Current Flow Mapping in Conducting Ferroelectric Domain Walls using Scanning NV-Magnetometry

The electrical conductivity of parallel plate capacitors, with ferroelectric lithium niobate as the dielectric layer, can be extensively and progressively modified by the controlled injection of conducting domain walls. Domain wall-based memristor devices hence result. Microstructures, developed as a result of partial switching, are complex and so simple models of equivalent circuits, based on the collective action of all conducting domain wall channels acting identically and in parallel, may not be appropriate. Here, we directly map the current density in ferroelectric domain wall memristors in-situ, by mapping Oersted fields, using nitrogen vacancy centre microscopy. Current density maps were found to directly correlate with the domain microstructure, revealing that a strikingly small fraction of the total domain wall network is responsible for the majority of the current flow. This insight forces a two order of magnitude correction to the carrier densities, previously inferred from standard scanning probe or macroscopic electrical characterisation.