Microscopic order parameters coupling at domain walls and its effect on macroscopic properties.

Domain and domain wall (DW) engineering provides an alternative model to tune the physical properties of materials, typically done via conventional materials chemistry. The interplay of coexisting non-ferroelectric structural order parameters, ferroelectric and magnetic order parameters at the DWs in hexagonal manganites provides a new pathway to determine macroscopic properties by tuning the DW characteristics [1]. Here, we report different types of domain structures and DW types associated with the crystal growth conditions in hexagonal manganites. We show that differences in the DW polar state manifest themselves as variations in the conductivity measured macroscopically. Piezo force microscopy and X-ray diffraction enables us to determine the plane of the DWs and hence, their strain state. The latter findings corroborate with the topographical study. Finally, these results show that DWs under strain lower the critical field of the magnetic phase transition compared to samples with strain-free DWs. This work represents the first example of non-local physical properties being determined by the presence of topographically protected DWs. [1] S. Artyukhin et al., Nat Mater \textbf{13} (2014)