Quantized Transport in Two-Dimensional Spin-Ordered Structures

TL;DR

This paper investigates the quantized transport phenomena in a 2D Kagome lattice model with spin textures, revealing a metal-insulator transition linked to spin canting angles and Berry phase effects.

Contribution

It explicitly derives the relationship between spin canting and Berry flux, and calculates conductivity quantization, connecting spin textures to topological transport in 2D systems.

Findings

Quantization of Hall conductivity derived from the model.

Existence of a metal-insulator transition as a function of spin canting angle.

Potential relevance to observable transitions in manganite and pyrochlore compounds.

Abstract

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 (2000). The relationship between the canting angle of the spin texture $\theta$ and the Berry phase field flux per triangular plaquette $\phi$ is derived explicitly and we emphasize the similarities between this model and Haldane's honeycomb lattice version of the quantum Hall effect (Haldane, 1988). The quantization of the transverse (Hall) conductivity $\sigma_{xy}$ is derived explicitly from the Kubo formula and a direct calculation of the longitudinal conductivity $\sigma_{xx}$ shows the existence of a metal-insulator transition as a function of the canting angle $\theta$ (or flux density $\phi$). 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.