Nearest-neighbor Coupling Constants Research Articles

Depletion-driven antiferromagnetic, paramagnetic, and ferromagnetic behavior in quasi-two-dimensional buckled colloidal solids.

We investigate quasi-two-dimensional buckled colloidal monolayers on a triangular lattice with tunable depletion interactions. Without depletion attraction, the experimental system provides a colloidal analog of the well-known geometrically frustrated Ising antiferromagnet [Y. Han et al., Nature 456, 898-903 (2008)]. In this contribution, we show that the added depletion attraction can influence both the magnitude and signof an Ising spin coupling constant. As a result, the nearest-neighbor Ising "spin" interactions can be made to vary from antiferromagnetic to para- and ferromagnetic. Using a simple theory, we compute an effective Ising nearest-neighbor coupling constant, and we show how competition between entropic effects permits for the modification of the coupling constant. We then experimentally demonstrate depletion-induced modification of the coupling constant, including its sign, and other behaviors. Depletion interactions are induced by rod-like surfactant micelles that change length with temperature and thus offer means for tuning the depletion attraction insitu. Buckled colloidal suspensions exhibit a crossover from an Ising antiferromagnetic to paramagnetic phase as a function of increasing depletion attraction. Additional dynamical experiments reveal structural arrest in various regimes of the coupling-constant, driven by different mechanisms. In total, this work introduces novel colloidal matter with "magnetic" features and complex dynamics rarely observed in traditional spin systems.

Thermal transport properties of Heisenberg antiferromagnet on honeycomb lattice: The effects of anisotropy

We study the thermal conductivity of a spin-1/2 two-dimensional anisotropic antiferromagnet on honeycomb lattice in the presence of antiferromagnetic long range ordering. The conductivity has been studied along zigzag direction. Next nearest neighbor exchange coupling has been added to the model Hamiltonian. The possible effects of spin–orbit coupling are investigated by adding Dzyaloshinskii–Moriya interaction to the model Hamiltonian. Such interaction creates anisotropic effects in the model Hamiltonian. The original antiferromagnetic model hamiltonian is mapped to a bosonic model via linear spin wave theory in the context of Holstein Primakoff transformations. The Green’s function approach is applied to obtain the energy spectrum of quasi-particle excitations responsible for thermal transport. We have found the temperature dependence of static thermal conductivity in the magnetic long range ordering phase for various next nearest neighbor coupling constant and anisotropy parameter. Furthermore we have studied the temperature dependence of the static thermal conductivity for various Dzyaloshinskii-Moriya interaction strength and next nearest neighbor coupling constants. Our results show that each curve for temperature dependence of thermal conductivity includes a peak so that the height of peak reduces with magnetic field however the temperature positions of peaks is independent of magnetic field value. Moreover the increase of anisotropic parameter leads to enhance thermal conductivity values. Also the next nearest neighbor coupling constant improves thermal conductivity of localized electrons on honeycomb structure . The exponential behavior for temperature dependence of thermal conductivity at low temperatures is the novel feature in thermal conductivity results. • Study of thermal conductivity of honeycomb lattics. • Study of anisotropic parameter on conductivity. • Study of magnetic field effects on conductivity.

Thermal Conductivity of Localized Electrons on Magnetic Ordered Monolayer Graphene

We study the thermal conductivity of a spin-1/2 two-dimensional anisotropic antiferromagnet on honeycomb lattice in the presence of antiferromagnetic long range ordering. The conductivity has been studied along zigzag direction. Next nearest neighbor exchange coupling has been added to the model Hamiltonian. The possible effects of spin-orbit coupling are investigated by adding Dzyaloshinskii-Moriya interaction to the model Hamiltonian. Such interaction creates anisotropic effects in the model Hamiltonian. The original antiferromagnetic model hamiltonian is mapped to a bosonic model via linear spin wave theory in the context of Holstein Primakoff transformations. The Green's function approach is applied to obtain the energy spectrum of quasi-particle excitations responsible for thermal transport. We have found the temperature dependence of static thermal conductivity in the magnetic long range ordering phase for various next nearest neighbor coupling constant and anisotropy parameter. Furthermore we have studied the temperature dependence of the static thermal conductivity for various Dzyaloshinskii-Moriya interaction strength and next nearest neighbor coupling constants.

