The third dimension of ferroelectric domain walls

Ferroelectric domain walls are quasi-2D systems that show great promise for the development of non-volatile memory, memristor technology and electronic components with ultra-small feature size. Electric fields, for example, can change the domain wall orientation relative to the spontaneous polarization and switch between resistive and conductive states, controlling the electrical current. Being embedded in a 3D material, however, the domain walls are not perfectly flat and can form networks, which leads to complex physical structures. We demonstrate the importance of the nanoscale structure for the emergent transport properties, studying electronic conduction in the 3D network of neutral and charged domain walls in ErMnO$_3$. By combining tomographic microscopy techniques and finite element modelling, we clarify the contribution of domain walls within the bulk and show the significance of curvature effects for the local conduction down to the nanoscale. The findings provide insights into the propagation of electrical currents in domain wall networks, reveal additional degrees of freedom for their control, and provide quantitative guidelines for the design of domain wall based technology.