  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.
