Anomalous Hall effect in half-metallic Heusler compound Co$_{2}$Ti$X$ ($X$=Si, Ge)

TL;DR

This paper investigates the anomalous Hall effect in Co$_2$Ti$X$ (X=Si, Ge) Heusler compounds, revealing that intrinsic Berry curvature effects dominate their magneto-transport properties, with quadratic scaling of Hall resistivity.

Contribution

It provides the first detailed experimental analysis of the AHE in Co$_2$Ti$X$ compounds, highlighting the dominance of intrinsic Berry phase mechanisms over extrinsic effects.

Findings

Quadratic scaling of anomalous Hall resistivity with longitudinal resistivity.

Intrinsic Berry phase mechanism dominates the AHE in these compounds.

Experimental evidence supports the role of Weyl fermions and Berry curvature in magneto-transport.

Abstract

Though Weyl fermions have recently been observed in several materials with broken inversion symmetry, there are very few examples of such systems with broken time reversal symmetry. Various Co$_{2}$-based half-metallic ferromagnetic Heusler compounds are lately predicted to host Weyl type excitations in their band structure. These magnetic Heusler compounds with broken time reversal symmetry are expected to show a large momentum space Berry curvature, which introduces several exotic magneto-transport properties. In this report, we present systematic analysis of experimental results on anomalous Hall effect (AHE) in Co$_2$Ti$X$ ($X$=Si and Ge). This study is an attempt to understand the role of Berry curvature on AHE in Co$_2$Ti$X$ family of materials. The anomalous Hall resistivity is observed to scale quadratically with the longitudinal resistivity for both the compounds. The detailed analysis indicates that in anomalous Hall conductivity, the intrinsic Karplus-Luttinger Berry phase mechanism dominates over the extrinsic skew scattering and side-jump mechanism.