Interplay of domain structure and phase transitions: theory, experiment and functionality

Domain walls and phase boundaries are fundamental ingredients of ferroelectrics and strongly influence their functional properties. Although both interfaces have been studied for decades, often only a phenomenological macroscopic understanding has been established. The recent developments in experiments and theory allow to address the relevant time and length scales and revisit nucleation, phase propagation and the coupling of domains and phase transitions. This review attempts to specify regularities of domain formation and evolution at ferroelectric transitions and give an overview on unusual polar topological structures that appear as transient states and at the nanoscale. We survey the benefits, validity, and limitations of experimental tools as well as simulation methods to study phase and domain interfaces. We focus on the recent success of these tools in joint scale-bridging studies to solve long lasting puzzles in the field and give an outlook on recent trends in superlattices.Financial support has been guaranteed by the Deutsche Forschungsgemeinschaft via Emmy Noether group GR 4792/2. MM would like to acknowledge the funding from the European Union's Horizon 2020 research and innovation programme under Marie Skłodowska-Curie Grant Agreement No. 665919. MM would like to thank Konstantin Shapovalov for fruitful discussions.With funding from the Spanish government through the ‘Severo Ochoa Centre of Excellence’ accreditation (CEX2019-000917-S).Peer reviewe