  We experimentally realize a spin-momentum lattice with a homogeneously
trapped Fermi gas. The lattice is created via cyclically-rotated atom-laser
couplings between three bare atomic spin states, and are such that they form a
triangular lattice in a synthetic spin-momentum space. We demonstrate the
lattice and explore its dynamics with spin- and momentum-resolved absorption
imaging. This platform will provide new opportunities for synthetic spin
systems and the engineering of topological bands. In particular, the use of
three spin states in two spatial dimensions would allow the simulation of
synthetic magnetic fields of high spatial uniformity, which would lead to
ultra-narrow Chern bands that support robust fractional quantum Hall states.
