  We investigate theoretically the spin splitting of the exciton states in
semiconductor coupled quantum dots (CQDs) containing a single magnetic ion. We
find that the spin splitting can be switched on/off in the CQDs \textit{via}
the \textit{sp-d}exchange interaction using the electric field. An interesting
bright-to-dark exciton transition can be found and significantly affects the
photoluminescence spectrum. This phenonmenon is induced by the transition of
the ground exciton state, arising from the hole mixing effect, between the
bonding and antibonding states.
