  Neutron spectroscopy measurements have been performed on single crystals of
the antiferromagnetic van der Waals compound NiPS$_3$. Linear spin wave theory
using a Heisenberg Hamiltonian with single-ion anisotropies has been applied to
determine the magnetic exchange parameters and the nature of the anisotropy.
The analysis reveals that NiPS$_3$ is less two-dimensional than its sister
compounds, with a relatively large ferromagnetic exchange of $J^{\prime} =
-0.3$ meV between the layered \emph{ab} planes. In-plane magnetic exchange
interactions up to the third nearest-neighbour were required to fit the data.
The nearest-neighbour exchange was ferromagnetic with $J_1 = -2.6$ meV, the
second neighbour was antiferromagnetic and small with $J_2 = 0.2$ meV, and the
dominant antiferromagnetic third neighbour exchange was $J_3 = 13.5$ meV. The
anisotropy was shown to be largely XY-like with a small uniaxial component,
leading to the appearance of two low-energy spin wave modes in the spin wave
spectrum at the Brillouin zone centre. The analysis could reproduce the spin
wave energies, however there are discrepancies with the calculated neutron
intensities hinting at more exotic phenomena.
