Low-temperature metastable states in a stacked triangular Ising antiferromagnet

We study low-temperature magnetization processes in a stacked triangular Ising antiferromagnet by Monte Carlo simulations. In increasing and decreasing magnetic fields we observe multiple steps and hysteresis corresponding to formation of different metastable states. Besides the equidistant threefold splitting of the 1/3 ferrimagnetic plateau, we additionally confirm a fourth plateau in the field-increasing branch and a sizable remanence when the field is decreased to zero. The newly observed plateau only appears at sufficiently low temperature and sufficiently large exchange interaction in the stacking direction. These observations reasonably reproduce low-temperatures measurements on the spin-chain compound Ca₃Co₂O₆.     

Phase diagram of a diluted triangular lattice Ising antiferromagnet in a field

Magnetization processes and phase transitions in a geometrically frustrated triangular lattice Ising antiferromagnet in the presence of an external magnetic field and a random site dilution are studied by the use of an effective-field theory with correlations. We find that the interplay between the applied field and the frustration-relieving dilution results in peculiar phase diagrams in the temperature-field-dilution parameter space.     

Critical behaviour of the ferromagnetic Ising model on a triangular lattice

We use a new updated algorithm scheme to investigate the critical behaviour of the two-dimensional ferromagnetic Ising model on a triangular lattice with the nearest neighbour interactions. The transition is examined by generating accurate data for lattices with L= 8, 10, 12, 15, 20, 25, 30, 40 and 50. The updated spin algorithm we employ has the advantages of both a Metropolis algorithm and a single-update method. Our study indicates that the transition is continuous at T_c= 3.6403({2}). A convincing finite-size scaling analysis of the model yields υ=0.9995(21), β / υ = 0.12400({17}), γ / υ = 1.75223(22), γ '/υ=1.7555(22), α/υ= 0.00077(420) (scaling) and α / υ = 0.0010(42) (hyperscaling). The present scheme yields more accurate estimates for all the critical exponents than the Monte Carlo method, and our estimates are shown to be in excellent agreement with their predicted values.     

Comparison of diluted antiferromagnetic Ising models on frustrated lattices in a magnetic field

We study diluted antiferromagnetic Ising models on triangular and kagome lattices in a magnetic field, using the replica-exchange Monte Carlo method. We observe seven and five plateaus in the magnetization curve of the diluted antiferromagnetic Ising model on the triangular and kagome lattices, respectively, when a magnetic field is applied. These observations contrast with the two plateaus observed in the pure model. The origin of multiple plateaus is investigated by considering the spin configuration of triangles in the diluted models. We compare these results with those of a diluted antiferromagnetic Ising model on the three-dimensional pyrochlore lattice in a magnetic field pointing in the [111] direction, sometimes referred to as the “kagome-ice” problem. We discuss the similarity and dissimilarity of the magnetization curves of the “kagome-ice” state and the two-dimensional kagome lattice.     

Partially disordered antiferromagnetic state in two-dimensional triangular-lattice antiferromagnet

The partially disordered antiferromagnetic (PDA) state, as an exotic phase peculiar to the antiferromagnet with Ising spin in triangular lattice, is investigated by using Monte Carlo simulations of Wang-Landau algorithm and Glauber algorithm. It is revealed that PDA state, as the ground state of the triangular antiferromagnetic system, presents the complicated spin configuration due to geometrical frustration. The formation of multi-domain structure within the framework of honeycomb antiferromagnet results in the high degeneracy of PDA state. And this degeneracy of ground state can be lifted by a small magnetic field. Consequently the system shows the ferrimagnetic state, and the magnetization plateau of 1/3 saturate value (Ms) is observed in many experiments. Moreover, due to the multi-domain structure of PDA state and those spins on domain walls, the metastable steps may manifest themselves superposed on the 1/3Ms plateau in some special cases.     

