# Ferromagnetic Anomalous Hall Effect in Cr-doped Bi$_2$Se$_3$ Thin Films via Surface-State Engineering

## TL;DR

This paper reports the successful induction of ferromagnetic anomalous Hall effect in Cr-doped Bi2Se3 thin films through surface-state engineering, revealing a sign behavior explained by Berry curvature calculations, advancing understanding of magnetic topological insulators.

## Contribution

It demonstrates a novel surface-state engineering approach to realize ferromagnetic AHE in Cr-doped Bi2Se3, previously unobserved in this material.

## Key findings

- Ferromagnetic AHE achieved in Cr-doped Bi2Se3 thin films.
- The AHE exhibits only positive slope regardless of carrier type.
- Berry curvature explains the sign behavior of the AHE.

## Abstract

The anomalous Hall effect (AHE) is a non-linear Hall effect appearing in magnetic conductors, boosted by internal magnetism beyond what is expected from the ordinary Hall effect. With the recent discovery of the quantized version of the AHE, the quantum anomalous Hall effect (QAHE), in Cr- or V-doped topological insulator (TI) (Sb,Bi)$_2$Te$_3$ thin films, the AHE in magnetic TIs has been attracting significant interest. However, one of the puzzles in this system has been that while Cr- or V-doped (Sb,Bi)$_2$Te$_3$ and V-doped Bi$_2$Se$_3$ exhibit AHE, Cr-doped Bi$_2$Se$_3$ has failed to exhibit even ferromagnetic AHE, the expected predecessor to the QAHE, though it is the first material predicted to exhibit the QAHE. Here, we have successfully implemented ferromagnetic AHE in Cr-doped Bi$_2$Se$_3$ thin films by utilizing a surface state engineering scheme. Surprisingly, the observed ferromagnetic AHE in the Cr-doped Bi$_2$Se$_3$ thin films exhibited only positive slope regardless of the carrier type. We show that this sign problem can be explained by the intrinsic Berry curvature of the system as calculated from a tight-binding model combined with a first-principles method.

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Source: https://tomesphere.com/paper/1905.01300