# Topology and control of self-assembled domain patterns in low-dimensional ferroelectrics

We report on the dynamics of nonequilibrium phase transitions in low-dimensional ferroelectrics and find that self-patterned polar textures exhibit evolutive topology that can be fathomed through the picture of phase separation kinetics.

Driven by complex relaxation dynamics, nonequilibrium phenomena such as self-assembly, pattern formation, and phase ordering kinetics endow phase-separating systems with incomparable richness of domain morphologies. This is particularly relevant in the case of ferroic materials, where complex domain wall arrangements primarily drive emergent phenomena. Understanding the intricate formation processes at play in the formation of modulated phases is thus pivotal for the development of future technologies, e.g., domain wall nanoelectronics, a field of research that has recently seen fiery surge of interest. So far, modulated phases of ferroelectric domains such as the dipolar maze or labyrinthine phase, and the nano-bubble or skyrmionic phase have been somewhat regarded as conceptually disparate. We here numerically predict and experimentally evidence that, depending on the magnitude of the external field, temperature and the kinetics of the phase separation, topologically non-trivial phases emerge upon sub-critically quenching tetragonal Pb(ZrxTi1 − x)O3 through either spinodal decomposition or nucleation processes. The resulting modulated phases are shown to harbor a variety of composite polar topological defects, such as the target skyrmion and the so-called bimeron, that emerge from different combinations of elementary defects. We also show that the self-assembled dipolar patterns, including the yet unreported disconnected labyrinthine and mixed bimerons-skyrmions phases, can be rationalized in their plurality through the unifying canvas of phase separation kinetics. This enables the treatment of chemically homogeneous low-dimensional and elastically constrained ferroelectrics as electrically manipulable phase-separating systems. We also show that the electric field control of skyrmions density elicits hysteretic behavior of conductance, a property that can be harnessed for solid-state neuromorphic computing. These results indicate that the coherent nanoscale intergrowth of topological orders leveraged thus far in diverse materials ranging from metallic alloys to liquid crystals and polymers, can be engineered in ferroic systems as well to enhance their functional topological-based properties.

### Yousra Nahas

Research Assistant Professor, University of Arkansas