  Active memristor elements, also called neuristors, are self-oscillating
devices that are very good approximations to biological neuronal functionality
and are crucial to the development of low-power neuromorphic hardware.
Materials that show conduction mechanisms that depend superlinearly with
temperature can lead to negative differential resistance (NDR) regimes, which
may further be engineered as self-oscillators. Thermal runaway, insulator to
metal phase transitions (IMT) can lead to such superlinearity and are being
extensively studied in systems such as TaO$_x$, NbO$_x$ and VO$_2$. However,
ReNiO$_3$ systems that offer large tunability in metal-insulator transition
temperatures are less explored so far. Here we demonstrate all-or-nothing
neuron-like self-oscillations at MHz frequency and low temperatures on thin
films of NdNiO$_3$, a model charge transfer insulator, and their frequency
coding behavior. We study the temperature dependence of NDR and show that it
vanishes even at temperatures below the IMT temperature. We also show that the
threshold voltages scale with device size and that a simple electrothermal
device model captures all these salient features. In contrast to existing
models, our model correctly predicts the independence of oscillation amplitude
with the applied voltage, offering crucial insights about the nature of fixed
points in the NDR region, and the dynamics of non-linear oscillations about
them. KEYWORDS: NDR, oscillations, thermal model.
