  The static and dynamic local spin susceptibility of the organic Mott
insulator $\kappa$-(ET)$_2$Cu$_2$(CN)$_3$, a model material of the spin- 1/2
triangular lattice, is studied by $^{13}$C NMR spectroscopy from room
temperature down to 20 mK. We observe an anomalous field-dependent spectral
broadening with the continuous and bipolar shift distribution, appearing
without the critical spin fluctuations. It is attributable to spatially
nonuniform magnetizations induced in the spin liquid under magnetic fields. The
amplitude of the magnetization levels off below 1 K, while the low-lying spin
fluctuations survive toward the ground state, as indicated by the temperature
profile of the relaxation rates.
