  A prototypical quasi-2D metallic compound, 1T-TaS_2 has been extensively
studied due to an intricate interplay between a Mott-insulating ground state
and a charge density-wave (CDW) order. In the low-temperature phase, 12 out of
13 Ta_{4+} 5\textit{d}-electrons form molecular orbitals in hexagonal
star-of-David patterns, leaving one 5\textit{d}-electron with \textit{S} = 1/2
spin free. This orphan quantum spin with a large spin-orbit interaction is
expected to form a highly correlated phase of its own. And it is most likely
that they will form some kind of a short-range order out of a strongly
spin-orbit coupled Hilbert space. In order to investigate the low-temperature
magnetic properties, we performed a series of measurements including neutron
scattering and muon experiments. The obtained data clearly indicate the
presence of the short-ranged phase and put the upper bound on ~ 0.4
\textit{\mu}_B for the size of the magnetic moment, consistent with the
orphan-spin scenario.
