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.
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