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Standing magnetic wave on Ising ferromagnet: Nonequilibrium phase transition

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.