Ground State of a Pair of Localized Spins in Metals

概要

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The ground state of a pair of localized spins interacting with conduction electrons via an antiferromagnetic s-d interaction is investigated based on the Yosida theory. In the zeroth approximation of the theory it is shown by the approximation essentially equivalent to that employed by Sato and Nagaoka that two electrons added in the Fermi sphere to form a local singlet state occupy the two sorts of orbitals, which are obtained for one added electron to form the doublet state with the pair of spins. On the basis of this analysis, the doublet bound states are investigated in higher order approximations. In the absence of the exchange interaction -W(S_1・S_2) between two localized spins, the T-matrix is obtained within the logarithmic accuracy by using Abrikosov's method, which coincides with the closed-form expression by Sato and Nagaoka with W=0 from their calculation up to the third Born approximation. By the use of this T-matrix, closed-form solutions for doublet bound states are obtained for W=0, where two sorts of the doublet states are degenerate to each other with the binding energy equal to that for an isolated spin. It is pointed out that the R-dependence of T_K of the binding energy E^^~ comes from the spin-spin interaction W.
理論物理学刊行会の論文
1973-12-25