  Some correlated materials display an insulator-to-metal transition as the
temperature is increased. In most cases this transition can also be induced
electrically, resulting in volatile resistive switching due to the formation of
a conducting filament. While this phenomenon has attracted much attention due
to potential applications, many fundamental questions remain unaddressed. One
of them is its characteristic lengths: what sets the size of these filaments,
and how does this impact resistive switching properties. Here we use a
combination of wide-field and scattering-type scanning near-field optical
microscopies to characterize filament formation in NdNiO3 and SmNiO3 thin
films. We find a clear trend: smaller filaments increase the current density,
yielding sharper switching and a larger resistive drop. With the aid of
numerical simulations, we discuss the parameters controlling the filament width
and, hence, the switching properties.
