  The dynamical response of an Ising ferromagnet to a plane polarised standing
magnetic field wave is modelled and studied here by Monte Carlo simulation in
two dimensions. The amplitude of standing magnetic wave is modulated along the
direction x. We have detected two main dynamical phases namely, pinned and
oscillating spin clusters. Depending on the value of field amplitude the system
is found to undergo a phase transition from oscillating spin cluster to pinned
as the system is cooled down. The time averaged magnetisation over a full cycle
of magnetic field oscillations is defined as the dynamic order parameter. The
transition is detected by studying the temperature dependences of the variance
of the dynamic order parameter, the derivative of the dynamic order parameter
and the dynamic specific heat. The dependence of the transition temperature on
the magnetic field amplitude and on the wavelength of the magnetic field wave
is studied at a single frequency. A comprehensive phase boundary is drawn in
the plane described by the temperature and field amplitude for two different
wavelengths of the magnetic wave. The variation of instantaneous line
magnetisation during a period of magnetic field oscillation for standing wave
mode is compared to those for the propagating wave mode. Also the probability
that a spin at any site, flips, is calculated. The above mentioned variations
and the probability of spin flip clearly distinguish between the dynamical
phases formed by propagating magnetic wave and by standing magnetic wave in an
Ising ferromagnet.
