Memristive devices whose resistance can be hysteretically switched by electric field or current are intensely pursued both for fundamental interest as well as potential applications in neuromorphic computing and phase-change memory. When the underlying material exhibits additional charge or spin order, the resistive states can be directly coupled, further allowing for electrical control of the collective phases. Here, we report the observation of abrupt, memristive switching of tunneling current in nanoscale junctions of ultrathin CrI$_3$, a natural layer antiferromagnet. The coupling to spin order enables both tuning of the resistance hysteresis by magnetic field, and electric-field switching of magnetization even in multilayer samples.
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