The direct current (d.c.) conductivity and emergent functionalities at ferroelectric domain walls are closely linked to the local polarization charges. Depending on the charge state, the walls can exhibit unusual d.c. conduction ranging from insulating to metallic-like, which is leveraged in domain-wall-based memory, multi-level data storage, and synaptic devices. In contrast to the functional d.c. behaviors at charged walls, their response to alternating currents (a.c.) remains to be resolved. Here, we reveal a.c. characteristics at positively and negatively charged walls in ErMnO3, distinctly different from the response of the surrounding domains. By combining voltage-dependent spectroscopic measurements on macroscopic and local scales, we demonstrate a pronounced non-linear response at the electrode-wall junction, which correlates with the domain-wall charge state. The dependence on the a.c. drive voltage enables reversible switching between uni-and bipolar output signals, providing conceptually new opportunities for the application of charged walls as functional nanoelements in a.c. circuitry.

Note: This paper is part of the Special Topic on Domains and Domain Walls in Ferroic Materials.

wide interfaces, for example, domain walls, have been reported to possess the same inherent electronic response as existing circuit elements, such as switches [6] and half-wave rectifiers. [7] In addition, ferroelectric domain walls can be reconfigured in situ by a variety of external fields which can lead to exotic bulk responses. Such bulk responses offer the opportunity to both enhance existing technology (e.g., magnetoresistance, [8] colossal dielectric constants, [9] memristive behavior [10] ) but also provide next generation functionality like, negative capacitance, [11] above band gap photovoltaic effects, [12] and domain wall nanoelectronics. [13] Such effects have been discussed from both a fundamental and a technological perspective in recent reviews. [14,15] For all of these bulk responses, the key requirement is for the domain walls to exhibit a different conductivity compared to the surrounding material. Therefore, much of the research has focused on ferroelectrics as the build up of screening charges at domain walls with polar discontinuities are known to modify the local conductivity. [13,14] Examples of this, in single crystals, include BaTiO 3 , [16] (Ca,Sr) 3 Ti 2 O 7 , [17] Cu-Cl boracite's, [18] LiNbO 3 , [19] h-RMnO 3 (R representing rare earth metals), [20] and GaV 4 S 8 . [8] Because of the energetically costly nature of such polar discontinuities, their spontaneous formations are normally restricted to improper ferroelectrics. [21,22] Indeed, so established is this screening charge mechanism that it is a surprise for an improper ferroelectric material, exhibiting polar discontinuities, not to have conducting domain walls. [23] In this scenario, the type of domain wall that is expected to have enhanced conductivity depends on the electronic structure of the host material: In a p-type (n-type) semiconductor the tail-to-tail (head-to-head) domain walls attract screening holes (electrons) and thus provide enhanced conductivity relative to the bulk. [24][25][26] The corresponding head-to-head (tail-to-tail) wall in a p-type (n-type) material is then expected to have reduced conductivity compared to the bulk. [13,21,22,27] Note, in ferroelectrics, particularly thin-films, further conductivity mechanisms have been reported. [6,[28][29][30][31][32] But it is challenging, especially in oxides, to disentangle intrinsic effects and those associated with, for example, enhanced defect density at domain walls, [33,34] which can change surface Schottky barriers and hence conductivity. [7] There have also been reports of domain wall conductivity and even superconductivity in non-ferroelectrics. Examples of the former case include, the antiferromagnetic insulators with conducting magnetic domain Rewritable nanoelectronics offer new perspectives and potential to both fundamental research and technological applications. Such interest has driven the research focus into conducting domain walls: pseudo-2D conducting channels that can be created, positioned, and deleted in situ. However, the study of conductive ...