Multilevel Strain Accomodation in an Single-Crystalline BiFeO₃ Thin Film at Multiple Length Scales

Multiferroic BiFeO₃ (BFO) thin film shows various functionalities as well as diverse metastable phases depending on misfit strain. Thus, understanding strain relief behavior is the key to unlocking the lattice strain-property relationship. It is known that strain-induced mixed phase nanostructure can evolve in response to strain accumulation as the film gets thicker. However, it is unclear how the misfit strain is accommodated in a single-crystalline BFO thin film seemingly without the intervention of its polymorphs, which then reasonably requires microscopic examination for how the lattices can be distorted to relieve the internal strain. In this study, a correlative strain analysis with the combination of dark field in-line electron holography (DIH) and quantitative scanning transmission electron microscopy (STEM) reveals a hierarchical structure of strain states and distorted lattices to effectively accommodate the misfit strain inside a single-crystalline BFO grown on SrRuO₃ electrode/SrTiO₃ substrate. From the nanoscale DIH strain analysis, a random combination of multiple strain states is uncovered to play as a primary strain relief, thus forming irregular strain nanodomains. STEM-based bond-length measurements for the corresponding strain nanodomains unveil a unique strain accommodation behavior being achieved by a statistical combination of multiple modes of distorted structures on the unit cell scale. Our discovery offers a new insight into fundamental understanding of strain accommodation behavior of ferroelectric oxide films like BFO with many low symmetry polymorphs.