As a relativistic quantum mechanical effect, it is shown that the electron field exerts a transverse force on an electron spin $1/2$ only if the electron is moving. The spin force, analogue to the Lorentz for an electron charge in a magnetic field, is perpendicular to the electric field and the spin current whose spin polarization is projected along the electric field. This spin-dependent force can be used to understand the Zitterbewegung of the electron wave packet with spin-orbit coupling and is relevant to the generation of the charge Hall effect driven by the spin current in semiconductors.

• Received 27 June 2005

DOI:https://doi.org/10.1103/PhysRevLett.95.187203