  Electronic conduction along individual domain walls (DWs) has been reported
in BiFeO$_3$ (BFO) and other nominally insulating ferroelectrics. DWs in these
materials separate regions of differently oriented electrical polarization
(domains) and are just a few atoms wide, providing self-assembled nanometric
conduction paths. In this work, it is shown that electronic transport is
possible also from wall to wall through the dense network of as-grown DWs in
BFO thin films. Electric field cycling at different points of the network,
performed locally by conducting atomic force microscope (cAFM), induces
resistive switching selectively at the DWs, both for vertical (single wall) and
lateral (wall-to-wall) conduction. These findings are the first step towards
investigating DWs as memristive networks for information processing and
in-materio computing.
