Effect of odd parameter on phase diagrams and hysteresis features in a 2D kinetic spin- 1 system

In this work, the dynamic magnetic characteristics of the spin-$1$ Blume-Emery-Griffiths (BEG) model under a time-varying magnetic field with odd parameter (dipolar-quadrupolar) interactions are investigated. We studied the system's hysteresis behavior and phase transitions using Glauber-type stochastic dynamics and a mean-field technique. The dynamic phase diagrams are constructed in the temperature-magnetic field $(T,h)$, dipolar-quadrupolar interaction parameter-temperature $(l,T)$, and crystal field parameter-temperature $(d,T)$ planes, revealing the existence of ferromagnetic (F), paramagnetic (D), and ferroquadrupolar (FQ) phases. At low $l$ values, mixed phases are observed, however, as $l$ increases, these mixed phases disappear, resulting in distinct phase boundaries and a smaller FQ phase region. Additionally, the system exhibits a dynamic tricritical point, a multicritical point (A), a critical end point (E), a bicritical point (B), and a zero temperature critical point (Z). Dynamic magnetic hysteresis curve analysis reveals asymmetric behavior in the ferromagnetic phase and symmetric behavior in the paramagnetic phase, with larger $l$ values leading to enhanced remanence and coercivity. We demonstrate that the dipolar-quadrupolar interaction significantly affects the dynamic magnetic properties of the system, leading to the emergence of various magnetic phases. Our results provide new insights into the dynamic magnetic properties of magnetic materials.