Nonlocal Kondo-exchange-driven intrinsic anomalous Hall effect in localized-$4f$ antiferromagnetic metals

The anomalous Hall effect in antiferromagnetic metals has attracted considerable attention. Most known realizations involve itinerant $d$ electrons that simultaneously mediate charge transport and magnetic order. Here, we focus on $f$-electron materials, where localized magnetic moments and conduction electrons are hosted in different orbitals. We develop a theoretical framework to describe the impact of localized antiferromagnetic order on itinerant electrons. Applying this approach to the recently discovered $4f$ antiferromagnetic metal $\mathrm{Ce}_{2}\mathrm{Cu}\mathrm{Ge}_{6}$, we identify the origin of both the intrinsic anomalous Hall conductivity and the spin splitting of the energy bands as spin-dependent intersite hopping induced by nonlocal Kondo exchange coupling, rather than a Zeeman-type effective field acting locally on the conduction electrons.