Linear magnetization dependence of the intrinsic anomalous Hall effect

TL;DR

This study combines experimental measurements and first-principles calculations to show that the intrinsic anomalous Hall conductivity in Mn$_5$Ge$_3$ thin films varies linearly with magnetization, aligning well across a range of temperatures.

Contribution

It demonstrates a clear linear relationship between intrinsic anomalous Hall conductivity and magnetization, supported by both experimental data and theoretical calculations.

Findings

Intrinsic anomalous Hall conductivity depends linearly on magnetization.

Good quantitative agreement between theory and experiment up to 240 K.

Separation of intrinsic and extrinsic contributions to the anomalous Hall effect.

Abstract

The anomalous Hall effect is investigated experimentally and theoretically for ferromagnetic thin films of Mn$_5$Ge$_3$. We have separated the intrinsic and extrinsic contributions to the experimental anomalous Hall effect, and calculated the intrinsic anomalous Hall conductivity from the Berry curvature of the Bloch states using first-principles methods. The intrinsic anomalous Hall conductivity depends linearly on the magnetization, which can be understood from the long wavelength fluctuations of the spin orientation at finite temperatures. The quantitative agreement between theory and experiment is remarkably good, not only near 0 K, but also at finite temperatures, up to about ~ 240 K (0.8 T$_C$})