The emergent behaviors in thin films of a multiaxial ferroelectric due to an electrochemical coupling between the rotating polarization and surface ions are explored within the framework of the 2-4 Landau-Ginzburg-Devonshire (LGD) thermodynamic potential combined with the Stephenson-Highland (SH) approach. The combined LGD-SH approach allows to describe the electrochemical switching and rotation of polarization vector in the multiaxial ferroelectric film covered by surface ions with a charge density dependent to the relative partial oxygen pressure. We calculate the phase diagrams and analyze the dependence of polarization components on the applied voltage, and discuss the peculiarities of quasi-static ferroelectric, dielectric and piezoelectric hysteresis loops in thin strained multiaxial ferroelectric films. The nonlinear surface screening by oxygen ions makes the diagrams very different from the known diagrams of e.g., strained BaTiO3 films. Quite unexpectedly we predict the appearance of the ferroelectric reentrant phases. Obtained results point on the possibility to control the appearance and features of ferroelectric, dielectric and piezoelectric hysteresis in multiaxial FE films covered by surface ions by varying their concentration via the partial oxygen pressure. The LGD-SH description of a multiaxial FE film can be further implemented within the Bayesian optimization framework, opening the pathway towards predictive materials optimization.
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