A macroscopic persistent current generation by merons in a spin density wave ordered state

We show that a stable spontaneous current appears in a system of a spin density wave order with merons, vortices in the spin configuration with winding number +1. A meron in the spin density wave order modifies the boundary condition for eigenfunctions around it to a sign-change one. As a consequence, two types of stable current states, one with a clockwise circulation and the other with a counterclockwise one, arise. When a magnetic field is present, one produces a diamagnetic current is chosen. A collection of such currents results in a large diamagnetic current; and if the meron density is sufficiently large, a perfect diamagnetism is realized. The stability of this diamagnetic current is attributed to the topological nature of the merons, and as long as the distribution of the merons remains the same the current will persist even in a macroscopic system.