Dynamic transition and hysteresis scaling in Heisenberg ferromagnet

Based on the mean-field treatment and Monte Carlo simulation, we studied the nature of the dynamic phase transition of two and three-dimensional magnetic films in Heisenberg model. The time averaged magnetization components ( mx , my, mz),the average hysteresis-loop area components A for magnetic films with different thickness have been calculated. The dynamic transition phase diagrams from <InlineEquation ID="Equ1"> <EquationSource Format="TEX">$Q=(1/\tau )\oint m(t)dt\neq 0$</EquationSource> </InlineEquation> to Q=0 for the 2D and 3D cases have been obtained. The relaxation times for different values of magnetic field, temperature, thickness of the films and the orientation number of spin have been simulated. It is found that the loop area follows the scaling relation, A-A0∝H0αω βT-γ, and the exponents β and γ increase with increasing thickness, while the exponent α decreases with increasing thickness. It was observed that the phase boundary line shrinks inward in the H0-T plane with decreasing value of the frequency of the magnetic field and thickness of multilayer film. The phase diagrams were explained by the competition between the relaxation time and the period of the external magnetic field. Moreover, it has been indicated that the dynamical behaviors for 2D and 3D cases derived by both mean-field method and Monte Carlo method in this work are consistent. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2005