Monte Carlo study of the magnetic properties of Fe0.9−qMn0.1Alq-disordered alloys

Within the framework of a random site-diluted Ising model with nearest-neighbor interactions, and using the Metropolis algorithm for equilibration and energy minimization, we have computed the ensemble and configurational averages for magnetization per site, magnetic susceptibility and specific heat of Fe_0.9−qMn_0.1Al_q-disordered alloys with 0.1q0.55. In the model, atoms have been randomly distributed on a body-centered cubic lattice in order to simulate the disorder and structure as that obtained in arc-melted Fe_0.9−qMn_0.1Al_q alloys treated at high temperatures during long periods of time and followed by fast quenching. Competitive interactions coming from Fe–Fe ferromagnetic bonds and Fe–Mn and Mn–Mn antiferromagnetic couplings, as well as the Al dilutor effect, have been taken into account in our study. Results allow us to conclude that, in agreement with previous Mössbauer data of the average hyperfine field, for which a comparison is also carried out, the Fe_0.9−qMn_0.1Al_q-disordered alloys are well characterized by a critical concentration at room temperature at around 40 at% Al, for which the system undergoes a transition from a ferromagnetic state to a paramagnetic one. The finite size scaling analysis to obtain the critical Al concentration in the thermodynamic limit, as well as the critical exponents, is also presented and discussed.     

Monte Carlo study of the critical behavior of pure and site-diluted Ising ferro-and ferrimagnets

Monte Carlo simulations are performed for pure and site-diluted Ising ferro- and ferrimagnets on a simple cubic lattice with up to 40³ sites and with impurity concentrationx. For the diluted ferromagnet (x=0.2) the exponent= 0.392±0.03 is definitely larger than the pure model value of=0.304±0.03. In contrast, for ferrimagnetic systems (x=0, 0.1, 0.2) the values appear to be independent ofx and within the error limits consistent with the value for the pure ferromagnet, possibly because the width of the asymptotic random critical regime (or of the crossover regime) is even smaller than in the case of ferromagnets.     

Monte Carlo evidence for a cusp in the uniform susceptibility of the site-diluted simple cubic Ising antiferromagnet

Monte Carlo simulations are performed for pure and site-diluted Ising antiferromagnets on a simple cubic lattice with up to 40³ sites and impurity concentrationx=0, 0.2. and 0.5. Forx=0.5 a cusp emerges for the temperature dependence of the uniform susceptibility at the critical temperature which is contrasted with the smooth behavior for a pure antiferromagnet, in agreement with the theoretical prediction of Fishman and Aharony.     

A Markov-property Monte Carlo method: One-dimensional Ising model

In this paper we introduce a new Monte Carlo procedure based on the Markov property. This procedure is particularly well suited to massively parallel computation. We illustrate the method on the critical phenomena of the well known one-dimensional Ising model. In the course of this work we found that the autocorrelation time for the Metropolis Monte Carlo algorithm is closely given by the square of the correlation length. We find speedup factors of the order of 1 million for the method as implemented on the CM2 relative to a serial machine. Our procedure gives error estimates which are quite consistent with the observed deviations from the analytically known exact results.     

Critical dynamics of the three-dimensional Ising model: A Monte Carlo study

Extensive Monte Carlo simulations have been performed to analyze the dynamical behavior of the three-dimensional Ising model with local dynamics. We have studied the equilibrium correlation functions and the power spectral densities of odd and even observables. The exponential relaxation times have been calculated in the asymptotic one-exponential time region. We find that the critical exponentz=2.09 ±0.02 characterizes the algebraic divergence with lattice size for all observables. The influence of scaling corrections has been analyzed. We have determined integrated relaxation times as well. Their dynamical exponentz _int agrees withz for correlations of the magnetization and its absolute value, but it is different for energy correlations. We have applied a scaling method to analyze the behavior of the correlation functions. This method verifies excellent scaling behavior and yields a dynamical exponentz _scal which perfectly agrees withz.     

Non-universal critical behaviour of heteronuclear dimers on a square lattice––A Monte Carlo study

Monte Carlo simulation within the grand canonical ensemble, the histogram reweighting technique, and finite size scaling analysis are used to explore the phase behaviour of heteronuclear dimers, composed of A and B type atoms, on a square lattice. We have found that for the models with attractive BB and AB nearest-neighbour energy, u_BB=u_AB=−1, and for non-repulsive energy between AA nearest-neighbour sites, u_AA<0, the system belongs to the universality class of the two-dimensional Ising model. However, when u_AA>0, the system exhibits a non-universal critical behaviour. We have evaluated the dependences of the critical point characteristics on the value of u_AA.     

