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.     

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.     

Two distinct magnetic susceptibility peaks and magnetic reversal events in a cylindrical core/shell spin-1 Ising nanowire

The magnetization and susceptibility of a cylindrical core/shell spin-1 Ising nanowire are investigated within the effective-field theory with correlations for both ferromagnetic and antiferromagnetic exchange interactions between the shell and the core. We find that the nanowire system exhibits two distinct susceptibility peaks and two successive phase transitions; either both of them are second-order transitions or one is a second-order transition and the other is a first-order transition for a small exchange interaction. The susceptibility versus switching field and the hysteresis behavior are investigated for different temperatures. It is found that the magnetization reversal events appear as peaks in the susceptibility versus switching field curve, the positions of which define the coercive field points of the nanowire system; the distance between the two susceptibility peaks decreases with increasing temperature.     

Magnetization and phase diagram of a cubic nanowire in the presence of the crystal field and the transverse field

Magnetic properties of the cubic nanowire, which consists of a ferromagnetic core of spin-1 and a ferromagnetic shell of spin-3/2 with ferrimagnetic interface coupling, are investigated by the use of the effective-field theory with correlations (EFT). Two compensation points have been found for certain values of the system parameters in the nanowire. In particular, the effects of the transverse field and the crystal field on the magnetization and phase transition are described in detail.     

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.     

Magnetic hysteresis,compensation behaviors,and phase diagrams of bilayer honeycomb lattices

Magnetic behaviors of the Ising system with bilayer honeycomb lattice(BHL) structure are studied by using the effective-field theory(EFT) with correlations. The effects of the interaction parameters on the magnetic properties of the system such as the hysteresis and compensation behaviors as well as phase diagrams are investigated. Moreover, when the hysteresis behaviors of the system are examined, single and double hysteresis loops are observed for various values of the interaction parameters. We obtain the L-, Q-, P-, and S-type compensation behaviors in the system. We also observe that the phase diagrams only exhibit the second-order phase transition. Hence, the system does not show the tricritical point(TCP).     

Surface effects on a multilayer and multisublattice cubic nanowire with core/shell

A multilayer and multisublattice cubic nanowire is studied based on a shell/core and the effective-field theory. The formulas of the longitudinal and transverse magnetization for each sublattice of the nanowire are given. The surface parameters have intense effects on the magnetizations and phase diagrams (phase transition temperatures and compensation temperatures) of the system. Two compensation points do exist for certain values of the surface transverse field, the surface single-ion anisotropy and the surface exchange coupling in the system. This interesting phenomenon may be potential applications in information storage technology.     

A quadrangular transverse Ising nanowire with an antiferromagnetic spin configuration

The phase diagrams and the temperature dependences of magnetizations in a transverse Ising nanowire with an antiferromagnetic spin configuration are investigated by the use of the effective-field theory with correlations (EFT) and the core–shell concept. Many characteristic and unexpected behaviors are found for them, especially for thermal variation of total magnetization m_T. The reentrant phenomenon induced by a transverse field in the core, the appearance of a compensation point, the non-monotonic variation with a compensation point, the reentrant phenomena with a compensation point and the existence of both a broad maximum and a compensation point have been found in the thermal variations of m_T.     

Dynamic behaviors of the hexagonal Ising nanowire

By utilizing the effective-field theory based on the Glauber-type stochastic dynamics, the dynamic behaviors of the hexagonal Ising nanowire (HIN) system in the presence of a time dependent magnetic field are obtained. The time variations of average order parameters and the thermal behavior of the dynamic order parameters are studied to analyze the nature of transitions and to obtain the dynamic phase transition points. The dynamic phase diagrams are introduced in the plane of the reduced temperature versus magnetic field amplitude. The dynamic phase diagrams exhibit coexistence phase region, several ordered phases and critical point as well as a reentrant behavior.     

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.     

Ferrimagnetism and reentrant phenomena in a tetragonal Ising nanoparticle

ABSTRACT

The phase diagrams and magnetizations in a tetragonal Ising nanoparticle have been investigated by using the effective-field theory with correlations and the core–shell model. For the spin-1/2 atoms in the shell, a transverse field is included to cant their spin direction. The results show that they are heavily dependent on the given physical parameters. The ferrimagnetic behaviours, as well as novel type behaviours, have been found in the thermal variation of magnetization. The reentrant phenomena are also obtained.     

Nanoparticle with a ferrimagnetic interlayer coupling in the presence of single-ion anisotropis

The magnetic properties of a nanoparticle described by the transverse Ising model with single-ion anisotropis, which consists of a concentric spin-3/2 core and a hexagonal ring spin-5/2 shell coupled with a ferrimamagnetic interlayer coupling, are studied by the effective-field theory with self-spin correlations. Particular emphasis is given to the effects of the both the transverse field and the single-ion anisotropis on the longitudinal and transverse magnetizations, phase diagrams of the nanoparticle. We have found that, for appropriate values of the system parameters, one or two compensation points may be obtained in the present systems.     

