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 $({\rm Ni}^{\rm II}_p {\rm Mn}^{\rm II}_{1-p})_{1.5}[{\rm Cr^{III}(CN)}_6] \cdot n {\rm H_2O}$ and confront our findings with those obtained by some approximative approaches and the experiments.Comment: 20 pages, 8 figure

Phase transitions in a triangular Blume-Capel antiferromagnet

We study the critical behavior of a frustrated Blume-Capel (BC) antiferromagnet on a triangular lattice by Monte Carlo simulations. For a reduced single-ion anisotropy strength $-1.47 \lesssim d < 0$ we find two phase transitions. The low-temperature phase is characterized by the antiferromagnetic long-range ordering (LRO) on two sublattices with the third one remaining in a non-magnetic state. At higher temperatures there is a critical region of the Berezinskii-Kosterlitz-Thouless (BKT) type with a power-law decaying spin-correlation function. For $-1.5 \le d \lesssim -1.47$, there is only one phase transition from the LRO to the paramagnetic region and the transition is of first order. The presence of the BKT phase in the current frustrated BC model is a new feature not observed in its non-frustrated counterparts. The values of the decay exponent $\eta$ of the BKT phase corresponding to upper and lower temperatures appear to be consistent with the theoretical predictions for the six-state clock model.Comment: 19 pages, 12 figure

Critical behavior of a triangular lattice Ising AF/FM bilayer

We study a bilayer Ising spin system consisting of antiferromagnetic (AF) and ferromagnetic (FM) triangular planes, coupled by ferromagnetic exchange interaction, by standard Monte Carlo and parallel tempering methods. The AF/FM bilayer is found to display the critical behavior completely different from both the single FM and AF constituents as well as the FM/FM and AF/AF bilayers. Namely, by finite-size scaling (FSS) analysis we identify at the same temperature a standard Ising transition from the paramagnetic to FM state in the FM plane that induces a ferrimagnetic state with a finite net magnetic moment in the AF plane. At lower temperatures there is another phase transition, that takes place only in the AF plane, to different ferrimagnetic state with spins on two sublattices pointing parallel and on one sublattice antiparallel to the spins on the FM plane. FSS indicates that the corresponding critical exponents are close to the two-dimensional three-state ferromagnetic Potts model values.Comment: 11 pages, 5 figure

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 and Monte Carlo simulation. 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 on 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. Some interesting finite-temperature properties of the clusters are also discussed and attention is drawn to their magnetocaloric properties.Comment: 15 pages, 7 figure

Phase diagram of a mixed spin-1 and spin-3/2 Ising ferrimagnet

Critical and compensation properties of a mixed spin-1 and spin-3/2 Ising ferrimagnet on a square lattice are investigated by standard and histogram Monte Carlo simulations. The critical temperature is studied as a function of a single-ion anisotropy strength. The second order of the phase transition is established by finite-size scaling for the entire boundary. Some previously obtained results, such as a tricritical point, predicted by the mean field theory (MFT) and effective field theory (EFT), or a first-order transition line separating two different ordered phases, obtained by the cluster variational theory (CVT), are deemed artifacts of the respective approximations. So is a reentrant phenomenon produced by CVT. Nevertheless, the multicompensation behavior predicted by MFT and EFT was confirmed.Comment: 14 pages, 5 figure

Frustrated mixed spin-1/2 and spin-1 Ising ferrimagnets on a triangular lattice

Mixed spin-1/2 and spin-1 Ising ferrimagnets on a triangular lattice with sublattices A, B and C are studied for two spin value distributions $(S_{\rm A},S_{\rm B},S_{\rm C})=(1/2,1/2,1)$ and $(1/2,1,1)$ by Monte Carlo simulations. The non-bipartite character of the lattice induces geometrical frustration in both systems, which leads to the critical behavior rather different from their ferromagnetic counterparts. We confirm second-order phase transitions belonging to the standard Ising universality class occurring at higher temperatures, however, in both models these change at tricritical points (TCP) to first-order transitions at lower temperatures. In the model $(1/2,1/2,1)$, TCP occurs on the boundary between paramagnetic and ferrimagnetic $(\pm 1/2,\pm 1/2,\mp 1)$ phases. The boundary between two ferrimagnetic phases $(\pm 1/2,\pm 1/2,\mp 1)$ and $(\pm 1/2,\mp 1/2,0)$ at lower temperatures is always first order and it is joined by a line of second-order phase transitions between the paramagnetic and the ferrimagnetic $(\pm 1/2,\mp 1/2,0)$ phases at a critical endpoint. The tricritical behavior is also confirmed in the model $(1/2,1,1)$ on the boundary between the paramagnetic and ferrimagnetic $(0,\pm 1,\mp 1)$ phases.Comment: 23 pages, 12 figure

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.Comment: 18 pages, 7 figure

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 $\rm{Ca}_3\rm{Co}_2\rm{O}_6$.Comment: 14 pages, 5 figure

Magnetism of the diluted Ising antiferromagnet in a magnetic field on the Kagome lattice: single-spin cluster approximation

An effective-field theory based on the single-spin cluster has been used to study of a diluted spin-$1/2$ Ising antiferromagnet on the Kagome lattice with nearest-neighbor interactions. We observe five plateaus in the magnetization curve of the diluted antiferromagnet when a magnetic field is applied which is in agreement with Monte Carlo calculation. The effect of the site-dilution on the magnetic susceptibility is also investigated and discussed. In particular, we have found that the frustrated Kagome lattice inverse susceptibility fall to zero at $0$K.Comment: 6 pages, 4 figures, work to be presented at CSMAG conferenc

Phase transitions in a frustrated Ising antiferromagnet on a square lattice

The phase transitions occurring in the frustrated Ising square antiferromagnet with first- ($J_1 < 0$) and second- ($J_2 < 0$) nearest-neighbor interactions are studied within the framework of the effective-field theory with correlations based on the different cluster sizes and for a wide range of $R = J_2/|J_1|$. Despite the simplicity of the model, it has proved difficult to precisely determine the order of the phase transitions. In contrast to the previous effective-field study, we have found a first-order transition line in the region close to $R = -0.5$ not only between the superantiferromagnetic and paramagnetic ($R<-0.5$) but also between antiferromagnetic and paramagnetic ($R>-0.5$) phases.Comment: 16 pages, 6 figure