An effective Hamiltonian scheme is used to reveal the properties of a multidomain structure in BiFeO${}_3$ consisting of alternating domains that are initially made of two phases, namely, $R3c$ (ferroelectric with antiphase oxygen octahedral tilting) versus $Pnma$ (antiferroelectric with in-phase and antiphase oxygen octahedral tiltings). These two types of domains dramatically modify their properties as a result of their cohabitation. The weak ferromagnetic vector and polarization rotate, and significantly change their magnitude, in the $R3c$-like region, while the $Pnma$-like region becomes polar along the direction of domain propagation. Moreover, the domain walls possess distinct polar and oxygen octahedral tilting patterns that facilitate the transition between these two regions. The studied multidomain is also predicted to exhibit other anomalous properties, such as its strain adopting several plateaus and steps when increasing the magnitude of an applied electric field.

• Received 9 March 2013

DOI:https://doi.org/10.1103/PhysRevB.88.134107