  Interfaces at the two-dimensional limit in oxide materials exhibit a rich
span of functionality that differs significantly from the bulk behavior. Among
such interfaces, domain walls in ferroelectrics draw special attention because
they can be moved deterministically with external voltage, while they remain at
place after voltage removal, paving the way to novel neuromorphic and low-power
data-processing technologies. Ferroic domains arise to release strain, which
depends on material thickness, following Kittel scaling law. Hence, a major
hurdle is to reduce the device footprint for a given thickness, i.e., to form
and move high-density domain walls. Here, we used transmission electron
microscopy to produce domain walls with periodicity as high as 2 nm without the
use of contact electrodes, while observing their formation and dynamics in situ
in $BaTiO_3$. Large-area coverage of the engineered domain walls was
demonstrated. The domain-wall density was found to increase with increasing
effective stress, until arriving to a saturation value that reflects 150-fold
effective stress enhancement. Exceeding this value resulted in strain release
by domain-wall rotation. In addition to revealing this multiscale
strain-releasing mechanism, we offer a device design that allows controllable
switching of domain-walls with 2-nm periodicity, reflecting a potential
$144-Tb/inch^2$ neuromorphic network.
