  \SCWO is a tetragonal ($I4/m$) double perovskite with diamagnetic W$^{6+}$
(5d$^0$) and (Jahn-Teller-active) Cu$^{2+}$ (3$d^9$) in a rocksalt-ordered
arrangement on the B sites, modelling an anisotropic fcc-lattice
antiferromagnet with $S=1/2$. We have studied the magnetic structure, dynamics
and thermodynamic properties of this material above and below the
\Neel{}-ordering transition at $T_{\textrm{N}} = 24$~K. Muon spin relaxation
spectroscopy, neutron diffraction and neutron spectroscopy experiments show
that the transition at $T_{\textrm{N}}$ on heating is from static 3D type-2
antiferromagnetism to 2D dynamic correlations that remain detectable up to
100~K. Above $T_{\textrm{N}}$ the muon relaxation is described by a compressed
exponential decay, revealing a strong correlation between the spin fluctuation
rate and the 2D correlation length. The low-temperature muon data and the
entropy release around $T_{\textrm{N}}$ as obtained from the heat capacity data
point to small magnetic domains, probably of the order of 60~\AA{}. We note
that the material behaves more like a quasi-2D square lattice antiferromagnet
than could be expected considering its structure only. A possible explanation
might lie in the unusual strong spin-orbit-coupled magnetism of the W 5$d$
levels, as the dominant exchange interaction is via the Cu-O-W-O-Cu pathway.
