Theory of Paramagnetic Solid Helium Three

The object of the present paper is the elaboration of a model formalism for solid ${\mathrm{He}}^3$. This is based on postulating isotropic first-neighbor antiferromagnetic — $J_1$ and second-neighbor ferromagnetic $J_2$ exchange interactions between pairs of atoms. Using some of the averaged pressure data along isochores of the unmagnetized and magnetized solid, due to Kirk and Adams, and assuming the exchange-strength functions to have constant logarithmic volume derivatives ${\gamma }_1$ and ${\gamma }_2$, we derive $-J_1\mathrm{}\left(V\right)\mathrm{}$, $J_2\mathrm{}\left(V\right)\mathrm{}$, ${\gamma }_1$, and ${\gamma }_2$; a satisfactory theoretical representation of all the isochore data, restricted to the asymptotic high-temperature range, is thereby achieved. The complete verification of the model formalism, however, can only be performed once data become available on various thermal properties of the solid, in absence and presence of external uniform and constant magnetic fields of moderate strength, at low enough temperatures $T<\mathrm{}10\mathrm{}$ mK. Earlier high-temperature nuclear-paramagnetic-susceptibility data of low precision can be accounted for by the model and its parameters at small-volume isochores, but numerical discrepancies develop at the larger volumes. Accurate susceptibility measurements are required for a detailed comparison of theoretical and experimental values of the asymptotic Curie temperatures of the solid along a series of isochores.