Scaling relation of the anomalous Hall effect in (Ga,Mn)As

TL;DR

This study investigates the anomalous Hall effect in (Ga,Mn)As across different conductivity regimes, revealing a universal scaling relation that aligns with a theoretical model and aids in determining hole concentrations.

Contribution

It establishes a universal scaling law for the anomalous Hall conductivity in (Ga,Mn)As, bridging high- and low-conductivity regimes and validating a theoretical framework.

Findings

Transition from Berry phase dominated behavior to a sigma_{xy}^(AH) ~ sigma_{xx}^{1.6} scaling in low-conductivity samples.

Universal scaling relation independent of growth conditions and material parameters.

Determination of hole diffusion constants in high-conductivity samples.

Abstract

We present magnetotransport studies performed on an extended set of (Ga,Mn)As samples at 4.2 K with longitudinal conductivities sigma_{xx} ranging from the low- to the high-conductivity regime. The anomalous Hall conductivity sigma_{xy}^(AH) is extracted from the measured longitudinal and Hall resistivities. A transition from sigma_{xy}^(AH)=20 Omega^{-1}cm^{-1} due to the Berry phase effect in the high-conductivity regime to a scaling relation sigma_{xy}^(AH) proportional to sigma_{xx}^{1.6} for low-conductivity samples is observed. This scaling relation is consistent with a recently developed unified theory of the anomalous Hall effect in the framework of the Keldysh formalism. It turns out to be independent of crystallographic orientation, growth conditions, Mn concentration, and strain, and can therefore be considered universal for low-conductivity (Ga,Mn)As. The relation plays a crucial role when deriving values of the hole concentration from magnetotransport measurements in low-conductivity (Ga,Mn)As. In addition, the hole diffusion constants for the high-conductivity samples are determined from the measured longitudinal conductivities.