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/τ due to nonmagnetic quenched disorder. Our most important result involves the temperature dependence of the single-particle relaxation rate in the ballistic limit τ²TϵF>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.