Theory of Anomalous Hall Effect in a Heavy fermion System with a Strong Anisotropic Crystal Field

TL;DR

This paper develops a theoretical framework for the anomalous Hall effect in heavy fermion systems with strong anisotropic crystal fields, revealing nearly isotropic anomalous Hall responses despite anisotropic magnetic susceptibilities.

Contribution

It introduces a generalized theory of the anomalous Hall effect accounting for anisotropic crystal fields in heavy fermion systems, extending previous models for ferromagnetic metals.

Findings

$R_H^{AHE}$ is nearly isotropic despite anisotropic susceptibility.

The theory generalizes the Karplus-Luttinger model for complex systems.

Experimental observations of isotropic AHE are explained by the theory.

Abstract

In a heavy fermion system, there exists the anomalous Hall effect caused by localized $f$-orbital freedom, in addition to the normal Hall effect due to the Lorentz force. In 1994, we found that the Hall coefficient caused by the anomalous Hall effect ($R_H^{AHE}$) is predominant and the relation $R_H^{AHE} \propto \rho^2$ ($\rho$ is the electrical resistivity) holds at low temperatures in many compounds. In this work, we study the system where the magnetic susceptibility is highly anisotropic due to the strong crystalline electric field on $f$-orbitals. Interestingly, we find that $R_H^{AHE}$ is nearly isotropic in general. This tendency is frequently observed experimentally, which has casted suspicion that the anomalous Hall effect may be irrelevant in real materials. Our theory corresponds to corrections and generalizations of the pioneering work on ferromagnetic metals by Karplus and Luttinger.