Hysteresis and chaos in anomalous Josephson junctions without capacitance

Overdamped Josephson junctions usually do not exhibit chaotic behavior in their phase dynamics, either because the phase-space dimension is less than $3$ (as in the case of a single overdamped ac-driven junction) or due to the general tendency of systems to become less chaotic with increasing dissipation (as in the case of coupled overdamped junctions). Here we consider the so-called ${\ensuremath{\varphi}}_{0}$ superconductor/ferromagnet/superconductor Josephson junction in which the current flowing through the junction may induce magnetization dynamics in the ferromagnetic interlayer. We find that due to the induced magnetization dynamics, even in the overdamped limit (i.e., for a junction without capacitance), the junction may exhibit chaos and hysteresis that in some cases leads to multiple branches in its current-voltage characteristics. We also show that pulsed current signals can be used to switch between the different voltage states, even in the presence of added thermal noise. Such switching could be used in cryogenic memory components.