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 4π 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.
@article{arxiv.1206.1295,
title = {Fractional Spin Josephson Effect and Electrically Controlled Magnetization in Quantum Spin Hall Edges},
author = {Qinglei Meng and Vasudha Shivamoggi and Taylor L. Hughes and Matthew J. Gilbert and Smitha Vishveshwara},
journal= {arXiv preprint arXiv:1206.1295},
year = {2013}
}