  The dynamical responses of XY ferromagnet driven by linearly polarised
propagating and standing magnetic field wave have been studied by Monte Carlo
simulation in three dimensions. In the case of propagating magnetic field wave
(with specified amplitude, frequency and the wavelength), the low temperature
dynamical mode is a propagating spin wave and the system becomes structureless
(or random) in the high temperature. A dynamical symmetry breaking phase
transition is observed at a finite (nonzero) temperature. This symmetry
breaking is confirmed by studying the statistical distribution of the angle of
the spin vector. The dynamic nonequilibrium transition temperature was found to
decrease as the amplitude of the propagating magnetic field wave increased. A
comprehensive phase boundary is drawn in the plane formed by temperature and
amplitude of propagating field wave. The phase boundary was observed to shrink
(in the low temperature side) for longer wavelength of the propagating magnetic
wave. In the case of standing magnetic field wave, the low temperature
excitation is a standing spin wave which becomes structureless (or random) in
the high temperature. Here also, like the case of propagating magnetic wave, a
dynamical symmetry breaking nonequilibrium phase transition was observed. A
comprehensive phase boundary is drawn. Unlike the case of propagating magnetic
wave, the phase boundary does not show any systematic variation with the
wavelength of the standing magnetic field wave. In the limit of vanishingly
small amplitude of the field, the phase boundaries approach the recent Monte
Carlo estimate of equilibrium transition temperature.
