Spin current and rectification in Luttinger liquids

We demonstrate that spin current can be generated by an ac voltage in a one-channel quantum wire with strong repulsive electron interactions in the presence of a non-magnetic impurity and uniform static magnetic field. In a certain range of voltages, the spin current can exhibit a power dependence on the ac voltage bias with a negative exponent. The spin current expressed in units of $\mathrm{\hslash }\mathrm{/}2$ per second can become much larger than the charge current in units of the electron charge per second. The spin current generation requires neither spin-polarized particle injection nor time-dependent magnetic fields.