Measurement of Rashba and Dresselhaus spin–orbit magnetic fields

Spin–orbit coupling is a manifestation of special relativity. In the reference frame of a moving electron, electric fields transform into magnetic fields, which interact with the electron spin and lift the degeneracy of spin-up and spin-down states. In solid-state systems, the resulting spin–orbit fields are referred to as Dresselhaus and Rashba fields, depending on whether the electric fields originate from bulk or structure inversion asymmetry, respectively. Yet, it remains a challenge to determine the absolute value of both contributions in a single sample. Here, we show that both fields can be measured by optically monitoring the angular dependence of the electrons' spin precession on their direction of motion with respect to the crystal lattice. Furthermore, we demonstrate spin resonance induced by the spin–orbit fields. We apply our method to GaAs/InGaAs quantum-well electrons, but it should be universally useful to characterize spin–orbit interactions in semiconductors, and therefore could facilitate the design of spintronic devices.