Compensation temperatures,magnetic susceptibilities and phase diagrams of a mixed ferrimagnetic ternary system on the Bethe lattice

Compensation behaviors, magnetic susceptibilities and the phase diagrams of the ternary system of the type ABC consisting of Ising spins σ = 1/2, S = 3/2 and m = 5/2 in the presence of a single-ion anisotropy are studied on the Bethe lattice within the framework of the exact recursion relations. Both ferromagnetic and antiferromagnetic exchange interactions are considered. The exact expressions for sublattice magnetizations and magnetic susceptibilities are obtained, and then thermal behaviors of the sublattice magnetizations, total magnetization, magnetic sublattice susceptibilities and total susceptibility are investigated. We find that the system only undergoes a second order phase transition for the different and same bilinear nearest-neighbor exchange interaction parameters, but displays compensation behaviors for only different bilinear interaction parameters. We also present the phase diagrams for the different and same bilinear nearest-neighbor exchange interaction parameters. A comparison is made with the other ternary system of the type ABC consisting of different spin values.     

Dynamic critical phenomena in a multilayer Ising system

Using the mixed-spin system, we precisely calculate the dynamic critical phenomena, namely dynamic compensation behaviors, dynamic phase diagrams and dynamic hysteresis loops in a multilayer Ising system that composes of four monoatomic layers. As the method, we use the mean-field theory based on Glauber-type stochastic dynamics. It is found that the Hamiltonian parameters have a strong effect on the dynamic critical phenomena. The system displays the P-, Q-, R-, and S-type compensations and multiple hysteresis loop behaviors. The results are qualitatively consistent with those of some theoretical and experimental studies.     

Cylindrical Ising nanowire with crystal field: existence of a dynamic compensation temperatures

We present a study, within a mean-field theory, of the kinetics of the spin-1 Blume–Capel model on cylindrical Ising nanowire in the presence of a time-dependent oscillating external magnetic field. We employ the Glauber transition rates to construct the mean-field dynamical equations. We investigate the thermal behavior of the dynamic order parameters. From these studies, we obtain the dynamic phase transition (DPT) points. Then, we study the temperature dependence of the dynamic total magnetization to find the dynamic compensation points as well as to determine the type of behavior. We also investigate the effect of interaction parameters on the compensation phenomenon and construct the phase diagrams in four different planes. The system exhibits the compensation temperatures, or the N-, P-, Q-, S-type behaviors. Furthermore, we also observed two-compensation temperatures, namely W-type behaviors, whose result is compared with some experimental works and a good overall agreement is found.     

Dynamic Phase Transitions and Compensation Temperatures in a Mixed Spin-3/2 and Spin-5/2 Ising System

We examine the dynamic phase transitions and the dynamic compensation temperatures, within a mean-field approach, in the mixed spin-3/2 and spin-5/2 Ising system with a crystal-field interaction under a time-varying magnetic field on a hexagonal lattice by using Glauber-type stochastic dynamics. The model system consists of two interpenetrating sublattices with σ=3/2 and S=5/2. The Hamiltonian model includes intersublattice, intrasublattice, and crystal-field interactions. The intersublattice interaction is considered antiferromagnetic and to be a simple but interesting model of a ferrimagnetic system. We employ the Glauber transition rates to construct the mean-field dynamic equations, and we solve these equations in order to find the phases in the system. We also investigate the thermal behavior of the dynamic sublattice magnetizations and the dynamic total magnetization to obtain the dynamic phase transition points and compensation temperatures as well as to characterize the nature (continuous and discontinuous) of transitions. We also calculate the dynamic phase diagrams including the compensation temperatures in five different planes. According to the values of Hamiltonian parameters, five different fundamental phases, three different mixed phases, and six different types of compensation behaviors in the Néel classification nomenclature exist in the system.     

Mixed-Spin Ising Model in an Oscillating Magnetic Field and Compensation Temperature

Godoy et al. (Phys. Rev. B 69, 054428, 2004) presented a study of the magnetic properties of a mixed spin (1/2,1), Ising ferrimagnetic model on a hexagonal lattice without an oscillating magnetic field. They employed dynamic mean-field calculations and Monte Carlo simulations to find the compensation point of the model and to present the phase diagrams. It has been found that the N-type compensation temperature appears only when the intrasublattice interaction between spins in the σ sublattice is ferromagnetic. Moreover, the system only undergoes a second-order phase transition. In this work, we extend the study a dynamic compensation temperature of a mixed spin-1/2 and spin-1 Ising ferrimagnetic system on a hexagonal lattice in the presence of oscillating magnetic field within the framework of dynamic mean-field calculations. We find that the system displays the N-type compensation temperature. We also calculate dynamic phase diagrams in which contain the paramagnetic, ferrimagnetic, nonmagnetic fundamental phases and two different mixed phases, depending on the interaction parameters and oscillating magnetic field. The system also exhibits tricritical and reentrant behaviors.     

