摘要
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) similar to sin(alpha + 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 (alpha = n pi, n is an integer) but determined by a controllable angle alpha(0), where alpha is the crossed angle between the two F magnetizations. The angle 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 phi(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.