NEW CALCULATION OF MAGNETIC SUSCEPTIBILITY FOR TAKANO-OGAWA THEORY OF KONDOS EFFECT IN DILUTE ALLOYS

We have reexamined the Takano-Ogawa theory of Kondo's effect between a localized spin and conduction electrons in metals. We find the results of their analysis to be incorrect above zero temperature because of improper evaluation of the integrals vn=-DDn(22)2f()d. We obtain new solutions for vn by not imposing the limit T0°K, D. This results in a new expression for the magnetic susceptibility which no longer diverges at the critical temperature TK: =(B2kT){1-(2)invcot[kT(T)]}, assuming antiferromagnetic coupling and J1. At T=0°K, =(5.4)(B2kTK). In the intermediate temperature range,(T)kT<TK, the susceptibility obeys a Curie-Weiss law with a negative Curie temperature (2)[(T)k] which decreases to zero as the temperature increases to TK. The effective moment (kT)12 increases from zero to its free value as the temperature increases from T=0°K to TK. Above TK the system exhibits free spin behavior. The impurity contribution to the resistivity is given by R=(2m*ne2){1+13[kT(T)]2}-1, which agrees with Nagaoka's result at low temperatures. Near TK the resistivity decreases with increasing temperature as [ln(TTK)]2. © 1968 The American Physical Society.