Frequency-dependent Hall effect in spintronic systems under zero magnetic field

It is shown that in an electronic system with finite Rashba coupling and in the absence of external magnetic field, the Hall resistivity (ρxy) is finite at both zero and finite frequencies. This Hall resistivity is determined by the reactive part (real part) of the inverse dielectric functions. This allows us to probe the real part of the dielectric function in a spintronic system by using a transport measurement.