Magnetic Field Effects in thes−dExchange Model of Dilute Magnetic Alloys

The effects of arbitrary external magnetic fields on the electronic properties of dilute magnetic alloys are calculated. Two-time thermodynamic Green's-function equations of motion are applied to the $s-d$ exchange model. We generalize Nagaoka's truncation procedure to finite field, conserving total angular momentum, and solve the resulting integral equations using the analytic properties of the Green's functions and a numerical procedure. We calculate the magnetoresistance, magnetization, and the spatial dependence of the conduction-electron spin polarization. The calculations have been performed using values of the model parameters corresponding to a Kondo temperature 16 °K and a $\mathrm{Cu}\mathrm{Fe}$ alloy system with an impurity spin of ½ and with equal conduction- and impurity-electron $g$ factors. Our results show a negative magnetoresistance qualitatively in agreement with experiment, but with the field effects somewhat overemphasized. It is found that there is no sizable contribution of the conduction electrons to the susceptibility, which is in agreement with the latest experimental results. Also, the apparent disappearance of the local moment with decreasing temperature is due to an increase in the spin correlation between conduction and impurity electrons, and not due to a spin-compensating electronic cloud forming about the impurity spin. For high temperatures and fields, significant effects of the exchange scattering still persist. There is a nonoscillating component in the conduction-electron spin polarization which damps out in what amounts to 10 lattice spacings for Cu. This is also in agreement with experiment in that no long-range nonoscillatory component has been detected by host NMR studies.