本研究利用 Metropolis Monte Carlo 模拟探讨了时空变化的高斯随机外磁场对三层 spin-1/2 Ising 亚铁磁体补偿现象的影响，发现随机场会导致补偿点偏移甚至消失，并揭示了无补偿相区域面积随外场标准差变化的标度关系。
摘要：
本研究进行了广泛的 Metropolis Monte Carlo 模拟，以探讨由具有特定时空变化的外部高斯随机磁场驱动的、具有方形单分子层的三层 spin-1/2 Ising 亚铁磁体的稳态磁性和热力学行为。这类亚铁磁薄膜系统表现出补偿现象，因此是多种技术应用的潜在候选者。这里，两种不同的理论原子 A 和 B 构成了 ABA 和 AAB 两种构型，其中同类原子（A-A 和 B-B）发生铁磁相互作用，不同类原子（A-B）发生反铁磁相互作用。根据时空变化的高斯随机场强度不同，补偿点和临界点发生偏移，且稳态磁行为在不同类型的亚铁磁行为之间发生转变。对于其他控制参数的特定选择，当磁场标准差超过有限阈值后，补偿现象甚至会消失。因此，在两种构型的 Hamiltonian 参数空间中，无补偿的亚铁磁相区域出现在无场情况下的有补偿相区域内。这些区域的面积随着外场标准差 σ 的增加而增大，遵循标度关系：f(σ, A(σ))=σ^{-b}A(σ)，其中 b_{ABA}=1.913±0.137，b_{AAB}=1.625±0.066。这些指数值在统计区间内与均匀随机磁场下获得的值相匹配。
英文摘要：
In this work, an extensive Metropolis Monte Carlo simulation is performed to investigate the steady-state magnetic and thermodynamic behaviour of a trilayered spin-1/2 Ising ferrimagnet with square monolayers, driven by external Gaussian random magnetic field with certain spatio-temporal variations. Such thin ferrimagnetic systems exhibit compensation phenomenon and thus are potentially interesting candidates for several technological applications. Here, two distinct theoretical atoms, A and B, make up the ABA and AAB types of configurations in which the like atoms (A-A and B-B) ferromagnetically interact and the unlike atoms (A-B) interact antiferromagnetically. Depending upon the strength of the spatio-temporally varying Gaussian random field, the compensation and critical points shift and steady-state magnetic behaviours change between the different distinct types of ferrimagnetic behaviours. The compensation phenomenon even vanishes after crossing a finite threshold of the standard deviation of the magnetic field for particular choices of the other controlling parameters. Consequently, in the Hamiltonian parameter space of both configurations, islands of ferrimagnetic phase without compensation appear within the phase area with compensation of field-free case. The areas of such islands grow with an increasing standard deviation of the external field, $σ$, obeying the scaling relation: $f(σ, A(σ))=σ^{-b}A(σ)$ with $b_{ABA}=1.913\pm 0.137$ and $b_{AAB}=1.625\pm 0.066$ . These values of exponents match within the statistical interval with those obtained with the uniform random magnetic field.
The trilayered Blume-Capel ($S=1$) magnet with nearest neighbour intralayer ferromagnetic and nearest neighbour interlayer antiferromagnetic interaction is studied by Monte Carlo simulation. Depending on the relative interaction strength and the value of anisotropy the critical temperature (where all the sublattice magnetisations and consequently the total magnetisation vanishes) and the compensation temperature (where the total magnetisation vanishes for a special combination of nonzero sublattice magnetisations) are estimated. The comprehensive phase diagrams with lines of critical temperatu…
Trilayered, Ising, spin-1/2, ferrimagnets are an interesting subject for simulational studies for they show compensation effect. A Monte Carlo study on such a system with sublayers on triangular lattice is performed in the current work. Three layers, making up the bulk, is formed completely by either A or B type of atoms. The interactions between like atoms (A-A; B-B) are ferromagnetic and between unlike ones (A-B) are anti-ferromagnetic. Thus the system has three coupling constants and manifests into two distinct trilayer compositions: AAB and ABA. Metropolis single spin flip algorithm is emp…
Trilayered spin-1/2 Ising ferrimagnets are interesting thin systems for compensation phenomenon. In this work, a Metropolis Monte Carlo study is performed on the magnetic and thermodynamic response of such a system on square Bravais lattice, driven by uniform random external magnetic field with spatio-temporal variations. In two distinct configurations, the surface layers are made up of A and the mid-layer is made up of B atoms in a ABA type stacking while in AAB type stacking, the top-layer and the mid-layer is made up of A-atoms while the bottom layer is made up of B-atoms. The magnetic coup…
The mean-field and effective-field approximations are applied in the study of magnetic and thermodynamic properties of a spin-$1/2$ Ising system containing three layers, each of which is composed exclusively of one out of two possible types of atoms, \textbf{A} or \textbf{B}. The \textbf{A-A} and \textbf{B-B} bonds are ferromagnetic while the \textbf{A-B} bonds are antiferromagnetic. The occurrence of a compensation phenomenon is verified and the compensation and critical temperatures are obtained as functions of the Hamiltonian parameters. We present phase diagrams dividing the parameter spac…
A two-dimensional spin-1/2 trilayer magnetic system with quenched non-magnetic impurity is studied. The lattice is formed by alternate layers of two different theoretical atoms A and B arranged in a particular fashion A-B-A. The compensation point appears below the critical temperature, for which total magnetization of the system becomes zero even though the sublattice magnetization has a nonzero value. For a range of values of the relative interaction strength in the Hamiltonian, a compensation point is observed. We considered the Ising mechanics and employed the Monte Carlo method to determi…
Critical, compensation and hysteresis behaviors studies in the ferrimagnetic Blume-Capel model with mixed half-integer spin-(3/2, 7/2): Exact recursion relations calculations
