Crossover from self-trapped bound states to perturbative scattering in the Heisenberg-Kondo lattice model

Abstract

We map out the complete transport phase diagram of the ferromagnetic Heisenberg-Kondo lattice model in two dimensions. The model involves tight-binding electrons with hopping $t$, coupled to classical spins with coupling $J'$, while the spins have a nearest neighbour coupling $J$ between them. We work with a fixed, small $J/t$, and study the temperature dependence of resistivity for varying electron density $n$ and coupling $J'/t$. Our magnetic configurations are generated by exact diagonalisation-based Langevin dynamics, while the conductivity is computed using the Kubo formula on exact eigenstates. We work on lattices of size $20 \times 20$ and can access electron density down to $n \sim 0.01$. The electron system remains homogeneous either when the mean density is large or when the coupling $J'$ is small. In these situations, the resistivity $\rho(T)$ displays a monotonic increase with temperature and can be understood within a perturbative framework. However, at very low density $n \lesssim 0.05$, strong coupling $J'/t \gtrsim 1$, and for $T \sim T_c$, the electrons can locally polarise the magnetic state, create a trapping potential, and form a bound state in it. The resistivity associated with this polaronic phase is distinctly non-monotonic, with a peak near $T_c$. We establish the boundary that separates the many-body polaronic window from traditional scattering and extract a universal form for the resistivity in the scattering regime. We suggest the origin of the `excess resistivity' in the polaronic regime in terms of an increasing fraction of localised states as the temperature tends to $T_c$. This pushes the mobility edge towards the chemical potential $\mu$ and results in enhanced scattering of momentum states near $k_F$. While our specific results are in two dimensions, the phenomenology we uncover should be valid even in three dimensions.