Critical and tricritical behavior of a selectively diluted triangular Ising antiferromagnet in a field

We study a geometrically frustrated triangular Ising antiferromagnet in an external magnetic field which is selectively diluted with nonmagnetic impurities employing an effective-field theory with correlations and Monte Carlo simulations. We focus on the frustration-relieving effects of such a selective dilution on the phase diagram and find that it can lead to rather intricate phase diagrams in the dilution-field parameters space. In particular, in a highly (weakly) diluted system the frustration is greatly (little) relieved and such a system is found to display only the second(first)-order phase transitions at any field. On the other hand, for a wide interval of intermediate dilution values the transition remains second-order at low fields but it changes to first-order at higher fields and the system displays a tricritical behavior. The existence of the first-order transition in the region of intermediate dilution and high fields is verified by Monte Carlo simulations.     

Effects of selective dilution on phase diagram and ground-state magnetizations of an Ising antiferromagnet on triangular and honeycomb lattices

We employ an effective-field theory with correlations in order to study the phase diagram and ground-state magnetizations of a selectively diluted Ising antiferromagnet on triangular and honeycomb lattices. Dilution of different sublattices with generally unequal probabilities results in a rather intricate phase diagram in the sublattice dilution parameters space. In the case of the frustrated triangular lattice antiferromagnet the selective dilution affects the degree of frustration which can lead to some peculiar phenomena, such as reentrant behavior of long-range order or unsaturated sublattice magnetizations at zero temperature. The selectively diluted Ising antiferromagnet on the honeycomb lattice is obtained as a special case when one sublattice of the triangular lattice is completely removed by dilution.     

Interface motion in a two-dimensional Ising model with a field

We determine by Monte Carlo simulations the width of an interface between the stable phase and the metastable phase in a two-dimensional Ising model with a magnetic field, in the case of nonconversed order parameter (Glauber dynamics). At zero temperature, the width increases ast with–1/3, as predicted by earlier theories. As temperature increases, the value of the effective exponent that we measure decreases toward the value 1/4, which is the value in the absence of magnetic field.     

The density of states for an antiferromagnetic Ising model on a triangular lattice

The Wang-Landau algorithm is an efficient Monte Carlo approach to the density of states of a statistical mechanics system. The estimation of state density would allow the computation of thermodynamic properties of the system over the whole temperature range. We apply this sampling method to study the phase transitions in a triangular Ising model. The entropy of the lattice at zero temperature as well as other thermodynamic properties is computed. The calculated thermodynamic properties are explained in the context of the magnetic phase transition.      

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.     

Phase diagrams of the transverse Ising antiferromagnet in the presence of the longitudinal magnetic field

In this paper we study the critical behavior of the two-dimensional antiferromagnetic Ising model in both uniform longitudinal (H$H$) and transverse (Ω$\Omega$) magnetic fields. Using the effective-field theory (EFT) with correlation in single site clusters we calculate the phase diagrams in the H−T$H-T$ and Ω−T$\Omega -T$ planes for the square lattice. We have only found second order phase transitions for all values of fields and reentrant behavior was not observed.     

The stochastic models method applied to the critical behavior of Ising lattices

The stochastic models (SM) computer simulation method for treating manybody systems in thermodynamic equilibrium is investigated. The SM method, unlike the commonly used Metropolis Monte Carlo method, is not of a relaxation type. Thus an equilibrium configuration is constructed at once by adding particles to an initiallyempty volume with the help of a model stochastic process. The probability of the equilibrium configurations is known and this permits one to estimate the entropy directly. In the present work we greatly improve the accuracy of the SM method for the two and three-dimensional Ising lattices and extend its scope to calculate fluctuations, and hence specific heat and magnetic susceptibility, in addition to average thermodynamic quantities like energy, entropy, and magnetization. The method is found to be advantageous near the critical temperature. Of special interest are the results at the critical temperature itself, where the Metropolis method seems to be impractical. At this temperature, the average thermodynamic quantities agree well with theoretical values, for both the two and three-dimensional lattices. For the two-dimensional lattice the specific heat exhibits the expected logarithmic dependence on lattice size; the dependence of the susceptibility on lattice size is also satisfactory, leading to a ratio of critical exponents/=1.85 ±0.08. For the three-dimensional lattice the dependence of the specific heat, long-range order, and susceptibility on lattice size leads to similarly satisfactory exponents:=0.12 ±0.03,=0.30 ±0.03, and=1.32 ±0.05 (assuming =2/3).     

