  Nuclear spins are known to experience spontaneous long-range correlations
only below 2.5 mili-Kelvin in superfluid $^3$He. Here we present the first
evidence of nuclear spin coupling in molecular hydrogen (H$_2$) at 74-92 Kelvin
using neutron scattering, showing a fundamental change in nature from the
incoherent scattering universally expected from hydrogen, which reflects single
particle properties of uncorrelated nuclear spins, to coherent, with a peak
materializing on the elastic line, indicating H$_2$-H$_2$ nuclear spin
correlations. In this novel phase, the dynamic response of the system also
changes nature, and collective excitations with an effective mass of nine H$_2$
are observed with inelastic scattering at momentum transfers up to 37
\AA$^{-1}$, corresponding to length scales smaller than the H-H bond, where
previous experiments have always found single atom excitations. This novel
behavior has only been observed from H$_2$ within the subnanometer sized
graphitic pores of a carbon material, marking the first demonstration that a
confined materials environment can be used to control nuclear spin
correlations.