Dynamic phase transitions and dynamic phase diagrams of the spin-2 Blume-Capel model under an oscillating magnetic field within the effective-field theory

The dynamic phase transitions are studied in the kinetic spin-2 Blume-Capel model under a time-dependent oscillating magnetic field using the effective-field theory with correlations. The effective-field dynamic equation for the average magnetization is derived by employing the Glauber transition rates and the phases in the system are obtained by solving this dynamic equation. The nature (first- or second-order) of the dynamic phase transition is characterized by investigating the thermal behavior of the dynamic magnetization and the dynamic phase transition temperatures are obtained. The dynamic phase diagrams are constructed in the reduced temperature and magnetic field amplitude plane and are of seven fundamental types. Phase diagrams contain the paramagnetic (P), ferromagnetic-2 (F₂) and three coexistence or mixed phase regions, namely the F₂+P, F₁+P and F₂+F₁+P, which strongly depend on the crystal-field interaction (D) parameter. The system also exhibits the dynamic tricritical behavior.     

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.     

Ferrimagnetic behaviors in a double-wall cubic metal nanotube

A double-wall cubic metal nanotube consists of the ferromagnetic spin-1 inner shell and spin-3/2 surface shell. It is of the ferrimagnetic exchange coupling between two shells. Considering the single-ion anisotropy and transverse field exist together, the magnetization, the initial susceptibility, the internal energy and the specific heat have been investigated by using the effective-field theory with correlations. Some interesting phenomena have been found in the thermal variations of the system. Magnetization appears two or three compensation points in certain parameters. It is an unconventional ferrimagnetic behavior in the nanotube. The shapes of total magnetization and the initial susceptibility are great influenced by the surface exchange coupling, surface single-ion anisotropy and surface transverse field. Some results of nanotube may have potential applications in different research fields, such as electronics, optics, mechanics, and even biomedicine and molecular devices.     

Hysteresis behaviors in a cylindrical Ising nanowire

The hysteresis behaviors of the cylindrical Ising nanowire are investigated within the effective-field theory with correlations at temperatures below, around and above the critical temperature. The hysteresis curves are obtained for different reduced temperatures both ferromagnetic and antiferromagnetic interactions between the shell and the core. We find that the hysteresis loop areas decrease when the reduced temperatures increase, and the hysteresis loops disappear at certain reduced temperatures. Moreover, for the antiferromagnetic nanowire the hysteresis loop areas disappear earlier than the ferromagnetic case as the reduced temperature increases. An unusual form of triple hysteresis behaviors is observed for the antiferromagnetic nanowire system. The thermal behaviors of the coercivities and remanent magnetizations are also investigated. The results are in good agreement with some experimental and theoretical results.     

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.     

Compensation temperature in a cylindrical Ising nanowire (or nanotube)

The critical temperature and the compensation temperature in a cylindrical Ising nanowire (or nanotube) with a negative interlayer coupling at the surface are investigated by the use of both the effective-field theory with correlations and the shell-core concept. Particular emphasis is given to the effects of the surface and its dilution on them. We have found that, for appropriate values of the system parameters, a compensation point may be obtained in the present systems.     

Dynamic magnetic properties of the kinetic cylindrical Ising nanotube

The nature (time variation) of response magnetizations m(wt) of the kinetic cylindrical Ising nanotube in the presence of a periodically varying external magnetic field h(wt) is studied by employing the effective-field theory (EFT) with correlations as well as the Glauber-type stochastic dynamics. We have determined the time variations of m(wt) and h(wt) for various temperatures, and investigated the dynamic magnetic hysteresis behavior. Temperature dependence of the dynamic magnetizations, hysteresis loop areas and correlations are investigated in order to characterize the nature (first- or second-order) of the dynamic transitions as well as to obtain the dynamic phase transition temperatures. We also present the dynamic phase diagrams in the three different planes and compare the results of the equilibrium and nonequilibrium states. The phase diagrams exhibit dynamic tricritical, isolated critical, multicritical and triple points. The results are in good agreement with some experimental and theoretical results.     

Magnetic properties of a hexagonal transverse Ising nanoisland

The magnetic properties of a hexagonal transverse Ising nanoisland have been calculated by the effective-field theory with correlations. The effects of surface coupling, interlayer coupling, and the competition between transverse fields at the surface shell and in the inner core on phase diagrams and magnetizations are examined. Meanwhile, the results are also compared with two different nanoislands which consist of two layers with nine atoms or five atoms in each of the layers.