Initial spin fluctuations as a probe of cluster spin structure in $^{16}\mathrm{O}$ and $^{20}\mathrm{Ne}$ nuclei

We investigate the imprint of $\alpha$ clustering on initial spin fluctuations in relativistic $^{16}\mathrm{O}+{}^{16}\mathrm{O}$ and $^{20}\mathrm{Ne}+{}^{20}\mathrm{Ne}$ collisions at $\sqrt{s_{\mathrm{NN}}}=5.36$~TeV. Utilizing \textit{ab initio} configurations from Nuclear Lattice Effective Field Theory (NLEFT) and phenomenological $\alpha$-cluster models within a Monte-Carlo Glauber framework, we compute the event-by-event variance of the initial net spin polarization. We find that the strong short-range spin--isospin correlations characteristic of $\alpha$ clusters lead to a significant suppression of spin fluctuations compared to a spherical Woods--Saxon baseline with uncorrelated spins. By constructing a scaled fluctuation observable that accounts for trivial finite-size effects, we demonstrate that this suppression exhibits a non-monotonic centrality dependence sensitive to the detailed cluster geometry. Furthermore, we propose the ratio of scaled spin fluctuations between $^{20}\mathrm{Ne}$ and $^{16}\mathrm{O}$ systems as a robust probe. Our results predict distinct percent-level deviations from the baseline for clustered nuclei, suggesting that measurements of final-state $\Lambda$-hyperon spin correlations can provide novel constraints on the ground-state spin structure of light nuclei.