  Strongly correlated electron systems such as the rare-earth nickelates
(RNiO3, R = rare-earth element) can exhibit synapse-like continuous long term
potentiation and depression when gated with ionic liquids; exploiting the
extreme sensitivity of coupled charge, spin, orbital, and lattice degrees of
freedom to stoichiometry. We present experimental real-time, device-level
classical conditioning and unlearning using nickelate-based synaptic devices in
an electronic circuit compatible with both excitatory and inhibitory neurons.
We establish a physical model for the device behavior based on electric-field
driven coupled ionic-electronic diffusion that can be utilized for design of
more complex systems. We use the model to simulate a variety of associate and
non-associative learning mechanisms, as well as a feedforward recurrent network
for storing memory. Our circuit intuitively parallels biological neural
architectures, and it can be readily generalized to other forms of cellular
learning and extinction. The simulation of neural function with electronic
device analogues may provide insight into biological processes such as decision
making, learning and adaptation, while facilitating advanced parallel
information processing in hardware.
