Strain-enhanced electronic ordering in La₃Ni₂O₇ thin films probed by Coherent X-ray Scattering

We report coherent soft x-ray scattering (CSX) measurements of epitaxial nickelate La₃Ni₂O₇ thin films to investigate nanoscale magnetic ordering associated with the (0.25, 0.25, L) superlattice peak at the Ni L₃ resonance (852 eV) and 100K. Using grazing and near-normal-incidence scattering geometries we observe presence of a resonant magnetic Bragg peak. Quantitative analysis of Lorentzian line shapes yields in-plane and out-of-plane correlation lengths of approximately 77 nm and 26 nm, respectively. Fixed-Q energy scans exhibit a pronounced resonance at the Ni L₃ edge, confirming the electronic origin of the modulation. Under coherent illumination, speckle patterns observed within the Bragg peak envelope directly reveal the magnetic domain structure. Time-correlation measurements revealed a gradual decay of speckle intensity under continuous exposure and the formation of localized beam induced damage patches. We quantified the speckle dynamics and found a consistent speckle lifetime τ ≈ 15 - 20 s from 20 - 80 K. Our results demonstrate enhanced in-plane correlations on SrTiO₃ substrates, electronic resonance behavior, and the stabilization of large, coherent magnetic domains in bilayer nickelates under tensile strain.