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

We propose a new way to treat 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 phonon spectra 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.