  Quantum entanglement effects between the electronic spin and charge degrees
of freedom are examined in an organic molecular solid, termed a dimer-Mott
insulating system, in which molecular dimers are arranged in a crystal as
fundamental units. A low energy effective model includes an antisymmetric
exchange interaction, as one of the dominant magnetic interactions. This
interaction favors a 90 degree spin configuration, and competes with the
Heisenberg-type exchange interaction. Stabilities of the magnetic ordered
phases are examined by using the spin-wave theory, as well as the
Schwinger-boson theory. It is found that the spin-charge interaction promotes
an instability of the long-range magnetic ordered state around a parameter
region where two spin-spiral phases are merged. Implication for the quantum
spin liquid state observed in $\kappa$-(BEDT-TTF)$_2$Cu$_2$(CN)$_3$ is
discussed.
