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.

Figure 1

The static structure factor $\mathcal{S}\left(\mathit{q}\right)$ over the Brillouin zone for (a) $T=J$, and (b) $T=10J$, respectively. (c) $\mathcal{S}(\mathit{q},\omega )$ over a momentum cut $K\to \mathrm{\Gamma }\to M\to X$, at $T=3J$. (d) The momentum-integrated structure factor for selected temperatures, together with the fit in Eq. (4).

Figure 2

The numerically evaluated electron self-energy ${\mathrm{\Sigma }}_{k_F}^{″}(0,T)$ (a) along the Fermi surface at $T=J$, and (b) for different $\theta$ along the Fermi surface as a function of temperature. Inset: The spin correlation length $\xi \left(T\right)$ extracted from $\mathcal{S}\left(\mathit{q}\right)$. (c), (d) With increasing temperature, ${\mathrm{\Sigma }}_{k_F}^{″}(q_{\perp },\omega )$ becomes featureless as a function of both $\omega$ and $q_{\perp }$.

Figure 3

(a) Frequency dependence of the self-energy at different angles along the Fermi surface with increasing temperature. (b) The function $h(\cdots )$ constructed out of the electron self-energy [Eq. (10)] exhibits a scaling collapse on a universal momentum-independent curve $\varphi (\omega ,\alpha \beta J)$ over a wide range of $T$, angle around the Fermi surface, and $q_{\perp }$.