DEPENDENCE OF THE RUDERMAN-KITTEL-KASUYA-YOSIDA INTERACTION ON NONMAGNETIC DISORDER

The influence of nonmagnetic disorder on the Ruderman-Kittel-Kasuya-Yo sida interaction of magnetic impurities diluted in a disordered metal is considered. Although the average value of the interaction is expone ntially suppressed at distances exceeding the mean free path, its root -mean-square (rms) value does not depend on the disorder parameter in the weak-disorder limit and is numerically larger than its amplitude i n pure metal. It is shown that with increase of the disorder the quant um interference corrections similar to those responsible for the weak- localization effects become important. These corrections do not change the power-law decay of all the even moments of the interaction, which remains the same as in the pure metal, but make the coefficients atta ched to these moments increase critically with the disorder. In the re gion where, due to the quantum corrections, the conductivity sigma dif fers considerably from its classical Drude value sigma0 so that sigma0 - sigma is similar to sigma, the 2sth moment of the interaction incre ases with disorder as (sigma0/sigma)8s2. As the higher moments increas e much faster than the variance, the rms value alone does not characte rize the interaction, in contrast to the weak-disorder limit where all the irreducible even moments of the interaction are of the same order of magnitude as an appropriate power of the variance. The interaction is characterized in this region by a very broad log-normal distributi on indicating that the fluctuations may become considerably larger tha n the typical value of the interaction. The present results have been obtained by extending the field-theoretical technique developed for tr eating mesoscopic conductance fluctuations to the treatment of thermod ynamic quantities, using the results of the one-loop renormalization-g roup analysis of the generalized nonlinear sigma model in two dimensio ns and 2 + epsilon expansion for the qualitative description in three dimensions. The limits of applicability of the present approach and th e relevance to experiments are discussed.