Kinetics of a mixed Ising ferrimagnetic system

Abstract

We present a study, within a mean-field approach, of the kinetics of a classical mixed Ising ferrimagnetic model on a square lattice, in which the two interpenetrating square sublattices have spins $\sigma = \pm1/2$ and $S = \pm 1,0$. The kinetics is described by a Glauber-type stochastic dynamics in the presence of a time-dependent oscillating external field and a crystal field interaction. We can identify two types of solutions: a symmetric one, where the total magnetization, $M$, oscillates around zero, and an antisymmetric one where $M$ oscillates around a finite value different from zero. There are regions of the phase space where both solutions coexist. The dynamical transition from one regime to the other can be of first or second order depending on the region in the phase diagram. Depending on the value of the crystal field we found up to two dynamical tricritical points where the transition changes from continuous to discontinuous. Also, we perform a similar study on the Blume-Capel ($S=\pm 1,0$) model and found strong differences between its behavior and the one of the mixed model.Comment: 7 pages, 10 figures, to be published in Phys. Rev. E. Vol. 58 (July 1998

Absence of first-order transition and tricritical point in the dynamic phase diagram of a spatially extended bistable system in an oscillating field

“…It was first observed during numerical integration of the mean-field equation of motion for the magnetization of a ferromagnet in an oscillating field [2,3]. Since then it has been the focus of investigation in numerous Monte Carlo simulations of kinetic Ising systems [1,4,5,6,7,8,9,10,11,12,13,14], further mean-field studies [5,7,8,15,16], and most recently in analytic studies of a bistable time-dependent Ginzburg-Landau (TDGL) model [17]. The DPT may also have been experimentally observed in Co on Cu(001) ultrathin magnetic films [18,19,20] and recently in numerical studies of fully frustrated Josephson-junction arrays [21] and anisotropic Heisenberg models [22].…”

Dynamic phase diagrams of the Blume–Capel model in an oscillating field by the path probability method

“…By comparison, since PPM contains two rate constants, which are important for the investigation of the dynamic behaviors of systems, it gives more interesting and more main different topological phase diagrams than those obtained from Glauber-type stochastic dynamics based on the MFT [17,19,20] and the EFT [23,24]. Moreover, the system exhibits reentrant behavior in the (T, h) plane within the PPM, but does not exhibit it within the previous two methods.…”

“…We present the dynamic phase diagrams in three planes, namely (T, h), (d, T) and (k 2 /k 1 , T), where T is the reduced temperature, h the reduced magnetic field amplitude, d the reduced crystal-field interaction and k 2 , k 1 the rate constants. We compare and discuss the dynamic phase diagrams with dynamic phase diagrams obtained within the Glauber-type stochastic dynamics based on the mean-field approximation [17,19,20] and the effective field theory [23,24]. It is worthwhile mentioning that the DPT in nonequilibrium systems in the presence of an oscillating external magnetic field has attracted much attention in the past few decades, theoretically (see [17,19,23,25] and references therein), analytically [26] and experimentally [27].…”

“…Buendía and Machado [17] presented two dynamic phase diagrams of the model in the presence of a time-dependent oscillating external magnetic field while studying the kinetics of a classical mixed spin-1/2 and spin-1 Ising system in detail within the Glauber-type stochastic dynamics based on the mean-field theory (MFT) [18]. Keskin et al [19,20] studied the dynamic phase transition (DPT) in the BC model under the presence of a time-dependent oscillating external magnetic field and constructed the dynamic phase diagrams by using Glauber-type stochastic dynamics based on the MFT.…”

Magnetic behavior of a mixed Ising ferrimagnetic model in an oscillating magnetic field

“…This behavior is related to the temperature dependence of the relaxation time in the different regions [21,22]. In the ferromagnetic phase we must take into account the relaxation time of both sublattices the σ and the S, whereas in the paramagnetic phase only the σ one is relevant because the S lattice follows the field with almost no delay [15]. We also notice in Fig.9 that when the field has a high frequency the maximum value of the coercive field (that occurs at the compensation temperature) does not reach the field amplitude, i.e., the coercive field does not reach its saturation value.…”