The thermal behaviors and phase diagrams of the Ising-type endohedral fullerene with magnetic core and diluted magnetic shell (Core@Shell<Subscript>20</Subscript>)

We have carried out theoretical studies on Ising-type endohedral fullerene (EF) structure with a dopant magnetic atom encaged within the diluted magnetic spherical cage to examine the evolution in magnetic behaviors. We show how the thermal behaviors and phase diagrams of Ising-type EF are affected by diluted surface, crystal field and exchange couplings. We have used to investigate theoretically the effect of Hamiltonian parameters the effective field calculations within Ising model framework. The model Hamiltonian includes nearest neighbor ferromagnetic and antiferromagnetic center-surface (C-S) interaction as well as ferromagnetic surface interaction. We have shown that the system exhibits the first and second order phase transitions as well as tricritical point. In particular, the conditions for the occurrence of these reentrant and double reentrant behaviors are given explicitly.     

Phase diagrams of a nonequilibrium mixed spin-1/2 and spin-2 Ising ferrimagnetic system under a time-dependent oscillating magnetic field

We present phase diagrams for a nonequilibrium mixed spin-1/2 and spin-2 Ising ferrimagnetic system on a square lattice in the presence of a time dependent oscillating external magnetic field. We employ the Glauber transition rates to construct the mean-field dynamical equations. The time variation of the average magnetizations and the thermal behavior of the dynamic magnetizations are investigated, extensively. The nature (continuous or discontinuous) of the transitions is characterized by studying the thermal behaviors of the dynamic magnetizations. The dynamic phase transition points are obtained and the phase diagrams are presented in two different planes. Phase diagrams contain paramagnetic (p) and ferrimagnetic (i) phases, and one coexistence or mixed phase region, namely the i+p, that strongly depend on interaction parameters. The system exhibits the dynamic tricritical point and the reentrant behaviors.     

An effective-field theory study of hexagonal Ising nanowire: Thermal and magnetic properties

By means of the effective-field theory （EFT） with correlations, the thermodynamic and magnetic quantities （such as magnetization, susceptibility, internal energy, specific heat, free energy, hysteresis curves, and compensation behaviors） of the spin-l/2 hexagonal Ising nanowire （HIN） system with core/shell structure have been presented. The hysteresis curves are obtained for different values of the system parameters, in both ferromagnetic and antiferromagnetic cases. It has been shown that the system only undergoes a second-order phase transition. Moreover, from the thermal variations of the total magnetization, the five compensation types can be found under certain conditions, namely the Q-, R-, S-, P-, and N-types.     

Phase diagrams in mixed spin-3/2 and spin-2 Ising system with two alternative layers within the effective-field theory

The phase diagrams in the mixed spin-3/2 and spin-2 Ising system with two alternative layers on a honeycomb lattice are investigated and discussed by the use of the effective-field theory with correlations. The interaction of the nearest-neighbour spins of each layer is taken to be positive (ferromagnetic interaction) and the interaction of the adjacent spins of the nearest-neighbour layers is considered to be either positive or negative (ferromagnetic or anti-ferromagnetic interaction). The temperature dependence of the layer magnetizations of the system is examined to characterize the nature (continuous or discontinuous) of the phase transitions and obtain the phase transition temperatures. The system exhibits both second-and first-order phase transitions besides triple point (T P ), critical end point (E), multicritical point (A), isolated critical point (C) and reentrant behaviour depending on the interaction parameters. We have also studied the temperature dependence of the total magnetization to find the compensation points, as well as to determine the type of behaviour, and N-type behaviour in N′eel classification nomenclature existing in the system. The phase diagrams are constructed in eight different planes and it is found that the system also presents the compensation phenomena depending on the sign of the bilinear exchange interactions.     

Characteristic phenomena in nanoscaled transverse Ising thin films with diluted surfaces

The phase diagrams and magnetizations of two nanoscaled thin films with a negative interlayer interaction and dilution at the surfaces, described by the transverse Ising model, are investigated by the use of the effective field theory with correlations. A lot of characteristic phenomena which heavily depend on the surface parameters can be found in them. In particular, the behaviors of a compensation point (or points) in these nanosystems with a negative interlayer interaction at the surfaces are examined by changing the transverse field and the physical parameters at the surfaces.     

