Effects of the randomly distributed magnetic field on the phase diagrams of the Ising Nanowire II: Continuous distributions

The effect of the random magnetic field distribution on the phase diagrams and ground state magnetizations of the Ising nanowire has been investigated with effective field theory with correlations. Gaussian distribution has been chosen as a random magnetic field distribution. The variation of the phase diagrams with that distribution parameters has been obtained and some interesting results have been found such as disappearance of the reentrant behavior and first order transitions which appear in the case of discrete distributions. Also for single and double Gaussian distributions, ground state magnetizations for different distribution parameters have been determined which can be regarded as separate partially ordered phases of the system.     

Random field effects on the anisotropic quantum Heisenberg model with Gaussian random magnetic field distribution

The effect of a zero-centered Gaussian random magnetic field distribution on the phase transition properties of the anisotropic quantum Heisenberg model has been investigated on a honeycomb lattice within the framework of effective field theory (EFT) for a two-spin cluster (which is abbreviated as EFT-2). Particular attention has been devoted to investigation of the effect of the anisotropy in the exchange interaction on a system with Gaussian random magnetic field distribution. The variation of the critical temperature with the randomness parameter (i.e., the width of the distribution) has been obtained for several anisotropy parameters. Critical Gaussian distribution width values, which make the critical temperature zero, have been obtained. Moreover, it has been concluded that all critical temperatures are of second order, and that reentrant behavior does not exist in the phase diagrams.     

双模随机晶场对纳米管上Blume-Capel模型磁化强度和相变的影响

近年来, 磁性纳米管的物理性质和相关应用得到了人们的广泛关注. 利用有效场理论研究了纳米管上双模随机晶场中Blume-Capel模型的磁化强度和相变性质, 得到了系统的磁化强度与温度和随机晶场的关系及其相图. 结果表明: 系统在稀释晶场、交错晶场和同向晶场中会表现出不同的磁学性质和相变行为; 稀释晶场和交错晶场会抑制系统的磁化强度, 导致其基态饱和值小于1, 而同向晶场则不会; 随着随机晶场参量的变化, 系统存在多个相变温度, 并呈现出三临界现象和重入现象.     

Parameter-tunable doublet–quadruplet transition in a three-electron quantum dot

A three-electron quantum dot under an external magnetic field was studied. A number of phase diagrams have been obtained to demonstrate how the variation of the magnetic field and/or the parameters of confinement would lead to the occurrence of doublet–quadruplet transitions. Both the confinement with parabolic potential and the square well potential have been considered. We show that the parameters of confinement alter the ground state of the quantum dot from a spin doublet to a spin quadruplet. This result indicates that the quantum dot can be used as a good candidate for qubit of a quantum computer.     

Magnetic properties of armchair graphene nanoribbons: A Monte Carlo study

The magnetic properties of armchair graphene nanoribbons have been studied using a Monte Carlo study. The ground state phase diagrams have been determined for mixed spins S={±2; ±1; 0} and σ={±5/2; ±3/2; ±1/2}. The topologies of the phase diagrams depend on the values of the parameters in the Hamiltonian such as exchange interactions, crystal field and external magnetic field. The some diagrams show some coexistence between regions. The Néel temperature t_N is obtained for different values of layer (n). The effect of reduced exchange interactions between the mixed spins σ and S and reduced crystal field on total magnetization has been given. Magnetic hysteresis cycles are given for different values of n, reduced exchange interactions and reduced temperatures. The double hysteresis loop and superparamagnetism were observed.     

Random crystal-field effects in a mixed spin-1/2 and spin-2 ferrimagnetic Ising system

The magnetic properties of a mixed spin ferrimagnetic system σ?=?1/2 and S?=?2 at the sites of a square lattice with a random crystal field are studied by the mean field approximation. The ground state of the system is determined and the total magnetization is plotted according to the model parameters. Different behaviors for the thermal dependence of the magnetization are highlighted. In particular, one sees the appearance of one or two compensating points and many types of phase diagrams with first and second order phase transition lines as well as isolated critical and tricritical points.     

Magnetic phase diagrams of axial third-nearest-neighbour Ising model

The magnetic phase diagrams of axial third-nearest-neighbour Ising (A3NNI) model under an external field have been studied by means of the molecular field approximation. The phase boundaries among paramagnetic, (anti)ferromagnetic and various modulated phases are determined by analysing the frequency-dependent susceptibility, or by solving the coupled equations for magnetisations for spins up to 17, iteratively. The resultant phase diagram is found to be very consistent with the exact results for the ground state spin ordering and to be far improved than existing finite temperature phase diagrams for the same model.     