Dynamical and static spin conductivities in the Heisenberg model on honeycomb lattice: The effects of magnetic long range ordering

We have studied both dynamical and static spin conductivities of Heisenberg antiferromagnet on honeycomb lattice in the presence of a magnetic long range ordering. The effects of spatial anisotropy as weak Dzyaloshinskii–Moriya interaction and next nearest neighbor exchange coupling on the behaviors of conductivities are discussed. A sublattice antiferromagnetic long range ordering has been considered for localized electrons on honeycomb lattice structure. Using Holstein–Primakoff bosonic transformations, the behaviors of spin transport properties have been studied by means of excitation spectrum of mapped bosonic gas. We have found the temperature dependence of static spin conductivity in the field induced gapped spin-polarized phase for various Dzyaloshinskii–Moriya interaction strengths. Furthermore we have studied the frequency dependence of dynamical spin conductivity for various Dzyaloshinskii–Moriya interaction strengths and different next nearest neighbor coupling constants. We find that the height of peak in the temperature dependence of static spin conductivity increases upon increasing the anisotropy parameter. The static spin conductivity is found to be monotonically increasing with anisotropy parameter due to increase of the energy gap in the excitation spectrum. Furthermore we have studied the temperature dependence of the spin conductivity for different next nearest neighbor coupling constants.

Spin transport properties of anisotropic Heisenberg antiferromagnet on honeycomb lattice in the presence of magnetic field

We have addressed the spin conductivity of a two-dimensional anisotropic antiferromagnet on honeycomb lattice in the presence of a longitudinal magnetic field. A spatial anisotropy in the form of a weak Dzyaloshinskii-Moriya interaction is considered in the model Hamiltonian. Next nearest neighbor exchange coupling has been added to the model Hamiltonian. We have investigated both dynamical and static spin conductivities in terms of the excitation spectrum by means of a hard core bosonic representation. The effects of next-nearest-neighbor coupling and the Dzyaloshinskii-Moriya interaction on the spin transport properties have also been studied via the bosonic model by a Green’s function approach. We have found the temperature dependence of static spin conductivity in the field induced gapped spin-polarized phase for various magnetic field and anisotropy parameters. Furthermore we have studied the magnetic field dependence of the static spin conductivity for various Dzyaloshinskii-Moriya interaction strength and the frequency dependence of the dynamical spin conductivity for various next nearest neighbor coupling constants. We find that the peak in the static spin conductivity moves to higher temperature upon increasing the magnetic field at fixed anisotropy parameter. The static spin conductivity is found to be monotonically decreasing with magnetic field due to increase of the energy gap in the excitation spectrum. Furthermore we have studied the temperature dependence of the spin conductivity for different magnetic field and various next nearest neighbor coupling constants.

Magnetic structure factors Heisenberg model for magnetic ordered graphene like structure

We have theoretically studied the magnetic structure factors of Heisenberg model on honeycomb lattice in the presence of anisotropic Dzyaloshinskii–Moriya interaction and next nearest neighbor coupling exchange constant. A sublattice antiferromagnetic long range ordering has been considered for localized electrons on honeycomb lattice structure. In particular, the frequency dependence of both longitudinal and transverse dynamical spin susceptibilities has been investigated for various physical parameters in the model Hamiltonian. Using Holstein–Primakoff bosonic transformations, the behavior of magnetic susceptibilities properties has been studied by means of excitation spectrum of mapped bosonic gas. Furthermore we have studied the dependence of static spin susceptibilities on Dzyaloshinskii–Moriya interaction strength for various next nearest neighbor interaction strengths. We have found the dependence of static longitudinal spin structure factor on Dzyaloshinskii–Moriya interaction strength shows a divergence behavior at phase transition point for various next nearest neighbor exchange constants. Also our results show the position of peak in the dynamical transverse spin structure factor at fixed value for Dzyaloshinskii Moriya interaction moves to lower frequency with next nearest neighbor coupling constant.

