  We demonstrate a bipartition technique using a super-lattice architecture to
access correlations between alternating planes of a mesoscopic array of spin-3
chromium atoms trapped in a 3D optical lattice. Using this method, we observe
that out-of-equilibrium dynamics driven by long-range dipolar interactions lead
to spin anti-correlations between the two spatially separated subsystems. Our
bipartite measurements reveal a subtle interplay between the anisotropy of the
3D dipolar interactions and that of the lattice structure, without requiring
single-site addressing. We compare our results to theoretical predictions based
on a truncated cumulant expansion and a new cluster semi-classical method that
we use to investigate correlations at the microscopic scale. Comparison with a
high-temperature analytical model reveals quantum thermalization at a high
negative spin temperature.
