Anomalous spin Josephson effect

Abstract

We report a theoretical study on the spin Josephson effect arising from the exchange coupling of the two ferromagnets (Fs), which are deposited on a two-dimensional (2D) time-reversal-invariant topological insulator. An anomalous spin supercurrent ${J}_{sz}\ensuremath{\sim}sin(\ensuremath{\alpha}+{\ensuremath{\alpha}}_{0})$ is found to flow in between the two Fs and the ground state of the system is not limited to the magnetically collinear configuration $(\ensuremath{\alpha}=n\ensuremath{\pi},n$ is an integer) but determined by a controllable angle ${\ensuremath{\alpha}}_{0}$, where $\ensuremath{\alpha}$ is the crossed angle between the two F magnetizations. The angle ${\ensuremath{\alpha}}_{0}$ is the dynamic phase of the electrons traveling in between the two Fs and can be controlled electrically by a gate voltage. This anomalous spin Josephson effect, similar to the conventional ${\ensuremath{\varphi}}_{0}$ superconductor junction, originates from the definite electron chirality of the helical edge states in the 2D topological insulator. These results indicate that the magnetic coupling in a topological system is different from the usual one in conventional materials.