Theory of disordered itinerant ferromagnets. I. Metallic phase

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Abstract
A comprehensive theory for electronic transport in itinerant ferromagnets is developed. We first show that the Q-field theory used previously to describe a disordered Fermi liquid also has a saddle-point solution that describes a ferromagnet in a disordered Stoner approximation. We calculate transport coefficients and thermodynamic susceptibilities by expanding about the saddle point to Gaussian order. At this level, the theory generalizes previous random-phase-approximation-type theories by including quenched disorder. We then study soft-mode effects in the ferromagnetic state in a one-loop approximation. In three dimensions, we find that the spin waves induce a square-root frequency dependence of the conductivity, but not of the density of states, that is, qualitatively the same as the usual weak-localization effect induced by the diffusive soft modes. In contrast to the weak-localization anomaly, this effect persists also at nonzero temperatures. In two dimensions, however, the spin waves do not lead to a logarithmic frequency dependence. This explains experimental observations in thin ferromagnetic films, and it provides a basis for the construction of a simple effective-field theory for the transition from a ferromagnetic metal to a ferromagnetic insulator.