Systematic investigations of transient response of nuclear spins in the presence of polarized electrons

We electrically probed the transient response of nuclear spins in an $n$-GaAs channel by performing Hanle signal and spin-valve signal measurements on an all-electrical spin-injection device having a half-metallic spin source of $\mathrm{C}{\mathrm{o}}_2\mathrm{MnSi}$. Furthermore, we simulated the Hanle and spin-valve signals by using the time evolution of nuclear-spin polarization under the presence of polarized electron spins by taking both $T_{1\mathrm{e}}$ and $T_1$ into consideration, where $T_{1\mathrm{e}}^{-1}$ is the polarization rate of nuclear spins through the transfer of angular momentum from polarized electron spins and $T_1^{-1}$ is the depolarization rate of nuclear spins through the interaction with the lattice. The simulation results reproduced our experimental results on all the nuclear-spin-related phenomena appearing in the Hanle and spin-valve signals at different measurement conditions, providing quantitative explanation for the transient response of nuclear spins in GaAs to a change in magnetic fields and an estimate of the time scales of $T_{1\mathrm{e}}$ and $T_1$. These experimental and simulated results will deepen the understanding of nuclear-spin dynamics in semiconductors.

Figure 1

(a) Schematic device structure of an all-electrical spin-injection device and circuit configuration for nonlocal Hanle and spin-valve measurements, (b) measurement configurations for an oblique Hanle signal, and (c) for a spin-valve signal, where ${\mathbf{B}}_{\mathbf{ap}}$ is the applied magnetic field, $B_{\mathrm{st}}$ is the stray field from the ferromagnetic electrodes, ${\mathbf{S}}_{\mathbf{0}}$ is the injected electron spin, and φ is the oblique angle from the $z$ axis in the $x-z$ plane.

Figure 2

(a) Experimental initialization-time ($t_{\mathrm{hold}}$) dependence of oblique Hanle signals for $t_{\mathrm{hold}}$ ranging from 25 to 150 s at a sweep rate of $r=0.7\mathrm{mT}/\mathrm{s}$ and (b) corresponding simulation result. Each single curve shows the change in $V_{\mathrm{NL}}$ while sweeping the magnetic field from $B_{\mathrm{ap}}=+48\mathrm{to}-48\mathrm{mT}$.

Figure 3

(a) Simulation result for an oblique Hanle signal at a sweep rate ($r=0.7\mathrm{mT}/\mathrm{s}$) faster than that one required to bring nuclear spins to their equilibrium conditions and (b) a corresponding schematic vector diagram for the relative orientation of the injected electron spin ${\mathbf{S}}_{\mathbf{0}}$, magnetic field B, and nuclear field ${\mathbf{B}}_{\mathbf{n}}$.

Figure 4

(a) Experimental results of sweep rate ($r$) dependence of oblique Hanle signals for $r$ ranging from 0.7 to 0.2 mT/s for $t_{\mathrm{hold}}=100\mathrm{s}$ and (b) corresponding simulation result.

Figure 5

Comparison of a steady-state solution of $V_{\mathrm{NL}}$ and transient solutions for $r=0.1$ and 0.3 mT/s.

Figure 6

(a) Experimental results of the nonlocal spin-valve signal measured at 4.2 K for a fixed bias current $I_{\mathrm{bias}}=-40\mu \mathrm{A}$. (b) Closed circles show the spin-valve signal for positive sweep only along with (red curve) fit with simulation result for parallel configuration. (c) Schematic vector diagrams showing relative orientations of ${\mathbf{S}}_{\mathbf{0}}$, B, and ${\mathbf{B}}_{\mathbf{n}}$ in the spin-valve measurement. (d) $V_{\mathrm{NL}}$ as a function of time ($t$). Open circles show the experimental result and the red curve indicates the simulation after ${\mathbf{B}}_{\mathbf{ap}}$ was switched off at $t=160\mathrm{s}$.