Control of spin relaxation anisotropy by spin-orbit-coupled diffusive spin motion

Spatiotemporal spin dynamics under spin-orbit interaction is investigated in a (001) GaAs two-dimensional electron gas using magneto-optical Kerr rotation microscopy. Spin-polarized electrons are diffused away from the excited position, resulting in spin precession because of the diffusion-induced spin-orbit field. Near the cancellation between the spin-orbit field and the external magnetic field, the induced spin precession frequency depends nonlinearly on the diffusion velocity, which is unexpected from the conventional linear relation between the spin-orbit field and the electron velocity. This behavior originates from an enhancement of the spin relaxation anisotropy by the electron velocity perpendicular to the diffused direction. We demonstrate that the spin relaxation anisotropy, which has been regarded as a material constant, can be controlled via diffusive electron motion.

Figure 1

(a) Sketch of a pump-probe scanning Kerr microscopy setup with Rashba $\left({\mathit{\Omega }}_{\mathrm{R}}\right)$, Dresselhaus (${\mathit{\Omega }}_{\mathrm{D}}$), and external magnetic fields (${\mathit{\Omega }}_{\mathrm{ex},x}$ and ${\mathit{\Omega }}_{\mathrm{ex},y}$) as precession vectors for $y$- and $x$-scan configurations, respectively. (b) Measured $s_z$ at different $x$ positions highlighted as colored circles in (a).

Figure 2

Measured spin precession frequency $|{\mathrm{\Omega }}_{\mathrm{meas}}|$ obtained for different ${\sigma }_{\mathrm{eff}}$'s and ${\mathit{B}}_{\mathrm{ex}}$'s and for scans of the pump-probe separation along (a) $x$ and (b) $y$. All symbols represent experimental data. All solid lines show linear fits. The dashed lines in (a) correspond to the nonlinear fits based on Eq. (3) with ${\mathrm{\Gamma }}_{\mathrm{at}}=-0.076\mathrm{GHz}$.

Figure 3

Maps of Kerr signal $s_z$ gathered along time $t$ and spactial displacement $x$ for experimental results (a) with ${\sigma }_{\mathrm{eff}}=5.6\mu \mathrm{m},B_y=-0.4\mathrm{T}$ and (d) with ${\sigma }_{\mathrm{eff}}=9.8\mu \mathrm{m},B_y=0.45\mathrm{T}$. Corresponding Monte Carlo simulations in (b) and (e) using experimentally determined SO coefficients and spot size. (c) and (f) show the line cut of $s_z$ at around $x=-8.7$ and $x=17.2\mu \mathrm{m}$ indicated by dashed lines in the maps. The diamonds represent data from experiment, whereas solids are from Monte Carlo simulation.

Figure 4

(a) $x$-scan configuration where the probe center is separated by a vector $(x,0)$ from the pump center (0,0). Electron trajectories exist with an average velocity that is tilted from the $x$ axis, contrary to the macroscopic diffusion velocity [Eq. (2)]. (b) Mean velocity components of horizontal and vertical directions $v_{\mathrm{h}}^{\pm }$ and $v_{\mathrm{v}}^{\pm }$. (c) Calculated $v_{\mathrm{h}}^{\pm },v_{\mathrm{v}}^{\pm }$ based on Eqs. (7) and (8).

Figure 5

(a) Calculated anisotropy term ${\mathrm{\Gamma }}_{\mathrm{at}}^{x,y}$ for the (a) $x$ scan and the (b) $y$ scan as obtained from using Eq. (9). Both ${\mathrm{\Gamma }}_{\mathrm{at}}^{x,y}$'s are modulated by $r$.

Figure 6

The frequency analysis is shown for $x$ scans for (a) ${\sigma }_{\mathrm{eff}}=5.6\mu \mathrm{m}$ at $B_y=-0.4\mathrm{T}$ and for (b) ${\sigma }_{\mathrm{eff}}=8.1\mu \mathrm{m}$ at $B_y=0.45\mathrm{T}$. All solid lines are ${\mathrm{\Omega }}_y^{*}$ calculated with new ${\mathrm{\Gamma }}_{\mathrm{at}}^x$, and dashed lines are with the conventional anisotropic term $-{\mathrm{\Gamma }}_y/2=-0.076\mathrm{GHz}$. (c) MC simulated time-space records of $s_z$ in a $y$ scan with ${\sigma }_{\mathrm{eff}}=5.6\mu \mathrm{m},B_x=0.4\mathrm{T}$, and $g=-0.268$: the solid line shows ${\mathrm{\Omega }}_x^{*}$ with new ${\mathrm{\Gamma }}_{\mathrm{at}}^y$; the dashed line is obtained with the conventional value of $-{\mathrm{\Gamma }}_x/2=-0.99\mathrm{GHz}$. The gray diamond is the extracted frequency from the (d) time evolution of $s_z$ at $y=-18.2\mu \mathrm{m}$ with the MC simulation (red solid) and the fitted curve (dotted black).