Spin-density induced by electromagnetic wave in two-dimensional electron gas

We consider the magnetic response of a two-dimensional electron gas (2DEG) with a spin-orbit interaction to a long-wave-length electromagnetic excitation. We observe that the transverse electric field creates spin polarization perpendicular to the 2DEG plane. The effect is more prominent in clean systems with resolved spin-orbit-split subbands, and reaches maximum when the frequency of the wave matches the subband splitting at the Fermi momentum. The relation of this effect to the spin-Hall effect is discussed. Spintronics is a fast developing field of research. While the spin-orbit effects in semiconductors have been discussed for a long time [1–3], recently discovered spin-Hall effect [4,5] has generated a lot of interest in applying spinorbit related effects to spintronics [6]. The promise of the spin-Hall effect is in the possibility of generation of non-equilibrium spin polarization by means of a DC electric field. However, after some discussions it was concluded that in two-dimensional electron gases with the Rashba and the Dresselhaus spin-orbit interactions, the spin-Hall effect vanishes for constant and homogeneous electric field [7–10]. At finite frequencies the spin-Hall effect is non-zero [8]. While for the homogeneous spin-Hall effect (uniform applied electric field) the out-of-plane spin polarization is expected to accumulate only at the edges of the sample [8], there is an alternative possibility that we propose to explore here: To create an out-of-plane inhomogeneous spin density in the bulk in response to a spatially-modulated field. Such bulk accumulation is free from the uncertainties associated with the charge and spin transport near the sample boundaries, and thus may provide an unambiguous method to detect the spin-Hall effect. A possible realization is shown in Fig. 1, and corresponds to a transverse electric field Ex changing in the y-direction. In the presence of the spin-Hall effect, the spin currents are expected to flow towards each other, with the spin density accumulating in the middle. From the Maxwell equation, rotE = −(1/c)Ḃ, a E E jspin spin density