Theory of Helimagnons in Itinerant Quantum Systems III: Quasiparticle Description

In two previous papers we studied the problem of electronic properties in a system with long-ranged helimagnetic order caused by itinerant electrons. A standard many-fermion formalism was used. The calculations were quite tedious because different spin projections were coupled in the action, and because of the inhomogeneous nature of a system with long-ranged helimagnetic order. Here we introduce a canonical transformation that diagonalizes the action in spin space, and maps the problem onto a homogeneous fermion problem. This transformation to quasiparticle degrees of freedom greatly simplifies the calculations. We use the quasiparticle action to calculate single-particle properties, in particular the single-particle relaxation rate. We first reproduce our previous results for clean systems in a simpler fashion, and then study the much more complicated problem of three-dimensional itinerant helimagnets in the presence of an elastic relaxation rate 1/tau due to nonmagnetic quenched disorder. Our most important result involves the temperature dependence of the single-particle relaxation rate in the ballistic limit, tau^2 T\epsilon_F > 1, for which we find a linear temperature dependence. We show how this result is related to a similar result found in nonmagnetic two-dimensional disordered metals.