Magnetism of Quantum Solid with Strong Zero Point Lattice Vibration. II. A Proposed Model for hcp ³He

Abstract

In a quantum lattice of closely packed hard core fermions such as hcp ³He, the tunneling motion for particle exchange is strongly coupled with zero-point lattice vibrations. The hybridization of the exchange tunneling and the zero-point vibration is considered by a simplified model. In this model the exchange of a nearest neighbour pair of fermions is supposed to grow rapidly when the third fermion closest to the pair is displaced to make enough space for the exchange tunneling.
Such displacement is assumed to be described by the Einstein model. The high temperature expansion series are obtained for the specific heat, for the pressure and for the susceptibility. It is shown that the susceptibility deviates from the Curie law in the direction usually seen in ferromagnets.
It is demonstrated, however, that the hcp quantum solid does not exhibit the simple ferromagnetic spin order in the low temperature phase.