Interlayer diffusion of nuclear spin polarization in $\nu =\frac{2}{3}$ quantum Hall states

At the spin transition point of $\nu =2/3$ quantum Hall states, nuclear spins in a two-dimensional electron gas are polarized by an electric current. Using GaAs/AlGaAs double-quantum-well samples, we first observed the spatial diffusion of nuclear spin polarization between the two layers when the nuclear spin polarization is current induced in one layer. By numerical simulation, we estimated the diffusion constant of the nuclear spin polarization to be $15\pm 7{\mathrm{nm}}^2/\mathrm{s}$.

Figure 1

Plot of saturated magnetoresistance enhancements $\Delta R_{\mathrm{sat}}=R_{\mathrm{sat}}-R_0$ versus pumping currents. DNP in the front layer is pumped by currents $I$ for 60 min so that the magnetoresistances $R$ of both layers increase to saturated values. For currents less than 10 nA, a negligible change in $R$ is observed. For higher currents, $\Delta R_{\mathrm{sat}}$ of the front layer (solid squares, red) increases with the current, whereas, that of the back layer (open circles, blue) also increases, although there is no current flowing in the back layer.

Figure 2

Time evolution of the magnetoresistance enhancements of the front and back layers. In the first 1860 s, DNP in the front layer is pumped by a 20-nA current. The magnetoresistance enhancement of the front layer $\Delta R_{\mathrm{front}}$ (solid squares, red, left axis), increases immediately and quickly approaches a saturated value. However, that of the back layer $\Delta R_{\mathrm{back}}$ (open circles, blue, right axis) increases more slowly after a delay of about 190 s. At time $\tau =1860\mathrm{s}$, the current is set to zero. $\Delta R_{\mathrm{front}}$ drops immediately and quickly saturates to the original value. However, $\Delta R_{\mathrm{back}}$ exhibits a delay of about 250 s and a slow decrease. The enlarged figures in the insets illustrate the delayed response of $\Delta R_{\mathrm{back}}$ to $\Delta R_{\mathrm{front}}$.

Figure 3

Time evolution of the magnetoresistance enhancement of the back layer after the front layer is set in a $\nu =1.15$ Skyrmion lattice state. The magnetoresistance enhancement of the back layer decreases slowly toward zero with a time constant of 1900 s. (Inset) DNP in the front layer, showing how it disappears completely after 10 s.

Figure 4

Time evolution of the magnetoresistance enhancement of the back layer $\Delta R_{\mathrm{back}}$ after electrons in both layers are depleted. Without charge carriers, $\Delta R_{\mathrm{back}}$ decays very slowly because of spin-lattice interaction. The solid line shows the exponential fit. The time constant is $T_{d0}=18\times {10}^3\mathrm{s}$.

Figure 5

Simulation results (lines) fitted to measured magnetoresistance enhancements (squares and circles). (a) Fit to data of Fig. 2; estimated values of the parameters are $D=20{\mathrm{nm}}^2/\mathrm{s}$ and $T_p=10\mathrm{s}$. (b) Fit to data of Fig. 3; estimated value of the diffusion constant is $D=8{\mathrm{nm}}^2/\mathrm{s}$.