A PMI/FCL Theory of Scale Selection in Twisted 2D Antiferromagnets

This manuscript develops a publication-ready PMI/FCL interpretation of super-moire spin textures in twisted double-bilayer CrI3 through a reproducible re-analysis of open experimental data associated with the Nature Nanotechnology report on super-moire magnetic states. The empirical core has three levels. First, the paper reproduces the two-dimensional autocorrelation logic used to estimate dominant texture scales from magnetic maps and confirms that the normalized magnetic texture scale R(θ)=a(θ)/aM(θ) is strongly amplified near 1.1° relative to 0.5°. Second, the analysis adds an independent morphology layer from segmented Mz domain maps, showing that the 1.1° state exhibits fewer, larger, and more spatially dominant bright domains than both 0.5° and 2.0°, whereas the 2.0° state is more fragmented and more elongated. Third, the paper treats the 2.0° branch as structured negative evidence: after prominence filtering, the radial autocorrelation contains no robust secondary peak and the radial power spectral density shows no genuine secondary feature beyond the central low-frequency component. Beyond re-analysis, the manuscript formulates a harder theoretical scaffold for the PMI/FCL law. The observed super-moire scale is modeled as the result of mismatch minimization between an intrinsic magnetic wavenumber k0 and the moire wavenumber kM(θ), with finite coherence length ξ cutting off the resonance. This produces a falsifiable phenomenological program: a resonant angular window near an optimal twist θ*, approximate symmetry of the normalized scale ratio around that optimum, and progressive turn-off away from the window. The decisive missing experiment is the clean 0.8° versus 1.4° comparison in a comparable system. The present paper therefore claims strong support for FCL/PMI as a framework of texture, scale selection, and regime change, while explicitly distinguishing established results from the still-open killer test.