomalous. One aspect of the anomaly corresponds to the appearance of a very shallow minimum of the transformation pressure. It arises from the negative or anomalous latent heat of transformation at low temperatures, wherein heat has to be supplied to the low-density cubic solid to change it into the high-density close-packed solid, the transformation proceeding at constant temperature and pressure. At temperatures which are high compared to the very low spin-ordering temperatures of these structures, the anomaly is independent of the nature, ferromagnetic or antiferromagnetic, of the spin-ordering processes in the two solids along the transformation line. The increase in the anomalous-transformation pressure with decreasing temperature is estimated to become observable in the several-millidegree temperature range, the pressure anomaly increasing hyperbolically with decreasing temperatures. On compressing solid ${\mathrm{He}}^3$, the strength of the assumed nearest-neighbor spin-dependent atomic pair interactions, as well as the attendant spin-ordering temperatures, decrease very rapidly. As a result, within the limits of validity of the interaction model, both the cubic and, above all, the hexagonal solid exhibit practically ideal nuclear paramagnetism down to very low temperatures. The possibility of exploiting this ideal magnetic behavior of solid ${\mathrm{He}}^3$ for the production and control, through static experiments, of very low temperatures is briefly discussed.