Second-order nonlinear optical effects of spin currents.

Pure spin currents carry information in spintronics and signify novel quantum spin phenomena such as topological insulators. Measuring pure spin currents, however, is difficult since they have no direct electromagnetic induction. Noticing that a longitudinal spin current, in which electrons move along their spin directions, is a chiral quantity, we envisage that it has a chiral sum-frequency optical effect. A systematic symmetry analysis confirms this idea and reveals the second-order optical effects of general spin currents with unique polarization dependence. Microscopic calculations based on the eight-band model of III-V compound semiconductors show that the susceptibility is sizable under realistic conditions. These findings form a basis for "seeing" spin currents where and while they flow with standard nonlinear optical spectroscopy, providing a toolbox to explore a wealth of physics connecting spins and photons.