Correlated atomic motion and spin-ordering in bcc $^{3}$He

Abstract

We propose a new way to treat the ordering of nuclear magnetism of solid $^{3}$He. We argue that the magnetic interaction arises indirectly as a consequence of correlated zero-point motion of the ions. This motion lowers the energy of the ground state, and results in a coherent state of oscillating electric dipoles. Distortion of the electronic wavefunctions leads to hyperfine magnetic interactions with the nuclear spin. Our model describes both the modification of the phonon spectra, localized modes ("vacancies") and the nuclear magnetic ordering of bcc $^{3}$He using a single parameter, the dipolar interaction energy $E_{0}$. The model yields correctly both the u2d2 symmetry of the ordered phase and the volume dependence of the magnetic interaction. We calculate the magnetic excitations in the u2d2 phase, which compare well with the measured specific-heat, free energy and entropy. We further give a description of the nature of the High-Field phase and the phase-transition lines as a function of magnetic field and volume.