Concentration Dependence of the Phase Shifts for Ordinary Scattering in Dilute Magnetic Alloys

It has recently been shown by us that the variation of the Kondo slopes d with the solute concentration c in dilute magnetic alloys is somewhat similar to the variation of the function f (= cos(6) eta cos 2 eta) with the phase shift t 1 for ordinary scattering, and that the variation of the extremum value S m of the thermoelectric power in these alloys with c is akin to the variation of the function f'(= cos(6) eta cos 2 eta) with eta. It is shown in the present paper that the temperature-independent (residual) component of the electrical resistivity per solute at. % in these alloys varies with c in a manner similar to that of the function f ''[= cos(4) eta(1-4 sin(2) eta)] with eta. We thus feel justified in considering the increasing mutual interactions between the magnetic solute ions, consequent upon the increase of c, in terms of an effective increase of eta. This is as if each impurity ion, on increasing c, effectively offers an increasing attractive potential to the conduction electrons. In such a case, introduction of more and more lattice defects into a dilute magnetic alloy having a given solute content should approximate the alloy more and more to the model of isolated impurity scattering, implicit in the theoretical discussions. The detailed measurements by Korn on the electrical resistivity and by Wiebking on the TEP of dilute magnetic alloy films in the quench-condensed and annealed states conform to our expectations based on such a picture. The variation of the relative depth of the resistance minimum due to changing the iron and tin contents in the dilute alloy system Cu-Fe-Sn can be understood if one assigns a net negative phase shift for ordinary scattering.