Quantized transport in two-dimensional spin-ordered structures

We study in detail the transport properties of a model of conducting electrons in the presence of double exchange between localized spins arranged on a 2D Kagome lattice, as introduced by Ohgushi, Murakami and Nagaosa. The relationship between the canting angle of the spin texture θ and the Berry phase field flux per triangular plaquette φ is derived explicitly and we emphasize the similarities between this model and Haldane's honeycomb lattice version of the quantum Hall effect. The quantization of the transverse (Hall) conductivity σ _xy is derived explicitly from the Kubo formula and a direct calculation of the longitudinal conductivity σ _xx shows the existence of a metal–insulator transition as a function of the canting angle θ (or flux density φ). This transition might be linked to that observable in the manganite compounds or in the pyrochlore ones, as the spin ordering changes from ferromagnetic to canted.