Electronic relaxation rates in metallic ferromagnets

Abstract

We show that the magnon-exchange contribution to the single-particle and transport relaxation rates in ferromagnetic metals, which determine the thermal and electrical conductivity, respectively, at asymptotically low temperature does not obey a power law as previously thought, but rather shows an exponential temperature dependence. The reason is the splitting of the conduction band that inevitably results from a nonzero magnetization. At higher temperatures there is a sizable temperature window where the transport rate shows a T 2 temperature dependence, in accord with prior results. This window is separated from the asymptotic regime by a temperature scale that is estimated to range from tens of mK to tens of K for typical ferromagnets. We motivate and derive a very general effective theory for metallic magnets that we then use to derive these results. Comparisons with existing experiments are discussed, and predictions for future experiments at low temperatures are made.

Generic non-Fermi-liquid behavior of the resistivity in magnets with ferromagnetic, helical, or skyrmionic order

“…This was noted before in Ref. 36 in the context of FMs. It is equally important for the HM cases discussed here, and it is the reason why the clean interband scattering rates have a stronger temperature dependence than the intraband ones, see Table I. It may not be obvious why the phase susceptibility in the skyrmionic case, Eq.…”

“…Shifting the momentum k by p and performing the p-integration yields Note the theta function, which leads to an exponentially small scattering rate at asymptotically low temperatures. 36 Weak disorder smears out the δ-function and we have, in the limit v F k λ and λτ 1,…”

Rigorous results for the electrical conductivity due to electron-phonon scattering

“…Remark 4.7 An explicit example is provided by ferromagnetic magnons, for which α = 2, β = 0, but the spectrum has a gap due to the exchange splitting T 0 . For |u| > T 0 one then has V ′′ 0 (u) ∝ sgn u [17,5]. The relaxation rates scale as Γ 0 ∼ T ln T , Γ 1 ∼ Γ 2 ∼ T 2 .…”

Anomalous Transport Behavior in Quantum Magnets

“…The behavior of both the electric and thermal resistivities in various temperature regimes was discussed in Ref. [15]. For helimagnets, the Goldstone modes and their contribution to the scattering rates were derived in Refs.…”

“…where v F is the Fermi velocity. The step function leads to the exponential suppression of the rates at asymptotically low temperatures mentioned above [15,37]. Weak disorder replaces the δ-function with a Lorentzian, and in the limit v F | k|/λ 1, λτ 0 1 the step function gets replaced by…”