  The precise measurement of neutron star (NS) spins can provide important
insight into the formation and evolution of compact binaries containing NS.
While traditional methods of NS spin measurement rely on pulsar observations,
gravitational wave detections offer a complementary avenue. However,
determining component spins with gravitational waves is hindered by the small
dimensionless spins of the NS and the degeneracy in the mass and spin
parameters. This degeneracy can be addressed by the inclusion of higher-order
modes in the waveform, which are important for systems with unequal masses.
This study shows the suitability of neutron star-black hole mergers, which are
naturally mass-asymmetric, for precise NS spin measurements. We explore the
effects of the black hole masses and spins, higher-mode content, inclination
angle, and detector sensitivity on the measurement of NS spin. We find that
networks with next-generation observatories like the Cosmic Explorer and the
Einstein Telescope can distinguish NS dimensionless spin of 0.04 (0.1) from
zero at $1-\sigma$ confidence for events within $\sim 350$ $(\sim 1000)$ Mpc.
Networks with A+ and A$^{\sharp}$ detectors achieve similar distinction within
$\sim 30$ $(\sim 70)$ Mpc and $\sim 50$ $(\sim 110)$ Mpc, respectively.
