  We report on spatially resolved measurements of the spin-orbit effective
magnetic field in a GaAs/InGaAs quantum-well. Biased gate electrodes lead to an
electric-field distribution in which the quantum-well electrons move according
to the local orientation and magnitude of the electric field. This motion
induces Rashba and Dresselhaus effective magnetic fields. The projection of the
sum of these fields onto an external magnetic field is monitored locally by
measuring the electron spin-precession frequency using time-resolved Faraday
rotation. A comparison with simulations shows good agreement with the
experimental data.