Degenerate ferrimagnetic ground state of frustrated kagome lattice

The frustrated Ising model on kagome lattice with nearest-neighboring antiferromagnetic interaction is investigated by using Monte Carlo simulation of the Wang-Landau algorithm and Glauber dynamics. The geometrical frustration leads to a particularly high degeneracy of ground states in this system. A small magnetic field applied can lift the degeneracy partially, and produce the magnetization plateau of 1/3 saturate value (Ms), which is analogous to the magnetic behavior in triangular antiferromagnetic system. However, different from the long-range ferrimagnetic state responsible for 1/3 Ms plateau in triangular lattice, the ferrimagnetic ground state corresponding to 1/3 Ms plateau in kagome lattice is short-ranged and still highly degenerate. Furthermore, the spin configuration of these degenerate ferrimagnetic ground states show an inherent characteristic that the spins along the magnetic field must be aligned on the closed loops, which can be well understood in terms of geometrical frustration.     

阻挫三角反铁磁AgCrO2螺旋自旋序的第一性原理研究

基于密度泛函理论的广义梯度近似(GGA)和投影缀加波(PAW)方法,分别从共线和非共线磁性结构出发,研究了自旋阻挫三角反铁磁AgCrO₂的基态、磁性以及电子结构,从理论计算的角度给出了基态磁性结构.计算结果表明:AgCrO₂具有120°螺旋自旋序反铁磁基态,其自旋螺旋面平行于(110)面或(11^-0)面;由于Cr离子间的自旋几何阻挫,导致沿晶体的a,b和a+b方向上均形成了螺旋自旋转动角为120°的 关键词： 第一性原理 交换相互作用 阻挫 反铁磁     

Magnetocaloric properties of frustrated tetrahedra-based spin nanoclusters

Magnetization, entropy and magnetocaloric properties of various geometrically frustrated tetrahedra-based Ising antiferromagnetic nanoclusters with corner-, edge-, and face-sharing topologies are studied by exact enumeration. It is found that the studied properties strongly depend on the nanocluster topology and can be very different from those of a single tetrahedron as well as the pyrochlore lattice formed by an infinite number of corner-sharing tetrahedra. From the magnetocaloric point of view an important difference from the latter two systems is the absence of the ground-state zero-magnetization plateau in most of the studied structures, which at low temperatures facilitates emergence of a giant magnetocaloric effect in a vanishing magnetic field in the adiabatic demagnetization process. Magnetic systems with such properties might be suitable candidates for technological application as efficient refrigerators to ultra-low temperatures.     

Corner transfer matrices of the triangular Ising model

Recently, a new technique for investigating the zero-field, eight-vertex model on the square lattice using corner transfer matrices was suggested by Baxter. In this paper these ideas are applied to the anisotropic, ferromagnetic, triangular Ising lattice in zero field below its critical temperature. The diagonal form of the corner transfer matrix for the triangular lattice shows essentially the same structure as that for the square Ising lattice. The spontaneous magnetization can be obtained easily and agrees with that previously derived.     

Entropy of spin clusters with frustrated geometry

Geometrically frustrated clusters of Ising spins of different shapes on a triangular lattice are studied by exact enumeration. The focus is laid on the ground-state energy and residual entropy behaviors as functions of the cluster shape and size, as well as the spin value. Depending on the cluster shape, the residual entropy density in approach to the thermodynamic limit can either vanish or remain finite and the dependence can be decreasing, increasing or non-monotonic. Nevertheless, the relative entropies normalized by the respective thermodynamic limit values turn out to be little sensitive to the spin value. Attention is drawn to magnetocaloric properties of systems of selected cluster shapes.     

Monte Carlo study of dynamic phase transition in Ising metamagnet driven by oscillating magnetic field

The dynamical responses of Ising metamagnet (layered antiferromagnet) in the presence of a sinusoidally oscillating magnetic field are studied by Monte Carlo simulation. The time average staggered magnetisation plays the role of dynamic order parameter. A dynamical phase transition was observed and a phase diagram was plotted in the plane formed by field amplitude and temperature. The dynamical phase boundary is observed to shrink inward as the relative antiferromagnetic strength decreases. The results are compared with that obtained from pure ferromagnetic system. The shape of dynamic phase boundary observed to be qualitatively similar to that obtained from previous meanfield calculations.     

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.