Nuclear magnetism of the two-dimensional solid He-3

Abstract

The multi-spin exchange interactions in the nuclear magnetism of solid He-3, which was formed into films by adsorption of He-3 on a graphite, have been studied. The effects of four-spin exchange interaction have been investigated. It was indicated that a quantum disordered ground state appears in the region where a competition of two-spin and four-spin exchanges is strong. For the case the four-spin exchange is dominant, a finite temperature phase transition was predicted due to chiral symmetry breaking. Critical phenomena of the chiral phase transition have been studied in the classical limit. Two-, three- and four-spin exchange interactions on the triangular lattice have been considered. Since the three-spin permutations can be written by two-spin exchanges, Hamiltonian was transformed and their parameter of J and K were discussed. The ground state of the Hamiltonian has been studied for various J with the mean-field approximation and four phases of ground states were obtained. The stability of chirality against quantum fluctuations has been investigated using the spin-wave approximation. It was shown that the tetrahedral phase is stable when the four-spin exchange is dominant. The chirality was pointed out to be an Ising-like variable and stable against the spin-wave fluctuations with long wave-length.

黒鉛上にHe-3を吸着させ薄膜状に形成した固体He-3の核磁気の多スピン交換相互作用を研究した。4-スピン交換相互作用の影響を検討した。2-スピンと4-スピン交換の競合が強い領域では、無秩序量子基底状態が現れることを指摘した。4-スピンが支配的な場合には、カイラル対称性の破壊による有限温度相転移になると予測した。カイラル相転移の臨界現象を古典的極限で研究した。3角格子上の2-、3-、4-スピン交換相互作用を考察した。3-スピン置換は2-スピン交換で書き換え可能なので、ハミルトニアンを変換し、そのパラメータJとKについて論じた。ハミルトニアンの基底状態を、種々のJについて平均場近似を用いて研究し、4種の基底状態の相を得た。量子のゆらぎに対するカイラリティの安定性をスピン波近似を用いて検討した。4-スピン交換が支配的なときには、正4面体相は安定していることが分かった。カイラリティはイジング様の変数であり、長波長によるスピン波のゆらぎに対して安定していることを指摘した。