Revealing tilt-driven structural heterogeneity in hybrid improper ferroelectrics by spatially-resolved crystallography

Abstract: Domain walls in ferroic oxides can host emergent functionalities that differ fundamentally from those of the surrounding bulk, making their microscopic structure central to understanding and controlling macroscopic behaviour. We use scanning three-dimensional X-ray diffraction to map the spatial evolution of coupled octahedral distortion modes across ferroelastic domain walls in the hybrid improper ferroelectric Ca$<em>{2.15}$Sr$</em>{0.85}$Ti$<em>{2}$O$</em>{7}$. By combining tomographic reconstruction with symmetry-adapted analysis of the octahedral rotation and tilt and associated strain modes, we map their spatial evolution across individual walls in the bulk crystal. We find that the walls are intrinsically extended, with widths far exceeding those expected for conventional Ising-like ferroic interfaces. The wall structure is characterised by a continuous rotation of the tilt order parameter through a tetragonal intermediate. These results provide new microscopic insight into the structural mechanisms governing ferroelastic wall formation, ferroelectric switching, and emergent functionality at domain walls.