# Anomalous Hall effect in 2$H$-phase transition-metal dichalcogenide monolayers on ferromagnetic substrates

## TL;DR

This paper investigates the anomalous Hall effect in monolayer transition-metal dichalcogenides influenced by ferromagnetic substrates, revealing how proximity-induced exchange fields and magnetization orientation affect Hall conductivity.

## Contribution

It demonstrates the impact of ferromagnetic proximity effects on the Hall effect in 2H-$MX_2$ monolayers and explores the sensitivity of Hall conductivity to magnetization tilting.

## Key findings

- Hall effect is prominent in the valence band with large spin splitting.
- Tilting magnetization affects Hall conductivity mainly on the electron side.
- In-plane magnetic fields induce Berry phase mixing in conduction bands.

## Abstract

We study the anomalous Hall effect in monolayers of transition-metal dichalcogenides 2H-$MX_2$ ($M$=Mo, W, and $X$=S, Se, Te) under a proximity effect of ferromagnetic substrate. If a proximity-induced exchange field is introduced, the spin-polarized energy bands in $K$ and $K'$ valleys are shifted in the opposite directions, and it causes the Hall effect by breaking time-reversal symmetry. The induced Hall effect is the most prominent in the valence band which has a large intrinsic spin splitting. Moreover, we find that tilting the magnetization from the perpendicular direction gives rise to a sensitive change in the Hall conductivity only in the electron side, and it is attributed to the mixing of the Berry phase by the in-plane field in the nearly degenerate conduction bands.