Spin coherence and dephasing of localized electrons in monolayer MoS$_2$

We report a systematic study of coherent spin precession and spin dephasing in electron-doped monolayer MoS$_2$. Using time-resolved Kerr rotation spectroscopy and applied in-plane magnetic fields, a nanosecond-timescale Larmor spin precession signal commensurate with $g$-factor $|g_0|\simeq 1.86$ is observed in several different MoS$_2$ samples grown by chemical vapor deposition. The dephasing rate of this oscillatory signal increases linearly with magnetic field, suggesting that the coherence arises from a sub-ensemble of localized electron spins having an inhomogeneously-broadened distribution of $g$-factors, $g_0 + \Delta g$. In contrast to $g_0$, $\Delta g$ is sample-dependent and ranges from 0.042 to 0.115.