  In a quantum Hall ferromagnet, the spin polarization of the two-dimensional
electron system can be dynamically transferred to nuclear spins in its vicinity
through the hyperfine interaction. The resulting nuclear field typically acts
back locally, modifying the local electronic Zeeman energy. Here we report a
non-local effect arising from the interplay between nuclear polarization and
the spatial structure of electronic domains in a $\nu=2/3$ fractional quantum
Hall state. In our experiments, we use a quantum point contact to locally
control and probe the domain structure of different spin configurations
emerging at the spin phase transition. Feedback between nuclear and electronic
degrees of freedom gives rise to memristive behavior, where electronic
transport through the quantum point contact depends on the history of current
flow. We propose a model for this effect which suggests a novel route to
studying edge states in fractional quantum Hall systems and may account for
so-far unexplained oscillatory electronic-transport features observed in
previous studies.
