Berry Phase Theory of Anomalous Hall Effect: Application to Colossal Magnetoresistance Manganites

TL;DR

This paper explains the anomalous Hall effect in manganites as a Berry phase phenomenon caused by carrier hopping in complex spin backgrounds, matching experimental temperature-dependent behavior.

Contribution

It introduces a Berry phase-based theoretical framework for the anomalous Hall effect in manganites, linking spin textures to Hall conductivity.

Findings

Berry phase contribution increases with temperature up to T_{max}

The magnitude of AHE peaks at T_{max} > T_c

The temperature dependence follows a power-law decay

Abstract

We show that the Anomalous Hall Effect (AHE) observed in Colossal Magnetoresistance Manganites is a manifestation of Berry phase effects caused by carrier hopping in a non-trivial spin background. We determine the magnitude and temperature dependence of the Berry phase contribution to the AHE, finding that it increases rapidly in magnitude as the temperature is raised from zero through the magnetic transition temperature T_c, peaks at a temperature $T_{max} > T_c$ and decays as a power of T, in agreement with experimental data. We suggest that our theory may be relevant to the anomalous hall effect in conventional ferromagnets as well.