# Second-order nonlinear optical e GLYPH<11> ects of spin currents 

Jing Wang, 1,2 Bang-Fen Zhu, 2,3 and Ren-Bao Liu 1, GLYPH<3> 

$^{1}$Department of Physics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong, China 

$^{2}$Department of Physics, Tsinghua University, Beijing 100084, P.R.China 

$^{3}$Institute of Advanced Study, Tsinghua University, Beijing 100084, P.R.China 

## Abstract 

A pure spin current formed by opposite spins moving in opposite directions is a rank-2 axial tensor which breaks the inversion symmetry. Thus a spin current has a second-order optical susceptibility, with unique polarization-dependence determined by the symmetry properties of the current. In particular, a longitudinal spin current, in which the spin polarization directions are parallel or anti-parallel to the moving directions, being a chiral quantity, leads to a chiral sum-frequency e GLYPH<11> ect. Microscopic calculations based on the eight-band model of a III-V compound semiconductor confirm the symmetry analysis and show that the susceptibility is quite measurable under realistic conditions. The second-order nonlinear optical e GLYPH<11> ects may be used for in-situ and non-destructive detection of spin currents, as a standard spectroscopy tool in research of spintronics. 

PACS numbers: 72.25.Dc, 42.65.An, 78.20.Ls 

