THEORETICAL STUDY OF EXCHANGE INTERACTION, PARTICULARLY, OF MULTIPLE-SPIN EXCHANGE INTERACTION.

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(1) I have successfully developed a method of calculating exchange interaction constants using the WKB method (the instanton method) and the numerical calculation. This method can make it possible to calculate the exchange constants much more precisely than ever within the WKB method. (2) I have first applied this method to the two-dimensional Wigner crystal and found that multiple-spin exchanges really work in this phase. I have also studied the effect of a magnetic field on the exchange processes and found that the field affects the exchange constants in a non-trivial way through the Aharanov-Bohm effect and can bring about a rich phase diagram of the two-dimensional Wigner crystal in a field. Spin exchange in a bilayer Wigner crystal phase is also studied, and it is found that the magnetic properties of this phase is welll described by the one-dimensional antiferriomagnetic Heisenberg model as long as the distance between the two layers is much smaller than the average interparticle distance. (3) The effect of the substrate potential on the exchange processes in the monolayer solid Helium 3 adsorbed on graphite is also studied using the WKB method. It is found that the substrate potential seriously affects the exchange processes in the dilute case, and brings about the density dependence of the exchange constants that is completely different from the dependence in the dense region.