Exact solution of the linearized Boltzmann equation for the low-temperature resistivity in metallic ferromagnets.

In clean metallic ferromagnets at asymptotically low temperature, the magnon-exchange contribution to the electrical resistivity is exponentially suppressed due to the exchange gap [1]. The power-law prefactor of the exponential term is difficult to determine because the gap provides an energy scale in addition to the temperature. To solve this problem, we developed a technique for obtaining exact solutions to the linearized Boltzmann equation in the low-temperature limit. Our method dispenses with the various uncontrolled approximations that have been used in all previous solutions of the integral equations for the transport coefficients. We present a rigorous proof of Bloch's T^5 law due to electron-phonon scattering [2] and give the corresponding result for scattering by magnons [3]; the prefactor of the exponential is asymptotically independent of the temperature.

[1] S. Bharadwaj, D. Belitz, and T.R. Kirkpatrick, Phys. Rev. B 89, 134401 (2014).
[2] J. Amarel, D. Belitz, and T.R. Kirkpatrick, arXiv:2001.01148; arXiv:2009.03234
[3] J. Amarel, D. Belitz, and T.R. Kirkpatrick, arXiv:2009.02787