Phase transition in antiferromagnets with anisotropic exchange interactions and uniaxial anisotropy

Abstract

Following the Bogoliubov variational principle, the equilibrium and stability equations of the free energy for the two sublattice antiferromagnetic system with inter- and intrasublattice exchange interactions and with an external magnetic field are investigated. For the Ising spin system with uniaxial anisotropy, the phase diagrams have been calculated for various values of anisotropy constant d and the ratio of intra- to intersublattice interaction constants γ. It is shown that first-order, as well as second-order transitions, occur for γ > 0, whereas only a second-order transition occurs for γ ≦ 0, irrespective of the sign of d. Furthermore, similar calculations are extended for the anisotropic Heisenberg spin system and quite interesting phase diagrams have been obtained. Next, the effects of the anisotropic exchange interactions on the magnetic ordered states and the magnetizations of the singlet ground state system of spin one and with a uniaxial anisotropy term are investigated in the vicinity of the level crossing field H ? D/gμ _B . A field-induced ordered state without the transverse component of magnetization is shown to appear in a certain range of magnetic field as the spin dimensionality decreases. It has also turned out that the phase transition between this ordered state and the canted antiferromagnetic state ordinarily found for the isotropic singlet ground state system is of first order. Lastly, the stable spin configurations at a temperature of absolute zero for a two-sublattice uniaxial antiferromagnet under an external magnetic field of arbitrary direction are studied. In particular, the effects of a single ionic anisotropy D-term and anisotropy in the exchange interactions on the magnetic phases are investigated. The antiferromagnetic state has turned out to appear only for the external magnetic field along the easy axis of sublattice magnetization, and makes a first-order phase transition to the canted-spin state or the ferromagnetic state. For other field directions, no antiferromagnetic state appears and only a second-order phase transition between the canted-spin and the ferromagnetic states occurs. The critical field as a function of external field direction has been calculated for several D-values.     

Ground states for lattices of ferromagnetic granules with dipolar magnetic interaction

The magnetic phase diagrams of 2D and 3D regular lattices formed by nonspherical single-domain ferromagnetic granules featuring a dipolar magnetic interaction are studied. The energy of a magnetic state of such systems is calculated using an approximate expression for the pair interaction of nonspherical granules. The character of the magnetic ground state of the system is determined by three geometric parameters: (i) the eccentricity of granules; (ii) the ratio of periods of the rectangular (2D) or tetragonal (3D) lattice; and (iii) the ratio of a lattice period to a granule size. In contrast to the case of lattices formed by point (or spherical) magnetic moments, in which the ground state is always antiferromagnetic or frustrated (for triangular lattices), the ground state of a 2D lattice composed of nonspherical granules can be ferromagnetic. The magnetic phase diagrams of the systems studied are constructed in the space of the above geometric parameters.     

Spin-1/2 Ising model on a AFM/FM two-layer Bethe lattice in a staggered magnetic field

A bilayer spin-1/2 Ising model consisting of two superposed Bethe lattices with antiferromagnetic/ferromagnetic interactions is studied by the use of exact recursion relations in a pairwise approach in the presence of an external staggered magnetic field. Besides the ground state phase diagrams calculated in different possible planes of the model parameters space, the thermal variations of the order-parameters and the free energy are investigated to obtain the temperature-dependent phase diagrams of the model for different values of the coordination numbers q. Our calculations reveal that depending on the strength of the model parameters, the model exhibits a variety of interesting phase transitions and therefore phase diagrams.     

Phenomenological analysis of thermal hysteresis in Ni-Mn-Ga Heusler alloys

The manipulation of thermal hysteresis in Ni-Mn-Ga Heusler alloys with coupled magnetostructural phase transition is studied theoretically using the Landau theory, including magnetic, elastic and crystal lattice modulation order parameters as well as an external magnetic field. It is shown that for the assigned combination of phenomenological parameters, in the phase diagrams, the Austenite–Martensite first-order phase transition has a finite (critical) point in which the thermal hysteresis is disappeared. Moreover, this point depends on the relation between modulation and elastic constants as well as on the magnetic field. Obtained results have been compared with other theoretical end experimental data.     

The mixed spin-1/2 and spin-1 Ising system on a two-layer Bethe lattice

Two layered magnetic Bethe lattice with varying coordination number q is introduced and numerically studied via exact recursion relations within a pairwise approach. The system is influenced by competing interlayer and intralayer nearest-neighbour (NN) coupling interactions and also by the crystal and external magnetic fields. Cases where both layers are ferromagnetic or one is ferro and the other antiferromagnetic are considered. System configurations’ energy calculations are used to devise some ground state phase diagrams that have proven useful for the investigation of the very low temperature behaviour of the model. Analysis of the thermal behaviours of the total magnetization within the model parameters’ space yield interesting phase diagrams which display fascinating properties, in particular the presence of tricritical points. Increasing negative values of the crystal field strength stabilizes the disordered paramagnetic phase and sometimes gives rise to wavy transition lines.     

