Spin-orbit coupling of light has come to the fore in nano-optics and plasmonics, and is a key ingredient of topological photonics and chiral quantum optics. We demonstrate a basic tool for incorporating analogous effects into neutron optics: the generation and detection of neutron beams with coupled spin and orbital angular momentum. $^3$He neutron spin-filters are used in conjunction with specifically oriented triangular coils to prepare neutron beams with lattices of spin-orbit correlations, as demonstrated by their spin-dependant intensity profiles. These correlations can be tailored to particular applications, such as neutron studies of topological materials.
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