TUNNELING AND EXCHANGE IN QUANTUM SOLIDS

Pairs of He3 atoms in solid bcc He3 have spatially symmetric or antisymmetric wave functions which correspond to energies ε+ and ε-, ε±=ε±12Δε. The energy difference ε+-ε-=Δε is due to a tunneling process and an interaction process. The effect of these two processes can be simulated by adding to the Hamiltonian of the solid an exchange Hamiltonian, Hx=-2Δεij′σ→i•σ→j=- 2(ΔεT+Δεx)ij′σ→i•σ→j, where Δε is a sum ΔεT (due to the tunneling process) and Δεx (due to the interaction process). A theory of the magnitude and sign of Δεx and ΔεT is given. We find ΔεT<0 and Δεx>0. Using quite general arguments, we show that |ΔεT|2|Δεx|. The exchange in bcc solid He3 is antiferromagnetic. Evaluation of the formulas for ΔεT and Δεx using the ground-state wave function of Guyer and Sarkissian leads to Δε=J, in good agreement with experiment. © 1969 The American Physical Society.