  We investigated the magnetism under a magnetic field in the
quasi-two-dimensional organic Mott insulator
$\kappa$-(BEDT-TTF)$_{2}$Cu[N(CN)$_{2}$]Cl through magnetization and
$^{13}$C-NMR measurements. We found that in the nominally paramagnetic phase
(i.e., above N\'eel temperature) the field-induced local moments have a
staggered component perpendicular to the applied field. As a result, the
antiferromagnetic transition well defined at a zero field becomes crossover
under a finite field. This unconventional behavior is qualitatively reproduced
by the molecular-field calculation for Hamiltonian including the exchange,
Dzyaloshinsky-Moriya (DM), and Zeeman interactions. This calculation also
explains other unconventional magnetic features in
$\kappa$-(BEDT-TTF)$_{2}$Cu[N(CN)$_{2}$]Cl reported in the literature. The
present results highlight the importance of the DM interaction in field-induced
magnetism in a nominally paramagnetic phase, especially in low-dimensional spin
systems.