Mixed spin-1 and spin-3/2 Ising system with two alternative layers of a honeycomb lattice within the effective-field theory

An effective-field theory with correlations is developed for a mixed spin-1 and spin-3/2 Ising system with two alternative layers of a honeycomb lattice. Spin-1 atoms and spin-3/2 atoms are distributed in alternative layers of a honeycomb lattice. We consider that the nearest-neighbor spins of each layer are coupled ferromagnetically and the interaction between the vertically aligned spins and adjacent spins are coupled either ferromagnetically or antiferromagnetically depending on the sign of the bilinear exchange interactions. We investigate the temperature dependence of the total magnetization to find the compensation points and to determine the type of compensation behavior. We present the phase diagrams in different planes for h=0, and the phase diagrams contain the paramagnetic, nonmagnetic and ferrimagnetic phases. The system also presents a tricritical behavior besides multicritical point (A), isolated critical point (C) and double critical end point (B) depending on the interaction parameters.     

Dynamic phase transitions in a cylindrical Ising nanowire under a time-dependent oscillating magnetic field

The dynamic phase transitions in a cylindrical Ising nanowire system under a time-dependent oscillating external magnetic field for both ferromagnetic and antiferromagnetic interactions are investigated within the effective-field theory with correlations and the Glauber-type stochastic dynamics approach. The effective-field dynamic equations for the average longitudinal magnetizations on the surface shell and core are derived by employing the Glauber transition rates. Temperature dependence of the dynamic magnetizations, the dynamic total magnetization, the hysteresis loop areas and the dynamic correlations are investigated in order to characterize the nature (first- or second-order) of the dynamic transitions as well as the dynamic phase transition temperatures and the compensation behaviors. The system strongly affected by the surface situations. Some characteristic phenomena are found depending on the ratio of the physical parameters in the surface shell and the core. According to the values of Hamiltonian parameters, five different types of compensation behaviors in the Néel classification nomenclature exist in the system. The system also exhibits a reentrant behavior.     

Effective field study of the magnetism and superconductivity in idealised Ising-type X@Y60 endohedral fullerene system

In this study, effective-field calculations within Ising model framework have been utilised to investigate theoretically the effect of temperature and interaction parameters on the magnetic and hysteretic processes in an idealised system used to represent endohedral fullerene (EF) with a dopant magnetic atom confined within a spherical cage. The thermal behaviour of the partial (centre and surface) and the total magnetizations are studied to determine the character of phase transition (continuous and discontinuous) and to elaborate the phase diagram in interaction parameters plane. The total and partial hysteresis curves with susceptibility peaks and coercive fields are also given and focused on the influence of the temperature and interaction parameters. According to values of Hamiltonian parameters, the system exhibits the first- and second-order phase transitions and three types of compensation behaviour, namely Q-, R-, and S-types. In the phase diagram of the system, when the centre–surface (C–S) interaction increases or decreases, the phase transition temperature increases symmetrically. Finally, from the hysteresis curves of the system, we observed that type II superconducting-like behaviour can appear by the presence of dopant centre magnetic atom.     

Influences of Crystal-Field and Interlayer Coupling Interactions on Dynamic Phase Diagrams of a Mixed-Spin(3/2,2) Bilayer System

Influences of crystal-fields(D_A and D_B) and interlayer coupling interactions(J_3) on dynamic magnetic critical behaviors of a mixed-spin(3/2, 2) bilayer system under an oscillating magnetic field are investigated by the Glauber-type stochastic dynamics based on the mean-field theory. For this purpose, dynamic phase diagrams are constructed in the reduced temperature and magnetic field amplitude plane for the ferromagnetic/ferromagnetic(FM/FM),antiferromagnetic/ferromagnetic(AFM/FM) and AFM/AFM interactions in detail. We observe that the influences of D_A, D_B and J_3 interactions parameters on the behavior of the dynamic phase diagrams are very much.     

Phase diagrams of a cylindrical transverse Ising ferrimagnetic nanotube; Effects of surface dilution

Phase diagrams (transition temperature and compensation temperature) of a cylindrical ferrimagnetic nanotube with a negative core–shell interaction, described by the transverse Ising model (TIM), are investigated by the use of the effective-field theory with correlations. The phase diagrams of the system are strongly affected by the surface dilution. The possibility of two compensation points is found in the phase diagram, in contrast to the case of a cylindrical TIM nanowire.     

