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Interfaces at the two-dimensional limit in oxide materials exhibit a richspan of functionality that differs significantly from the bulk behavior. Amongsuch interfaces, domain walls in ferroelectrics draw special attention becausethey can be moved deterministically with external voltage, while they remain atplace after voltage removal, paving the way to novel neuromorphic and low-powerdata-processing technologies. Ferroic domains arise to release strain, whichdepends on material thickness, following Kittel scaling law. Hence, a majorhurdle is to reduce the device footprint for a given thickness, i.e., to formand move high-density domain walls. Here, we used transmission electronmicroscopy to produce domain walls with periodicity as high as 2 nm without theuse of contact electrodes, while observing their formation and dynamics in situin $BaTiO_3$. Large-area coverage of the engineered domain walls wasdemonstrated. The domain-wall density was found to increase with increasingeffective stress, until arriving to a saturation value that reflects 150-foldeffective stress enhancement. Exceeding this value resulted in strain releaseby domain-wall rotation. In addition to revealing this multiscalestrain-releasing mechanism, we offer a device design that allows controllableswitching of domain-walls with 2-nm periodicity, reflecting a potential$144-Tb/inch^2$ neuromorphic network.

Formation and manipulation of domain walls with 2-nm domain periodicity in $BaTiO_3$ without contact electrodes