Theory of Magnetized Solid Helium Three

Experiments on the thermodynamic properties of magnetized solid ${\mathrm{He}}^3$ at accessible temperatures and fields are shown to be a conveneint and powerful method of studying the nature and form of the nuclear spin interaction in solid ${\mathrm{He}}^3$. In particular, it should be possible to determine whether these properties are described in a satisfactory way by an exchange-interaction model assumed to be proportional to the scalar product of nuclear spin vectors of nearest-neighbor atoms of the solid. Independently of this model, it is shown that measurements of the magnetic modification of the melting pressure, at low but readily accessible temperatures and moderate field strengths, correspond to almost absolute measurements, of good accuracy, of the nuclear paramagnetic susceptibility of the solid at melting. The entropy diagram of the magnetized model solid enables one to describe with precision the isothermal magnetization and adiabatic demagnetization processes, which should contribute to the verification of the model through their experimental investigation. The increase in the heat capacity on magnetization is large enough to be maesured accurately and to test the validity of the model. An interesting effect is that the thermally anomalous unmagnetized solid becomes normal on magnetization, over a finite and low but accessible temperature range, and at intermediate field strengths. Experimental investigations of various equilibrium thermal properites of magnetized solid ${\mathrm{He}}^3$ could thus contribute significantly toward the elucidation of the behavior of its nuclear spin system which alone determines its thermal properties over the currently accessible low temperatures.