  Nuclear-spin diffusion in double quantum wells (QWs) is examined by using
dynamic nuclear polarization (DNP) at a Landau level filling factor $\nu=2/3$
spin phase transition (SPT). The longitudinal resistance increases during the
DNP of one of the two QW (the polarization QW) by means of a large applied
current and starts to decrease just after the termination of the DNP. On the
other hand, the longitudinal resistance of the other QW (the detection QW)
continuously increases for approximately 2h after the termination of the DNP of
the polarization QW. It is therefore concluded that the nuclear spins diffuse
from the polarization QW to the detection QW. The time evolution of the
longitudinal resistance of the polarization QW is explained mainly by the
nuclear-spin diffusion in the in-plane direction. In contrast, that of the
detection QW manifests much slower nuclear diffusion in the perpendicular
direction through the AlGaAs barrier.
