Quantized Transport in Two-Dimensional Spin-Ordered Structures

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 $\varphi$ 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 $\varphi$). 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.

17 pages, 12 figures

References in corpus (5)

• Spin Anisotropy and Quantum Hall Effect in the Kagome Lattice - Chiral Spin State based on a Ferromagnet-
• Electronic Hamiltonian for Transition Metal Oxide Compounds
• Delocalization of 2D Dirac Fermions: the Role of a Broken Supersymmetry
• Scaling Behavior and Universality near the Quantum Hall Transition
• Is the Peak Value of ${\sigma }_{xx}$ at the Quantum Hall Transition Universal?

Cited by in corpus (4)

• Kagome Lattice from Exciton-Polariton Perspective
• Valley symmetry breaking and gap tuning in graphene by spin doping
• Control of valley optical conductivity and topological phases in buckled hexagonal lattice by orientation of in-plane magnetic field
• Circular edge states in photonic crystals with a Dirac node