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 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 ). 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.