  We study collective spin excitations in two-dimensional diluted magnetic
semiconductors, placed into external magnetic field. Two coupled modes of the
spin waves (the electron and ion modes) are found to exist in the system along
with a number of the ion spin excitations decoupled from the electron system.
We calculate analytically the spectrum of the waves taking into account the
exchange interaction of itinerant electrons both with each other and with
electrons localized on the magnetic ions. The interplay of these interactions
leads to a number of intriguing phenomena including tunable anticrossing of the
modes and a field-induced change in a sign of the group velocity of the ion
mode.