Thermodynamic properties of Heisenberg model for magnetic ordered graphene sheet

We study the thermodynamic properties of two dimensional Heisenberg antiferromagnet on the honeycomb lattice in the presence of anisotropic Dzyaloshinskii-Moriya interaction and next nearest neighbor coupling exchange constant. A sublattice antiferromagnetic long range ordering has been considered for localized electrons on honeycomb lattice structure. In particular, the temperature dependence of specific heat has been investigated for various physical parameters in the model Hamiltonian. Using Holstein-Primakoff bosonic transformations, the behavior of thermodynamic properties has been studied by means of excitation spectrum of mapped bosonic gas. Furthermore we have studied the dependence of specific heat and magnetization on Dzyaloshinskii-Moriya interaction strength for various next nearest neighbor interaction strengths. At low temperatures, the specific heat is found to be monotonically increasing with temperature. We have found the dependence of specific heat on Dzyaloshinskii-Moriya interaction strength shows a monotonic increasing behavior for various next nearest neighbor exchange constants. Also we have studied the temperature dependence of staggered magnetization for different next nearest neighbor coupling constants. Our results show the critical temperature moves to higher amounts with reduction of Dzyaloshinskii-Moriya interaction strength.

Longitudinal magnetization and specific heat of the anisotropic heisenberg antiferromagnet on honeycomb lattice

We study the effects of longitudinal magnetic field and temperature on the thermodynamic properties of two dimensional Heisenberg antiferromagnet on the honeycomb lattice in the presence of anisotropic Dzyaloshinskii-Moriya interaction and next nearest neighbor coupling exchange constant. In particular, the temperature dependence of specific heat have been investigated for various physical parameters in the model Hamiltonian. Using a hard core bosonic representation, the behavior of thermodynamic properties has been studied by means of excitation spectrum of mapped bosonic gas. The effect of Dzyaloshinskii-Moriya interaction term on thermodynamic properties has also been studied via the bosonic model by Green's function approach. Furthermore we have studied the magnetic field dependence of specific heat and magnetization for various anisotropy parameters. At low temperatures, the specific heat is found to be monotonically increasing with temperature for magnetic fields in the gapped field induced phase region. We have found the magnetic field dependence of specific heat shows a monotonic decreasing behavior for various magnetic fields due to increase of energy gap in the excitation spectrum. Also we have studied the dependence of magnetization on Dzyaloshinskii-Moriya interaction strength for different next nearest neighbor coupling constant.

First-principles study of structural, electronic, and magnetic properties of double perovskiteHo2MnFeO6

Using first-principles calculations, we investigate the structural, electronic, and magnetic properties of the designed double-perovskite-oxide ${\text{Ho}}_{2}{\text{MnFeO}}_{6}$ within generalized gradient approximation (GGA) and the $\text{GGA}+U$ methods. The calculations on electronic structure indicate the material to be half-metallic ferromagnets. Structural parameters are optimized using GGA method and different positional orderings and magnetic-coupling schemes are investigated. We also investigate the effect of Hubbard parameter $U$ on the ground-state structural parameters and electronic properties. We discuss the magnetic-coupling interactions for the ${\text{Mn}}^{3+}({d}^{4}){\text{-Fe}}^{3+}({d}^{5})$ system with special orbital ordering and calculate the magnetic nearest-neighbor coupling constants using Anderson's superexchange model and then obtain a mean-field approximation for the magnetic-ordering temperatures.

Electronic Structure and Spin Exchange Interactions in Na2V3O7: a Vanadium(IV) Oxide Nanotubular Phase

The electronic structure of the inorganic nanotubular phase Na(2)V(3)O(7) has been studied by means of first-principles DFT calculations. The magnetic behavior in this system is relatively complex to study because there are as many as 30 different exchange interactions in the unit cell. The coupling constants are computed directly from the energy differences of several spin configurations. It is found that because of the special geometry of the nanotube, the nearest-neighbor coupling constants are not the only important ones and other next-nearest-neighbor constants cannot be neglected. In contrast with previous studies, it is found that at least 12 different coupling constants must be considered to correctly describe the spin arrangement in this system. However, to get more meaningful values for the smaller constants, a larger set of at least 17 constants must be explicitly taken into account. The lowest-energy collinear spin configuration is found to exhibit ferromagnetic coupling between the rings of the nanotube, whereas the coupling can be ferro- or antiferromagnetic within those rings. This leads to two important spin-frustrated interactions. Use of the so-called dimer approximation (i.e., substituting 16 paramagnetic V(IV) ions of the nanotube by 16 diamagnetic Ti(IV) ions, thus keeping the total charge of the system constant and leaving only two magnetic centers) is found to give invaluable hints concerning the nature of the magnetic interactions. This procedure may be helpful to analyze the magnetic properties of similar non-trivial systems with many paramagnetic centers.

