  Ferroelectrics that are also ionic conductors offer possibilities for novel
applications with high tunability, especially if the same atomic species causes
both phenomena. In particular, at temperatures just below the Curie
temperature, polarized states may be sustainable as the mobile species is
driven in a controlled way over the energy barrier that governs ionic
conduction, resulting in unique control of the polarization. This possibility
was recently demonstrated in CuInP2S6, a layered ferroelectric ionic conductor
in which Cu ions cause both ferroelectricity and ionic conduction. Here, we
show that the commonly used approach to calculate the polarization of evolving
atomic configurations in ferroelectrics using the modern theory of
polarization, namely concerted (synchronous) migration of the displacing ions,
is not well suited to describe the polarization evolution as the Cu ions cross
the van der Waals gaps. We introduce an asynchronous Cu-migration scheme, which
reflects the physical process by which Cu ions migrate, resolves the
difficulties, and describes the polarization evolution both for normal
ferroelectric switching and for transitions across the van der Waals gaps,
providing a single framework to discuss ferroelectric ionic conductors.
