Imaging Spin Flows in Semiconductors Subject to Electric, Magnetic, and Strain Fields

Using scanning Kerr microscopy, we directly acquire two-dimensional images of spin-polarized electrons flowing laterally in bulk epilayers of $n:\mathrm{GaAs}$. Optical injection provides a local dc source of polarized electrons, whose subsequent drift and/or diffusion is controlled with electric, magnetic, and—in particular—strain fields. Spin precession induced by controlled uniaxial stress along the $⟨110⟩$ axes demonstrates the direct $\mathbf{k}$-linear spin-orbit coupling of electron spin to the shear (off diagonal) components of the strain tensor, ${ϵ}_{xy}$.

Figure 1

(a) $70\times 140\mu \mathrm{m}$ image of electron spin polarization in a $1\mu \mathrm{m}$ thick $n:\mathrm{GaAs}$ epilayer ($n_e={10}^{16}{\mathrm{cm}}^{-3}$) at 4 K, acquired via Kerr-rotation (KR) microscopy. A circularly polarized 1.58 eV laser focused to a $4\mu \mathrm{m}$ spot provides a local, dc source of spin-polarized electrons; this image indicates 2D spin diffusion. Inset: KR vs probe photon energy near the 1.515 eV GaAs band edge. (b) With $E=10\mathrm{V}/\mathrm{cm}$ lateral electrical bias, showing spin diffusion and drift. (c) Cross sections of spin flow vs bias; dotted line shows $5.5\mu \mathrm{m}$ resolution.

Figure 2

(a)–(c) $80\times 80\mu \mathrm{m}$ images of 2D spin flow ($E=10\mathrm{V}/\mathrm{cm}$) at 4 K, showing induced spin precession with increasing [110] uniaxial stress. (d) KR vs probe photon energy for the images, showing blueshift of GaAs band edge with stress. (e) Line cuts through the images. Inset: Spatial frequency of spin precession vs band edge shift.

Figure 3

(a)–(c) $80\times 80\mu \mathrm{m}$ images of 2D spin flow ($E=10\mathrm{V}/\mathrm{cm}$) at 4 K, with increasing applied magnetic field ${\mathbf{B}}_{\mathrm{app}}=3.5$, 9, and 32 G along $[1\overline{1}0]$. (d) Line cuts through the images. Inset: Line cuts through Figs. 2c (black) and 3c (red).

Figure 4

$50\times 50\mu \mathrm{m}$ images of 2D spin diffusion ($E=0$) at 4 K. (a) Stress, ${\mathbf{B}}_{\mathrm{app}}=0$. (b) $\mathrm{\text{Stress}}=0$, ${\mathbf{B}}_{\mathrm{app}}=16\mathrm{G}$ along $[1\overline{1}0]$ as shown. (c) ${\mathbf{B}}_{\mathrm{app}}=16\mathrm{G}$, with [110] uniaxial stress. Spins diffusing to the right precess; those diffusing to the left do not. Thus ${\mathbf{B}}_{ϵ}$ is chiral for radially diffusing spins (see diagram). (d)–(g) Keeping [110] stress, ${\mathbf{B}}_{\mathrm{app}}$ is rotated 180° in plane. (h) Stress is switched to $[1\overline{1}0]$, reversing ${\mathbf{B}}_{ϵ}$ chirality.

Figure 5

$50\times 80\mu \mathrm{m}$ images of 2D spin flow at 4 K with increasing $|\mathbf{k}|$ (current). (a–c) With [110] stress and ${\mathbf{B}}_{\mathrm{app}}=0$. Spatial period of precession is fixed. (d)–(f) $\mathrm{\text{Stress}}=0$, ${\mathbf{B}}_{\mathrm{app}}=6\mathrm{G}$; spatial period varies. Images (c’) and (f’) are simulations of (c) and (f), using the model described in text.