Berry phase mechanism of the anomalous Hall effect in a disordered two-dimensional magnetic semiconductor structure.

L N Oveshnikov,B A Aronzon,K I Kugel,V A Kulbachinskii,A B Davydov,V Tripathi,N S Averkiev,I V Rozhansky

doi:10.1038/srep17158

Abstract

The anomalous Hall effect (AHE) arises from the interplay of spin-orbit interactions and ferromagnetic order and is a potentially useful probe of electron spin polarization, especially in nanoscale systems where direct measurement is not feasible. While AHE is rather well-understood in metallic ferromagnets, much less is known about the relevance of different physical mechanisms governing AHE in insulators. As ferromagnetic insulators, but not metals, lend themselves to gate-control of electron spin polarization, understanding AHE in the insulating state is valuable from the point of view of spintronic applications. Among the mechanisms proposed in the literature for AHE in insulators, the one related to a geometric (Berry) phase effect has been elusive in past studies. The recent discovery of quantized AHE in magnetically doped topological insulators - essentially a Berry phase effect - provides strong additional motivation to undertake more careful search for geometric phase effects in AHE in the magnetic semiconductors. Here we report our experiments on the temperature and magnetic field dependences of AHE in insulating, strongly-disordered two-dimensional Mn delta-doped semiconductor heterostructures in the hopping regime. In particular, it is shown that at sufficiently low temperatures, the mechanism of AHE related to the Berry phase is favoured.

Highlights

The dominant mechanisms governing anomalous Hall effect (AHE) in different parameter regimes
The quantized AHE is the result of two-dimensionality and strong spin-orbit coupling in the topological insulator and is directly related to the quantization of the geometric flux accumulated by Bloch states around the Brillouin zone, analogous to the quantized ordinary Hall effect[10]
We have performed a detailed experimental study of AHE in strongly-disordered insulating 2D semiconductor heterostructures consisting of a quantum well spatially separated from a layer of Mn-dopants that is the source of ferromagnetism

Summary

Introduction

An intriguing mechanism of AHE proposed for disordered ferromagnetic insulators[8], involving a subtle quantum interference of triads of misaligned spin states on the dominant conducting paths, has proved very difficult to confirm. Such a purely geometrical quantum interference effect is an instance of the well-known Berry-Pancharatnam phase. While the Berry phase mechanism of AHE has eluded detection in ferromagnetic semiconductors in the insulating state, it has seen spectacular confirmation in other insulating systems with simultaneous presence of ferromagnetic polarization and strong spin-orbit coupling. We find that at higher temperatures, AHE is governed by an alternative mechanism based on a spin-dependent hopping of 2D holes in a quantum well (QW) interacting with remote magnetic layer, which has been predicted[7] and observed[12] for bulk magnetic semiconductors

Methods

Results

Conclusion