Intermediate-scale theory for electrons coupled to frustrated local moments

A classic route for destroying long-lived electronic quasiparticles in a weakly interacting Fermi liquid is to couple them to other low-energy degrees of freedom that effectively act as a bath. We consider here the problem of electrons scattering off the spin fluctuations of a geometrically frustrated antiferromagnet, whose nonlinear Landau-Lifshitz dynamics, which remains nontrivial at all temperatures, we model in detail. At intermediate temperatures and in the absence of any magnetic ordering, the fluctuating local moments lead to a nontrivial angular anisotropy of the scattering rate along the Fermi surface, which disappears with increasing temperature, elucidating the role of "hot spots." Over a remarkably broad window of intermediate and high temperatures, the electronic properties can be described by employing a local approximation for the dynamical spin response. This we contrast with the more familiar setup of electrons scattering off classical phonons, whose high-temperature limit differs fundamentally on account of their unbounded Hilbert space. We place our results in the context of layered magnetic delafossite compounds.