Fractional Spin Josephson Effect and Electrically Controlled Magnetization in Quantum Spin Hall Edges

TL;DR

This paper investigates a fractional spin Josephson effect in topological insulator-based junctions, revealing a $4\,\pi$ periodic spin current with potential for electrical detection and control.

Contribution

It introduces the concept of a fractional spin Josephson effect mediated by bound states at topological insulator-ferromagnet interfaces, with detailed analysis of its properties and measurable consequences.

Findings

Discovery of a $4\pi$ periodic fractional spin Josephson effect.

Proposal of electrical measurement methods for the spin current.

Identification of a fractional AC spin-Josephson effect.

Abstract

We explore a spin Josephson effect in a system of two ferromagnets coupled by a tunnel junction formed of 2D time-reversal invariant topological insulators. In analogy with the more commonly studied instance of the Josephson effect for charge in superconductors, we investigate properties of the phase-coherent {\it spin} current resulting from the misalignment of the in-plane magnetization angles of the two ferromagnets. We show that the topological insulating barrier offers the exciting prospect of hosting a {\it fractional} spin Josephson effect mediated by bound states at the ferromagnet-topological insulator interface. We provide multiple perspectives to understand the $4\pi$ periodic nature of this effect. We discuss several measurable consequences, such as, the generation of a transverse voltage signal which allows for purely electrical measurements, an inverse of this effect where an applied voltage gives rise to a transverse spin-current, and a fractional AC spin-Josephson effect.