Crystallography of periodic nanotextures in a strained Mott insulator

Here we investigate stripes of alternating structural phases spontaneously forming in epitaxially strained $Ca_2RuO_4$ thin films below the metal-insulator transition. Using large-volume X-ray reciprocal-space mapping, we show that satellite-pattern intensities across 24 symmetry-inequivalent Bragg reflections collapse onto a single parameter-free curve. The collapse identifies a coherent martensitic laminate of few-nm-wide domains separated by ${012}$ interfaces, with displacements along $\left\langle01\bar{2}\right\rangle$. Satellite-extinction analysis demonstrates that both coexisting phases retain the bulk orthorhombic space group despite the pseudocubic $LaAlO_3$ substrate, biaxial epitaxial strain, and intrinsic strain at the interfaces. Classical invariant-plane-strain crystallography thus governs the nanoscale domain geometry of a Mott insulator with intertwined magnetic, electronic, and lattice order.