Spin-excitation spectra and resistance minima in amorphous ferromagnetic alloys

Resistance minima have been found in recent years to occur in amorphous ferromagnetic alloys below the magnetic ordering temperature. Although a well-developed theory exists for resistance minima in very dilute alloys, the meaning of the phenomena has remained in question for alloys in which the neglect of spin-spin interactions is not justifiable. In this paper it is shown that the observation of resistance minima implies that these alloys have a finite density of near zero frequency excitations. Specifically, the theory of inverse transport coefficients, reformulated in terms of linear response, is used to derive a general expression for the resistivity due to the conduction-electron-spin interaction. Expanding perturbatively, the nth-order contribution is determined by an nth-order spin correlation function. To third order it is shown that the coefficient of the $\ln kT$ term responsible for the resistance anomaly according to the accepted Kondo theory receives contributions in the low-temperature limit only from those parts of the spin correlation functions which have frequencies less than $\frac{k{T}_K}{\hslash }$ where $T_K$ is the Kondo temperature.