Monte Carlo study of the critical behavior and magnetic properties of La2/3Ca1/3MnO3 thin films

Critical exponents offer important information concerning the interaction mechanisms near the paramagnetic to ferromagnetic transition. In this work a Monte Carlo-Metropolis simulation of the critical behavior in La_2/3Ca_1/3MnO₃ thin films is addressed. Canonical ensemble averages for magnetization per site, magnetic susceptibility and specific heat of stoichiometric manganite within a three-dimensional classical Heisenberg model with nearest magnetic neighbor interactions are computed. The La_2/3Ca_1/3MnO₃ thin films were simulated addressing the thickness influence and thermal dependence. In the model, Mn magnetic ions are distributed on a simple cubic lattice according to the perovskite structure of this manganite. Ferromagnetic coupling for the bonds Mn³⁺-Mn³⁺(e_g-e_g′), Mn³⁺-Mn⁴⁺(e_g-d³) and Mn³⁺-Mn⁴⁺(e_g′-d³) were taken into account. On the basis of finite-size scaling theory, our best estimates of critical exponents, linked to the ferromagnetic to paramagnetic transition, for the correlation length, specific heat, magnetization and susceptibility are, respectively: v=0.56±0.01, α=0.16±0.03, β=0.34±0.04γ and γ=1.17±0.05. These theoretical results are consistent with the Rushbrooke equalitiy α+2β+γ=2.     

Critical phenomena of amorphous Nd4(Fe0.75Cr0.25)77.5B18.5 alloys

The magnetic behavior of amorphous Nd₄(Fe_0.75Cr_0.25)_77.5B_18.5 alloys was investigated in the critical region. The Curie temperature T_C and critical exponents β, γ and δ are found to be 141 K, 0.45±0.02, 1.64±0.08 and 4.66±0.10, respectively. The data are fitted to a magnetic equation of state characteristic of a second-order phase transition over a rather wide range of temperatures both above and below T_C. It is noted that the values of the exponents are in disagreement with those derived for a three-dimensional Heisenberg ferromagnet and show an enhancement. This anomalous critical behavior may originate from magnetic inhomogeneity.     

Monte Carlo simulation of magnetic ordering in the Gd3Fe5O12 Ising ferrite with garnet structure

The simulation of magnetic properties in extended quantum spin networks can be done in good conditions with Ising models within Monte Carlo–Metropolis algorithms, as our systematic studies, employing original computer codes, proved. The present analysis provides interesting insights into the exchange interactions governing the magnetic behavior of the Gd₃Fe₅O₁₂ system, taken as a prototype for ferrites with garnet structure. Effective exchange interaction parameters are estimated by fitting the computed with experimental compensation temperature and temperature dependence of the magnetization.     

Phase diagrams and magnetic properties of CaCu3Fe2Os2O12 quadruple perovskite: Monte Carlo study

In this paper, a Monte Carlo Simulation (MCS) has been used to study the quadruple perovskite oxide CaCu₃Fe₂Os₂O₁₂. The system has been conceived as a mixture of atoms with the magnetic moments Cu (±1/2), Fe (±5/2, ±3/2, ±1/2) and Os (±3/2, ±1/2). Phase diagrams depending on reduced exchange couplings and reduced crystal fields have been established. A stable ferromagnetic phase at the ground state has been found. Investigation of magnetic properties has been focused on the finite size analysis of magnetization and magnetic susceptibility according to reduced temperatures. Critical temperature has been calculated through simulation and the compound has been found to belong in the three-dimensional Ising model universality class.     

Series and Monte Carlo study of high-dimensional Ising models

Ising models in high dimensions are used to compare high-temperature series expansions with Monte Carlo simulations. Simulations of the magnetization on four-, six-, and seven-dimensional hypercubic lattices give consistent values of the critical temperature from both equilibrium and nonequilibrium data ford=6 and 7. We tabulate 15 terms of series expansions for the susceptibility for generald and giveJ/k _B T _c =0.092295 (3) and 0.077706 (2) ford=6 and 7. In contrast to five dimensions, where earlier series found nonanalytic scaling corrections, for d=6 and 7 the leading scaling correction may be analytic inT-T _c . In most cases these expansions gave more accurate results than these simulations.     

Critical behaviour of the specific heat of La0.9Ag0.1MnO3 manganite

 For the first time the specific heat of polycrystalline La_0.9Ag_0.1MnO₃ manganite near the Curie temperature was precisely measured by AC calorimetry and its critical behaviour was studied. The critical behaviour of the specific heat was approximated by the relationship taking into account corrections to the scaling. The regularities of variations in the universal critical parameters near the critical point are determined, and their values are calculated. Detailed analysis and comparison of the received results with the theoretical predictions and other experimental results was carried out.     

Monte Carlo simulation of magnetic and magnetocaloric properties of binary alloy Gd1−xCx

The Potts-like model is utilized to describe an alloy Gd_1−xC_x with x=0, 0.025, 0.06, 0.09, and the magnetic and magnetocaloric properties are calculated by Monte Carlo method. The effect of the local distortion of the lattice due to adulterated C atom on the exchange interaction between Gd atoms can be considered. The spontaneous magnetization, specific heat, and magnetic susceptibility are calculated. It is found that the magnetization at low temperature decreases but phase transition temperature from ferromagnetic to paramagnetic increases, as the concentration of the C atom in the system increases. Moreover, the specific heat and the susceptibility exhibit peaks at the transition temperature. For two external magnetic field h/J=0.25 and 10.0, the magnitude of the isothermal magnetic entropy change in binary alloy is more than in pure Gd system. Furthermore, the range of temperature of half peak in the curve of the magnetic entropy change becomes wide and the refrigerant capacity increases in the alloy.     

