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Charged domain walls and boundaries in ferroelectric materials displaydistinct phenomena, such as an increased conductivity due to the accumulationof bound charges. Here, we report the electron microscopy observations ofatomic-scale arrangements at charged domain boundaries in the hybrid improperferroelectric Ca$_{2.46}$Sr$_{0.54}$Ti$_2$O$_7$. Like in the prototype improperferroelectric YMnO$_3$, we find that charged domain boundaries inCa$_{2.46}$Sr$_{0.54}$Ti$_2$O$_7$ correspond to out-of-phase boundaries, whichseparate adjacent domains with a fractional translational shift of the unitcell. In addition, our results show that strontium ions are located at chargeddomain boundaries. The out-of-phase boundary structure may decrease thepolarization charge at the boundary because of the ferrielectric nature ofCa$_{2.46}$Sr$_{0.54}$Ti$_2$O$_7$, thereby promoting the stabilization of thecharged state. By combining atomic-resolution imaging and density-functionaltheory calculations, this study proposes an unexplored stabilization mechanismof charged domain boundaries and structural defects accompanying out-of-phasetranslational shifts.

Charged domain boundaries stabilized by translational symmetry breaking in the hybrid improper ferroelectric Ca$_{3-x}$Sr$_x$Ti$_2$O$_7$