  Ferroelectric domain walls represent multifunctional 2D-elements with great
potential for novel device paradigms at the nanoscale. Improper ferroelectrics
display particularly promising types of domain walls, which, due to their
unique robustness, are the ideal template for imposing specific electronic
behavior. Chemical doping, for instance, induces p- or n-type characteristics
and electric fields reversibly switch between resistive and conductive
domain-wall states. Here, we demonstrate diode-like conversion of
alternating-current (AC) into direct-current (DC) output based on neutral
180$^{\circ}$ domain walls in improper ferroelectric ErMnO$_3$. By combining
scanning probe and dielectric spectroscopy, we show that the rectification
occurs for frequencies at which the domain walls are fixed to their equilibrium
position. The practical frequency regime and magnitude of the output is
controlled by the bulk conductivity. Using density functional theory we
attribute the transport behavior at the neutral walls to an accumulation of
oxygen defects. Our study reveals domain walls acting as 2D half-wave
rectifiers, extending domain-wall-based nanoelectronic applications into the
realm of AC technology.