Nanocrystallization behaviour of a ternary amorphous alloy during isothermal annealing： a Monte Carlo simulation

The nanocrystallization behaviour of Zr70Cu20Ni10 metallic glass during isothermal annealing is studied by employing a Monte Carlo simulation incorporating with a modified Ising model and a Q-state Potts model. Based on the simulated microstructure and differential scanning calorimetry curves, we find that the low crystal-amorphous interface energy of Ni plays an important role in the nanocrystallization of primary Zr2Ni. It is found that when T〈T1max （where T1max is the temperature with maximum nucleation rate）, the increase of temperature results in a larger growth rate and a much finer mierostrueture for the primary Zr2Ni, which accords with the microstructure evolution in ＂flash annealing＂. Finally, the Zr2Ni/Zr2Cu interface energy σG contributes to the pinning effect of the primary nano-sized Zr2Ni grains in the later formed normal Zr2Cu grains.     

Critical behavior of the specific heat for pure and site-diluted simple cubic Ising systems

The exponent of the specific heatC is determined for the pure and the site-diluted simple cubic Ising model (concentrationx=0, 0.2, 0.4 of nonmagnetic sites) by a finite-size scaling analysis of the peak value C_max(L) for systems of linear dimensionsL=8, 16, 32, and 64. The C_max values are obtained by the Ferrenberg-Swendsen algorithm, using Monte Carlo data from a fully-vectorized multi-spin coding program. We obtain =0.11 for x=0 and a crossover to a negative value upon dilution, with =–0.029(4) both forx=0.2 andx=0.4.     

Monte Carlo study of the antiferromagnetical Ising model on a centred honeycomb lattice

We use the Monte Carlo method to study an antiferromagnetical Ising spin system on a centred honeycomb lattice, which is composed of two kinds of 1/2 spin particles A and B. There exist two different bond energies J_A-A and J_A-B in this lattice. Our study is focused on how the ratio of J_A-B to J_A-A influences the critical behaviour of this system by analysing the physical quantities, such as the energy, the order parameter, the specific heat, susceptibility, {etc} each as a function of temperature for a given ratio of J_A-B to J_A-A. Using these results together with the finite-size scaling method, we obtain a phase diagram for the ratio J_A-B / J_A-A. This work is helpful for studying the phase transition problem of crystals composed of compounds.     

The roughening transition of the three-dimensional Ising interface: A Monte Carlo study

We study the roughening transition of an interface in an Ising system on a 3D simple cubic lattice using a finite-size scaling method. The particular method has recently been proposed and successfully tested for various solid-on-solid models. The basic idea is the matching of the renormalization-groupflow of the interface with that of the exactly solvable body-centered cubic solid-on-solid model. We unambiguously confirm the Kosterlitz-Thouless nature of the roughening transition of the Ising interface. Our result for the inverse transition temperatureK _r=0.40754(5) is almost two orders of magnitude more accurate than the estimate of Mon, Landau, and Stauffer.     

Monte Carlo investigation of the correlation between magnetic and chemical ordering in NiFe alloys

The Ni_xFe_1−x alloys close to the stoichiometric Ni₃Fe composition are modeled by means of Monte Carlo simulations. To describe the atomic and magnetic configurations, the Ising and Heisenberg models with nearest-neighbor interactions have been used, respectively. The pairwise interactions have been fitted to the experimentally measured Curie and Kurnakov temperatures, the Fe-Fe magnetic exchange interaction has been considered antiferromagnetic. The mutual influence of the magnetic and chemical ordering is evidenced and a good agreement with the phase diagram is obtained. Our numerical results show that the magnetic order is able to increase the Kurnakov temperature and, reciprocally, the chemical order is responsible for a rise in the Curie temperature. Also, the influence of the applied magnetic field on the chemical order is investigated and an increase of the Kurnakov temperature with the external field is observed.     

Critical and compensation phenomena in a mixed-spin ternary alloy: A Monte Carlo study

By means of standard and histogram Monte Carlo simulations, we investigate the critical and compensation behaviour of a ternary mixed spin alloy of the type AB_pC_1−p on a cubic lattice. We focus on the case with the parameters corresponding to the Prussian blue analog and confront our findings with those obtained by some approximative approaches and the experiments.     

Monte Carlo simulation of the compensation and critical behaviors of a ferrimagnetic core/shell nanoparticle Ising model

A Monte Carlo simulation has been used to study the magnetic properties and the critical behaviors of a single spherical nanoparticle, consisting of a ferromagnetic core of spins surrounded by a ferromagnetic shell of S=±1, 0 or , spins with antiferromagnetic interface coupling, located on a simple cubic lattice. A number of characteristic phenomena has been found. In particular, the effects of the shell coupling and the interface coupling on both the critical and compensation temperatures are investigated. We have found that, for appropriate values of the system parameters, two compensation temperatures may occur in the present system.