Spin Josephson effect at the quantum spin Hall edge

We study a spin Josephson effect in a ferromagnetic junction at the quantum spin Hall (QSH) edge. The helical nature of the QSH edge states has striking consequences for the transport properties of such a junction. We derive an expression for the spin current through the junction as a function of the change in magnetization, similar to the current-phase relation of a Josephson junction. We discuss the novel transport properties of the junction that result from fractionally charged excitations hosted by the QSH edge.