**1. Introduction**

In recent years, increasing efforts have been made to develop novel non-volatile memory concepts to meet the increasing demands in terms of scalability and energy consumption. Conductive ferroelectric domain walls (DWs) appear an interesting approach, as ferroelectric DWs are topological defects on the atomic scale and can be created, moved and erased solely by the application of an electric field. Following the discovery of the effect of conductance of DWs in thin-film bismuth ferrite (BFO) [1,2] similar behavior was observed in various other ferroelectric thin films such as lead-zirconate titanate (PZT) [3] and lithium niobate (LNO) [4,5].

The application to non-volatile memories lies in the contradiction in ferroelectrics. Typically, they are known for their very large bandgaps. Thus, one can observe a huge variation in the conductivity between the insulating domain and the conductive domain wall. Various explanations have been made to describe the conductivity of ferroelectric DWs, ranging from oxygen or cation accumulation at the DW to polaron or electron gas formation [6–9] In various reports, the conductivity was proven to be correlated with the charge state of the DW; i.e., DWs inclined to the polar axis showed increased conductance [10–12] Tuning of the DW conductance was also possible by the application of an external field, which resulted in an increase in DW inclination [13].

In this publication, we want to present that precise control over the conductance of domain walls in single-crystalline LNO thin films, thus, implicitly, the inclination angle to the polar axis, can result in an efficient nonvolatile memory element. Moreover, by precise control of the inclination angle, various conductance levels can be distinguished, which is interesting for the application of non-volatile memories. Particularly, multilevel non-volatile memories could be implemented into crossbars to store weight matrixes for neuromorphic computing [14].