Dynamic phase transitions in the kinetic mixed spin-1/2 and spin-5/2 Ising model under a time-dependent oscillating magnetic field

We calculate the dynamic phase transition (DPT) temperatures and present the dynamic phase diagrams in the kinetic mixed spin-1/2 and spin-5/2 Ising model under the presence of a time-dependent oscillating external magnetic field. We employ the Glauber transition rates to construct the set of mean-field dynamic equations. The time variation of the average magnetizations and the thermal behavior of the dynamic magnetizations are investigated, extensively. The nature (continuous or discontinuous) of the transitions is characterized by studying the thermal behaviors of the dynamic magnetizations. The DPT points are obtained and the phase diagrams are presented in two different planes. Phase diagrams contain four fundamental phases and three coexistence or mixed phases, which strongly depend on interaction parameters. The phase diagrams are discussed and a comparison is made with the results of the other mixed spin Ising systems.     

Some characteristic phenomena in a transverse Ising nanotube

The phase diagram and magnetizations of a cylindrical nanotube described by the transverse Ising model are investigated by the use of the effective field theory with correlations. Some comparisons between the nanotube and the nanowire have been given for the phase diagrams. In particular, the temperature dependences of longitudinal magnetization in the system with a negative shell–core interaction are investigated. Some characteristic phenomena (new types in ferrimagnetism) which have not been observed in the nanowire as well as similar phenomena are found in the thermal variations, depending on the ratio of the physical parameters in the surface shell and the core. The possibilities of two compensation points and a field induced compensation point in the nanotube are also discussed.     

The effects of surface dilution on magnetic properties in a transverse Ising nanowire

The phase diagrams (transition temperature and compensation temperature) and magnetizations of a cylindrical nanowire with a (positive or negative) core–shell interaction and a surface dilution, described by the transverse Ising model (TIM), are investigated by the use of the effective-field theory with correlations. The magnetic properties of the system are strongly affected by the surface dilution. In particular, the temperature dependences of magnetizations in the system have shown many characteristic phenomena, depending on the selected physical parameters.     

Dynamic magnetic behavior of the mixed spin （2, 5/2） Ising system with antiferromagnetic/antiferromagnetic interactions on a bilayer square lattice

Using the mean-field theory and Glauber-type stochastic dynamics, we study the dynamic magnetic properties of the mixed spin （2, 5/2） Ising system for the antiferromagnetic/antiferromagnetic （AFM/AFM） interactions on the bilayer square lattice under a time varying （sinusoidal） magnetic field. The time dependence of average magnetizations and the thermal variation of the dynamic magnetizations are examined to calculate the dynamic phase diagrams. The dynamic phase diagrams are presented in the reduced temperature and magnetic field amplitude plane and the effects of interlayer coupling interaction on the critical behavior of the system are investigated. We also investigate the influence of the frequency and find that the system displays richer dynamic critical behavior for higher values of frequency than that of the lower values of it. We perform a comparison with the ferromagnetic/ferromagnetic （FM/FM） and AFM/FM interactions in order to see the effects of AFM/AFM interaction and observe that the system displays richer and more interesting dynamic critical behaviors for the AFM/AFM interaction than those for the FM/FM and AFM/FM interactions.     

Dynamic compensation temperature in kinetic spin-5/2 Ising model on hexagonal lattice

We present a study of the dynamic behavior of a two-sublattice spin-5/2 Ising model with bilinear and crystal-field interactions in the presence of a time-dependent oscillating external magnetic field on alternate layers of a hexagonal lattice by using the Glauber-type stochastic dynamics. The lattice is formed by alternate layers of spins σ=5/2 and S=5/2. We employ the Glauber transition rates to construct the mean-field dynamic equations. First, we investigate the time variations of the average sublattice magnetizations to find the phases in the system and then the thermal behavior of the dynamic sublattice magnetizations to characterize the nature (first- or second-order) of the phase transitions and to obtain the dynamic phase transition (DPT) points. We also study the thermal behavior of the dynamic total magnetization to find the dynamic compensation temperature and to determine the type of the dynamic compensation behavior. We present the dynamic phase diagrams, including the dynamic compensation temperatures, in nine different planes. The phase diagrams contain seven different fundamental phases, thirteen different mixed phases, in which the binary and ternary combination of fundamental phases and the compensation temperature or the L-type behavior strongly depend on the interaction parameters.