Electronic Relaxation Rates in Clean Metalic Ferromagnets

In clean metallic ferromagnets at asymptotically low temperature the magnon-exchange contribution to the single-particle and transport relaxation rates is exponentially suppressed due to the exchange gap [1]. The power-law prefactor of the exponential term is difficult to determine since the gap provides an energy scale in addition to the temperature. To answer this question we present an asymptotically exact evaluation of the Kubo formula. Our solution also clarifies the relation between the integral equation inherent in the Kubo formula and the Boltzmann equation.

[1] S. Bharadwaj, D. Belitz, and T.R. Kirkpatrick, Phys. Rev. B 89, 134401 (2014).