Discovery of spontaneous mesoscopic strain waves in nematic domains using dark-field x-ray microscopy.

Electronic nematic order arises when correlated electrons spontaneously break the rotational symmetry of a crystal lattice. When electronic nematic order couples bilinearly to symmetry-breaking lattice strain, both appear together at a single ferroelastic phase transition, producing structural twin domains with distinct orientations of the nematic director. While the effects of applied strain on these domains are well established, the intrinsic behavior of spontaneous subdomain strain fields has remained unexplored. Here, we report the discovery of spontaneous mesoscopic strain waves within individual nematic domains of an iron-based superconductor, observed using dark-field x-ray microscopy (DFXM). Using this advanced full-field imaging technique, we visualize subdomain strain modulations emerging concurrently with nematic order. Elastic compatibility relations governing inhomogeneous strains provide a natural mechanism for the strain waves. Our findings reveal a broadly relevant form of strain self-organization and position DFXM as a powerful probe of the local interplay between lattice strain and electronic order.