Low-Temperature Spin Correlations about a Localized Magnetic Impurity Moment

The interaction of a localized impurity magnetic moment interacting with an electron gas by means of the $s-d$ exchange interaction leads to the Kondo spin-compensated state at low temperatures, in which the moment of the impurity is greatly reduced. We have examined the electron-spin-impurity-spin correlation function in the ground state of the Nagaoka theory as well as those of the singlet theories due to Heeger and Jensen and to Kondo and Appelbaum. It is shown that the dominant behavior of the spin correlation function is given by $\frac{\left({sin}^2{k}_{F}r\right)}{{\left(k_{F}r\right)}^2}$. It is also shown that the size of the spin-compensated state is characterized by a length $\xi$, which is inversely proportional to the energy parameter $T_K$ in the Nagaoka theory, and to the binding energy $\epsilon$ of the singlet states in the singlet theories.