Phase transition in the Blume-Capel model with second neighbour interaction

A two dimensional antiferromagnetic spin-1 Ising model with negative next- nearest neighbour interaction (J ₂ <0) and under an external magnetic field is investigated by two methods: The mean-field theory and Finite-Size-Scaling based on transfer matrix (TMFSS) calculations. The ground state diagrams exhibit several new phases including frustrated ones. At finite temperature we obtain by these two methods quite rich phase diagrams, with several multicritical points. While Mean field approximation yields phase diagrams which are sometimes even qualitatively incorrect, accurate results are obtained from transfer matrix finite size scaling calculations. For a certain range of interaction parameters, the model is shown to violate the ordinary universality hypothesis. Received: 3 November 1997 / Revised: 31 March 1998 / Accepted: 7 April 1998     

Reentrant behavior of magnetic ordered phase in spin-crossover solids with quenched disordered ligand field

The Ising-like model of spin-crossover solid compounds with quenched random ligand field has been investigated by the mean-field (infinite-range) approximation. An exact solution for the problem is found within the replica formalism. The magnetic diagrams are obtained; the relations between the intermolecular coupling and the temperature as well as the reentrant phenomena of the magnetic ordered phase are discussed.     

Thermodynamic Properties of Random Transverse Field Mixed Spin System in the Presence of Single-Ion Anisotropy

We study the thermodynamic properties of random transverse field mixed spin system in the presence of single-ion anisotropy on a square lattice. By making use of the effective field theory and a cutting approximation, the detailed phase diagrams are described and some interesting results are found under trimodal random transverse field distribution. A small single-ion anisotropy can magnify magnetic ordering region at low temperatures and existence of a large transverse field can assist the occurrence of reentrant phenomena. With increasing disorder, second-order phase transitions are shown to change into first-order phase transitions. The trajectory of the tricritical point in the phase space as a function of disorder is presented. These indicate a strong correlation with the corresponding to trimodal transverse field distribution.     

Stationary State Solutions of a Bond Diluted Kinetic Ising Model: An Effective-Field Theory Analysis

We examined the stationary state solutions of a bond diluted kinetic Ising model under a time dependent oscillating magnetic field within the effective-field theory (EFT) for a honeycomb lattice (q=3). The effects of the Hamiltonian parameters on the dynamic phase diagrams have been discussed in detail. Bond dilution process on the kinetic Ising model causes a number of interesting and unusual phenomena such as reentrant phenomena and has a tendency to destruct the first-order transitions and the dynamic tricritical point. Moreover, we have investigated the variation of the bond percolation threshold as functions of the amplitude and frequency of the oscillating field.     

双模随机交错晶场对spin-1和spin-1/2混合自旋纳米管中Blume-Capel模型磁化强度的影响

利用有效场理论研究了纳米管上双模随机交错晶场中混合自旋Blume-Capel模型格点的平均磁化强度,得到了系统格点的平均磁化强度与双模随机晶场的取值概率、外磁场、晶场参数和晶场强度比值的关系.结果表明:取值概率、外磁场、交换相互作用、晶场强度比值和晶场强度等诸多因素相互竞争,使系统表现出比恒定晶场作用的Blume-Capel模型更为丰富的磁化现象;双模随机交错晶场会抑制系统的平均磁化强度,使其基态饱和值小于5/6;外磁场导致系统的二级相变消失;一定条件下系统发生一级相变;系统的平均磁化强度呈现部分缺失和负值现象.     

双模随机同向晶场对spin-1和spin-1/2混合自旋纳米管中Blume-Capel模型平均磁化强度的影响

利用有效场理论研究了纳米管上双模随机同向晶场中混合自旋Blume-Capel模型格点的平均磁化强度,得到了系统格点的平均磁化强度与双模随机晶场的取值概率、外磁场、晶场参数和晶场强度比值的关系。结果表明：取值概率、外磁场、交换相互作用、晶场强度比值和晶场强度等诸多因素相互竞争,使系统表现出比恒定晶场作用的Blume-Capel模型更为丰富的磁化现象;双模随机同向晶场会抑制系统的平均磁化强度,使其基态饱和值小于5/6;外磁场导致系统的二级相变消失;一定条件下系统发生一级相变;系统的平均磁化强度呈现部分缺失和负值现象。