A Schrödinger equation is derived which allows an improvement in the wave function of a quantum crystal inside the tunneling duct for exchange. This equation is used to derive a simple estimate of the exchange rate accurate enough to be used to compare various exchange mechanisms (two-body, three-body cyclic, etc.). We find that the 3He bulk hcp crystal and 3He surface triangular crystals have their exchange dominated by three-body cyclic exchange. Therefore the dominant part of the spin Hamiltonian will be Heisenberg nearest neighbor ferromagnetic. This result explains the ferro-magnetic tendency observed in adsorbed 3He films. A ferromagnetic transition in hcp 3He at the lowest pressures is predicted at 0.05±0.01 mK, corresponding to a Curie-Weiss constant of 0.075 \+ -0.015 mK.
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Delrieu, J.M., Roger, M. & Hetherington, J.H. Exchange and magnetic order in HCP 3He and adsorbed 3He with triangular lattice. J Low Temp Phys 40, 71–87 (1980). https://doi.org/10.1007/BF00115983
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DOI: https://doi.org/10.1007/BF00115983