A spin-1/2, Ising trilayered ferrimagnetic system on square Bravais lattice is studied, employing Monte-Carlo simulation with the single spin-flip Metropolis algorithm. The bulk of such a system is formed by three layers, each of which is composed entirely either by A or B type of atoms, resulting in two distinct compositions: ABA and AAB and two different types of magnetic interactions: ferromagnetic between like atoms and antiferromagnetic between unlike atoms. For such systems, Inverse Absolute of Reduced Residual Magnetisation is the absolute value of the ratio of the extremum of the magne…
In this work, we have performed Monte Carlo simulations to study phase transitions in a mixed spin-1 and spin-3/2 Ising ferrimagnetic system on the square and cubic lattices and with two different single-ion anisotropies. This lattice is divided in two interpenetrating sublattices with spins $S^A = 1$ (states $\pm1$ and 0) on the sublattice $A$ and $S^B = 3/2$ (states $\pm 3/2$, $\pm 1/2$) on the sublattice $B$. We have used single-ion anisotropies $D_{A}$ and $D_{B}$ acting on the sites of the sublattice $A$ and $B$, receptively. We have determined the phase diagrams of the model in the tempe…
Magnetic properties of an Ising bilayer system defined on a honeycomb lattice with non-magnetic interlayers which interact via an indirect exchange coupling have been investigated by Monte Carlo simulation technique. Equilibrium properties of the system exhibit ferrimagnetism with $P$-, $N$- and $Q$- type behaviors. Compensation phenomenon suddenly disappears with decreasing strength of indirect ferrimagnetic interlayer exchange coupling. Qualitative properties are in a good agreement with those obtained by effective field theory. In order to investigate the stochastic dynamics of kinetic Isin…
Phase transitions, compensation phenomenon and magnetization of a ferro-ferrimagnetic ternary alloy AB$_ρ$C$_{1-ρ}$ composed of three different kinds of magnetic ions A, B and C with the spin magnitude 1/2, 1 and 3/2 are examined within the framework of a mixed-spin Ising model on a honeycomb lattice with a selective annealed site disorder on one of its two sublattices. It is supposed that the first sublattice of a bipartite honeycomb lattice is formed by the spin-1/2 magnetic ions, while the sites of the second sublattice are randomly occupied either by the spin-1 magnetic ions with a probabi…
The magnetic properties and phase diagrams of the mixed spin Ising model, with spins S=1 and σ=1/2 on a centered rectangular structure, have been investigated using Monte Carlo simulations based on the Metropolis algorithm. Every spin at one lattice site has four nearest-neighbor spins of the same type and four of the other type. We have assumed ferromagnetic interaction between the same spins type, antiferromagnetic for different spin types. An additional single-site crystal field term on the S=1 site was considered. We have shown that the crystal field enhances the existence of the compensat…
We study the thermodynamic and magnetic properties of an Ising bilayer ferrimagnet. The system is composed of two interacting non-equivalent planes in which the intralayer couplings are ferromagnetic while the interlayer interactions are antiferromagnetic. Moreover, one of the planes is randomly diluted. The study is carried out within a Monte Carlo approach employing the multiple histogram reweighting method and finite-size scaling tools. The occurrence of a compensation phenomenon is verified and the compensation temperature, as well as the critical temperature for the model, are obtained as…
We present a Monte Carlo study of the magnetic properties of an Ising multilayer ferrimagnet. The system consists of two kinds of non-equivalent planes, one of which is site-diluted. All intralayer couplings are ferromagnetic. The different kinds of planes are stacked alternately and the interlayer couplings are antiferromagnetic. We perform the simulations using the Wolff algorithm and employ multiple histogram reweighting and finite-size scaling methods to analyze the data with special emphasis on the study of compensation phenomena. Compensation and critical temperatures of the system are o…
The magnetic properties and phase diagrams of the mixed spin-1 and spin-1/2 Ising model on a checkerboard square structure have been studied using the Monte Carlo simulations based on the Metropolis update protocol. The system consists of four quartets of alternative spin configuration. The effect of the exchange interactions J and crystal field D on the magnetic properties, critical and compensation temperatures, susceptibility, and specific heat of the system have been investigated. The phase diagrams, T-J and T-D, for different values of the exchange interactions and crystal field have been…
We used mean-field theory based on the Bogoliubov inequality for the Gibbs free energy to examine the magnetic properties of a mixed spin-5/2 and spin-7/2 Blume-Capel ferrimagnetic system. The thermal behaviours of the system magnetization are classified according to the extended Néel nomenclature. The system exhibits compensation phenomena where a complete cancellation of sublattice magnetizations is observed below the critical temperature. Temperature-dependent phase diagrams are constructed for the case of unequal sublattice crystal field interactions. Under appropriate conditions, our calc…
