Mapping orthorhombic domains with geometrical phase analysis in rare-earth nickelate heterostructures

Most perovskite oxides belong to the Pbnm space group, composed of an anisotropic unit cell, A-site antipolar displacements, and oxygen octahedral tilts. Mapping the orientation of the orthorhombic unit cell in epitaxial heterostructures that consist of at least one Pbnm compound is often needed for understanding and controlling the different degrees of coupling established at their coherent interfaces and, therefore, their resulting physical properties. However, retrieving this information from the strain maps generated with high-resolution scanning transmission electron microscopy can be challenging, because the three pseudocubic lattice parameters are very similar in these systems. Here, we present a novel methodology for mapping the crystallographic orientation in Pbnm systems. It makes use of the geometrical phase analysis algorithm, as applied to aberration-corrected scanning transition electron microscopy images, but in an unconventional way. The method is fast and robust, giving real-space maps of the lattice orientations in Pbnm systems, from both cross section and plan-view geometries, and across large fields of view. As an example, we apply our methodology to rare-earth nickelate heterostructures, in order to investigate how the crystallographic orientation of these films depends on various structural constraints that are imposed by the underlying single crystal substrates. We observe that the resulting domain distributions and associated defect landscapes mainly depend on a competition between the epitaxial compressive/tensile and shear strains, together with the matching of atomic displacements at the substrate/film interface. The results point toward strategies for controlling these characteristics by appropriate substrate choice.