Effects of temperature and electric field on order parameters in ferroelectric hexagonal manganites

Abstract

In Landau-Devonshire phase transition theory, the order parameter represents a unique property for a disorder-order transition at the critical temperature. Nevertheless, for a phase transition with more than one order parameter, such behaviors can be quite different and system-dependent in many cases. In this work, we investigate the temperature (T) and electric field (E) dependence of the two order parameters in improper ferroelectric hexagonal manganites, addressing the phase transition from the high-symmetry P63/mmc structure to the polar P63cm structure. It is revealed that the trimerization as the primary order parameter with two components: the trimerization amplitude Q and phase Φ, and the spontaneous polarization P emerging as the secondary order parameter exhibit quite different stability behaviors against various T and E. The critical exponents for the two parameters Q and P are 1/2 and 3/2, respectively. As temperature increases, the window for the electric field E enduring the trimerization state will shrink. An electric field will break the Z2 part of the Z2×Z3 symmetry. The present work may shed light on the complexity of the vortex-antivortex domain structure evolution near the phase transition temperature.