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In a quantum Hall ferromagnet, the spin polarization of the two-dimensionalelectron system can be dynamically transferred to nuclear spins in its vicinitythrough the hyperfine interaction. The resulting nuclear field typically actsback locally, modifying the local electronic Zeeman energy. Here we report anon-local effect arising from the interplay between nuclear polarization andthe spatial structure of electronic domains in a $\nu=2/3$ fractional quantumHall state. In our experiments, we use a quantum point contact to locallycontrol and probe the domain structure of different spin configurationsemerging at the spin phase transition. Feedback between nuclear and electronicdegrees of freedom gives rise to memristive behavior, where electronictransport through the quantum point contact depends on the history of currentflow. We propose a model for this effect which suggests a novel route tostudying edge states in fractional quantum Hall systems and may account forso-far unexplained oscillatory electronic-transport features observed inprevious studies.

Non-local polarization feedback in a fractional quantum Hall ferromagnet