Interlayer Diffusion of Nuclear Spin Polarization in $\nu =2\mathrm{/}3$ Quantum Hall States

At the spin transition point of $\nu =2\mathrm{/}3$ 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 $15 \pm 7$nm$^2$/s.