Properties of Pb(Zr,Ti)O₃ ultrathin films under stress-free and open-circuit electrical boundary conditions

A first-principles-based scheme is developed to simulate properties of (001) PbO-terminated Pb(Zr$_{1-x}$Ti$_{x}$)O$_3$ thin films that are under stress-free and open-circuit boundary conditions. Their low-temperature spontaneous polarization never vanishes down to the minimal thickness, and continuously rotates between the in-plane <010> and <110> directions when varying the Ti composition around x=0.50. Such rotation dramatically enhances piezoelectricity and dielectricity. Furthermore, the order of some phase transitions changes when going from bulk to thin films.