Electronic Spin Polarization around a Magnetic Impurity Using Perturbation Theory

Abstract

The electronic spin polarization $p\left(\mathcal{r}\right)$ arising from the $s-d$ exchange interaction is computed using iterated solutions of Nagaoka's truncated equations and direct perturbation theory. Most of our detailed calculations are only to order $J^2$ (where $J$ is the exchange constant). However, arguments are given to suggest that certain qualitative features [such as the oscillatory behavior of $p\left(\mathcal{r}\right)$] will remain even if we work to all orders in $J$. We critically discuss the work of Falk and Fullenbaum as well as Suhl, whose results agree with ours apart from the important difference that our Ruderman-Kittel-Kasuya-Yosida term is proportional to the average of an effective spin rather than the bare impurity spin. This effective spin also enters the static susceptibility $\chi$. In one of the Appendices, we briefly consider the effect of potential scattering on the spin polarization.