What Is the Spin Hamiltonian of Solid BCC 3He?

Abstract

Solid helium is a quantum crystal, i.e., a crystal in which the ratio of the zero-point energy to the binding energy is of order unity. This allows the atoms in the solid to have an unusually large mobility. This mobility of helium atoms becomes experimentally observable in solid 3He because of its magnetic moment. Nuclear magnetic relaxation (NMR) experiments observe the hopping directly. The hopping leads to a spin ordering which effects the thermodynamics of solid 3He at low temperatures. Hence a measurement of thermodynamic properties such as pressure, susceptibility, entropy, etc., allows us to garner information about the hopping helium atoms. The Heisenberg Hamiltonian, $$\mathcal{H} = - 2\hbar \sum\limits_{{i < j}} {{{J}_{2}}} (ij){{\sigma }_{i}}.{{\sigma }_{j}} $$ has been used to describe solid 3He, where J 2(ij) is the exchange frequency between the pair of atoms at lattice sites i and j and σ i is the spin of the atom on the ith lattice site.