Translation domains in multiferroics

We describe the behavior of translation domains that is domains resulting from the breaking of translation rather than point symmetries in multiferroics with simultaneous magnetic and ferroelectric order. First, we review the structure of order parameters describing translation domains. Then, we report our spatially resolved measurements of translation domains using piezoresponse force microscopy and optical second harmonic generation in two types of multiferroics. In the split-order-parameter multiferroic hexagonal YMnO3, we show that commensurate structural translation domains are rigidly coupled to the ferroelectric orientation domains so that the orientation domains adopt the translation domain structure. In contrast, in the joint-order-parameter multiferroic MnWO4, incommensurate magnetic translation domains are largely decoupled from the ferroelectric orientation but nevertheless limited by stability criteria. These pronounced manifestations of the generally hidden translation domains emphasize that their presence should be taken into account when discussing the physical properties and functionalities of multiferroics.