Anomalous Hall Effect and Skyrmion Number in Real and Momentum Spaces

Onoda Masaru, Tatara Gen, Nagaosa Naoto

doi:10.48550/arxiv.cond-mat/0405634

Anomalous Hall Effect and Skyrmion Number in Real and Momentum Spaces

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Onoda Masaru

Correlated Electron Research Center (CERC), National Institute of Advanced Industrial Science and Technology (AIST)
Tatara Gen

Graduate School of Science, Osaka University
Nagaosa Naoto

Correlated Electron Research Center (CERC), National Institute of Advanced Industrial Science and Technology (AIST) Department of Applied Physics, University of Tokyo

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説明

We study the anomalous Hall effect (AHE) for the double exchange model with the exchange coupling |J_H| being smaller than the bandwidth |t| for the purpose of clarifying the following unresolved and confusing issues: (i) the effect of the underlying lattice structure, (ii) the relation between AHE and the skyrmion number, (iii) the duality between real and momentum spaces, and (iv) the role of disorder scatterings; which is more essential, σ_H (Hall conductivity) or ρ_H (Hall resistivity)? Starting from a generic expression for σ_H, we resolve all these issues and classify the regimes in the parameter space of J_Hτ (τ: elastic scattering time) and λ_s (length scale of spin texture). There are two distinct mechanisms of AHE; one is characterized by the real-space skyrmion number and the other by the momentum-space skyrmion density at the Fermi level, which occur in different regimes of the parameter space.