Experimentální pozorování spinového Hallova jevu v dvojrozměrných polovodičových systémech se spinově-orbitální vazbou

J. Wunderlich, B. Kaestner, J. Sinova, and T. Jungwirth

We report the experimental observation of the spin-Hall effect in a 2D hole system with spin-orbit coupling. The 2D hole layer is a part of a p-n junction light-emitting diode with a specially designed coplanar geometry which allows an angle-resolved polarization detection at opposite edges of the 2D hole system. Here we report the experimental observation of a new member of the Hall family—the spin-Hall effect (SHE) [1].

While predictions of the spin-Hall effect were reported, within different physical contexts, experimentally, it has been elusive because in nonmagnetic systems the transverse spin currents do not lead to net charge imbalance across the sample, precluding the simple electrical measurement. To demonstrate the spin-Hall effect, we have developed a novel p-n junction light-emitting diode (LED) microdevice that couples two-dimensional hole and electron doped systems.

Fig. 1. The schematic cross section of the coplanar p-n junction LED device. At forward bias of order of the GaAs band gap, electrons move from the 2DEG to the 2DHG where they recombine. The highest intensity of the emitted light is in the p region near the junction step edge.

Fig. 2. Numerical simulations of the conduction and valence band profiles along the ⟨001⟩ growth direction (z axis) in the unetched part of the wafer near the step edge. Black lines correspond to an unbiased p-n junction and red lines to a forward bias of 1.5 V across the junction. In the detailed image of the upper (AlGa)As/GaAs interface (with the conduction band shifted down in energy for clarity), we indicated possible sub-GaAs-gap radiative recombinations with the 2DHG involving either 3D electrons in the conduction band (red arrow) or impurity states (black arrow). The black line corresponds to unbiased wafer 1 and the blue line to wafer 2.

The detection of spin-polarization phenomena is done by measuring circular polarization (CP) of the light. A finite CP along a given direction of the propagating light indicates a finite spinpolarization in this direction of carriers involved in the recombination.
In the SHE, nonzero ⟨s_z⟩ occurs as a response to external electric field and the carries with opposite spins are deflected to opposite edges of the sample parallel to the SHE driving electrical current. A microdevice that allows us to induce and detect such a response is shown in Fig. 3(a).
The occurrence of the SHE upon applying I_p is demonstrated in Fig. 3(b). To highlight the consistency of the signal with the unique SHE phenomenology, we compare in Fig. 3(c) CPs obtained in experiment where I_p was fixed and either LED 1 or LED 2 was activated.

Fig. 3. The SHE experiment. (a) Scanning electron microscopy image of the SHE LED device. The top (LED 1) or bottom (LED 2) n contacts are used to measure the EL at opposite edges of the 2DHG p channel parallel to the SHE driving current I_p. (b) Polarization along z axis measured with active LED 1 for two opposite I_p current orientations. Spectral region of peak B of the high bias EL curve of wafer 1 is shown. Nonzero and opposite out-of-plane polarization for the two I_p orientations demonstrates the SHE. (c) Polarization along z axis measured with fixed I_p current and for biased LED 1 or LED 2. The data show opposite polarizations at opposite edges of the 2DHG channel confirming the SHE origin of the measured signal. (d) Theoretical intrinsic SHE conductivity in units of e/8π versus quasiparticle lifetime broadening and 2D hole density. Parameters corresponding to our 2DHG, indicated by a white dot, fall into the strong intrinsic SHE part of the theoretical diagram.

To stimulate a detailed microscopic analysis of the observed SHE, including the discussion of the role of disorder, we present in Fig. 3(d) Kubo formula calculations for wafer 1 of the spin-Hall conductivity, σ_SH, which is derived directly from spin-orbit coupled band structure and approaches a disorder independent value in high mobility systems.

[1] J. Wunderlich, B. Kaestner, J. Sinova, and T. Jungwirth: Experimental Observation of the Spin-Hall Effect in a Two-Dimensional Spin-Orbit Coupled Semiconductor System, Phys. Rev. Lett. 94, 047204 (2005), doi: 10.1103/PhysRevLett.94.047204.