  Machine learning has emerged as a powerful tool for the analysis of
mesoscopic and atomically resolved images and spectroscopy in electron and
scanning probe microscopy, with the applications ranging from feature
extraction to information compression and elucidation of relevant order
parameters to inversion of imaging data to reconstruct structural models.
However, the fundamental limitation of machine learning methods is their
correlative nature, leading to extreme susceptibility to confounding factors.
Here, we implement the workflow for causal analysis of structural scanning
transmission electron microscopy (STEM) data and explore the interplay between
physical and chemical effects in ferroelectric perovskite across the
ferroelectric-antiferroelectric phase transitions. The combinatorial library of
the Sm-doped BiFeO3 is grown to cover the composition range from pure
ferroelectric BFO to orthorhombic 20% Sm-doped BFO. Atomically resolved STEM
images are acquired for selected compositions and are used to create a set of
local compositional, structural, and polarization field descriptors. The
information-geometric causal inference (IGCI) and additive noise model (ANM)
analysis are used to establish the pairwise causal directions between the
descriptors, ordering the data set in the causal direction. The causal chain
for IGCI and ANM across the composition is compared and suggests the presence
of common causal mechanisms across the composition series. Ultimately, we
believe that the causal analysis of the multimodal data will allow exploring
the causal links between multiple competing mechanisms that control the
emergence of unique functionalities of morphotropic materials and ferroelectric
relaxors.
