Translation domains differing in the phase but not in the orientation of the corresponding order parameter are resolved in two types of multiferroics. Hexagonal (h-) YMnO$_3$ is a split-order-parameter multiferroic in which commensurate ferroelectric
translation domains are resolved by piezoresponse force microscopy whereas MnWO$_4$ is a joint-order-parameter multiferroic in which incommensurate magnetic translation domains are observed by optical second harmonic generation. The pronounced manifestation of the generally rather hidden translation domains in these multiferroics and the associated drastic reduction of symmetry emphasize that the presence of translation domains must not be neglected when discussing the physical properties and functionalities of multiferroics.
We present a full analysis of the contrast mechanisms for the detection of ferroelectric domains on all faces of bulk single crystals using scanning force microscopy exemplified on hexagonally poled lithium niobate. The domain contrast can be attribu
ted to three different mechanisms: i) the thickness change of the sample due to an out-of-plane piezoelectric response (standard piezoresponse force microscopy), ii) the lateral displacement of the sample surface due to an in-plane piezoresponse, and iii) the electrostatic tip-sample interaction at the domain boundaries caused by surface charges on the crystallographic y- and z-faces. A careful analysis of the movement of the cantilever with respect to its orientation relative to the crystallographic axes of the sample allows a clear attribution of the observed domain contrast to the driving forces respectively.
