Elastic relaxation and correlation of local strain gradients with ferroelectric domains in (001) BiFeO3 nanostructures

We report an elasticrelaxation and increase in local strain variation correlated with ferroelectric domains within epitaxial BiFeO3thin filmnanostructuresfabricated by combined electron-beam and focused ion-beam nanolithography. Nano-focused x-ray diffraction microscopy provided new insights into the relationship between film strain and ferroelectric domains in nanostructures, namely: (i) an out-of-plane (C-axis) elasticrelaxation of as much as −1.8% Δc/c in a BFO film-based nanostructure relative to the planar filmlattice constant; (ii) an out-of-plane rotation trending from the center towards all released edges of the nanostructure; and (iii) an increase of inter-domain strain variation within the nanostructure of approximately 10 times the inter-domain variation found within the planar film, correlated with ferroelectric domain boundaries as confirmed by piezoresponse-force microscopy. These results indicate that the release of in-plane BFO/SRO mismatch strain in a planar film is taken up by the local ferroelectric domain structure after patterning, resulting in greatly increased mechanical strain gradients within the structure.