  Memristors are considered key building blocks for the development of
neuromorphic computing hardware. For ferroelectric memristors with a
capacitor-like structure, the polarization direction modulates the height of
the Schottky barriers -- present at ferroelectric/metal interfaces -- that
control the device resistance. Here, we unveil the coexistence of multiple
memristive mechanisms in Pt/Ca:HfO$_2$/Pt devices fabricated on silicon by a
simple and effective low-toxicity chemical solution method. Depending on the
fabrication conditions, either dielectric or ferroelectric devices are
obtained, each one presenting a distinct memristive response. The devices are
forming-free and can sustain ferroelectric switching and memristive behavior
simultaneously. Aided by numerical simulations, we describe this behavior as a
competition of different mechanisms, including the effect of the ferroelectric
polarization on Schottky interfaces and oxygen vacancy electromigration.
Finally, we propose a simple learning algorithm for time-series recognition,
designed to take advantage of the resistance relaxations present in the case of
the ferroelectric devices.