Entanglement in the three-qubit Heisenberg model with next nearest neighbor interaction and a nonuniform magnetic field

Pairwise thermal entanglement in the three-qubit XXX Heisenberg model with next nearest neighbor interaction and a nonuniform magnetic field has been studied. It's found that the next nearest neighbor interaction has a great effect on the entanglement between the next nearest neighbor sites, but has slight effect on the nearest neighbor entanglement (NNE). Applying a magnetic field at the middle site enhances the next nearest neighbor entanglement (NNNE) sharply when there is a small field at the side sites and the next nearest neighbor coupling constant is positive. A staggered magnetic field helps to maintain nearest neighbor entanglement obviously.

First principles study of the multiferroicsBiFeO3,Bi2FeCrO6, andBiCrO3: Structure, polarization, and magnetic ordering temperature

We present results of an {\it ab initio} density functional theory study of three bismuth-based multiferroics, BiFeO$_{3}$, Bi$_{2}$FeCrO$_{6}$, and BiCrO$_{3}$. We disuss differences in the crystal and electronic structure of the three systems, and we show that the application of the LDA+$U$ method is essential to obtain realistic structural parameters for Bi$_{2}$FeCrO$_{6}$. We calculate the magnetic nearest neighbor coupling constants for all three systems and show how Anderson's theory of superexchange can be applied to explain the signs and relative magnitudes of these coupling constants. From the coupling constants we then obtain a mean-field approximation for the magnetic ordering temperatures. Guided by our comparison of these three systems, we discuss the possibilities for designing a multiferroic material with large magnetization above room temperature.

Solution of the Goldfish N-Body Problem in the Plane with (Only) Nearest-Neighbor Coupling Constants All Equal to Minus One Half

The (Hamiltonian, rotation- and translation-invariant) “goldfish” N-body problem in the plane is characterized by the Newtonian equations of motion written here in their complex version, entailing the identification of the real “physical” plane with the complex plane. In this paper we exhibit in completely explicit form the solution of the initial-value problem for this N-body model in the special case in which the two-body interaction only acts among “nearest neighbors” (namely, only among particles whose labels differ by one unit: a n,m = 0 unless |n − m| = 1) and the corresponding coupling constants all equal minus one half, a n,n+1 = a n+1,n = −1/2, n = 1, 2, ..., N − 1. This result implies that, if ω is a real nonvanishing constant, say, without loss of generality, ω > 0, then all the solutions of this N-body model are completely periodic indeed isochronous with period T = 2π / ω. An analogous conclusion holds as well for the model in which also the first and last particle interact with the same coupling constant, namely a 1,N = a N,1 = −1/2 (rather than vanishing).

Simulation of Four Dimensional Ising Model on Creutz Cellular Automaton\footnote

The four dimensional Ising model is simulated on Creutz cellular automaton [1,2].The preliminary results computed for the critical temperature T_c=6.7 (in units of J/k_B where J is the nearest neighbor coupling constant and k_B is the Boltzmann constant) and the effective critical exponents for the order parameter \beta=0.4 and the susceptibility \gamma=1.1 are in agreement with their values obtained by different methods [3].

Slow quenching for a one-dimensional kinetic Ising model: Residual energy and domain growth

A one-dimensional kinetic Ising model with Glauber dynamics subjected to a slow continuous quench to zero temperature is studied. For a rather general class of cooling schemes, described by a time-dependent temperatureT(t), the mean domain sizeL(t) is calculated along with the residual energyeres(r) as a function of the cooling rater. If the attempt frequency α=α0 exp(−e/kT), entering into the transition rates, is temperature dependent (i.e., the barrier e is non-zero), the asymptotic growth ofL(t) is given byL(∞)−L(t)~exp[−e/kT(t)]. For this case the residual energy exhibits a power-law behavioreres(r) ~rδ/2(1 + δ) forr small, where δ=4J/e andJ is the nearest neighbor coupling constant. For e=0 and for certain cooling schemes the residual energy is zero andL(t)~t1/2, independent ofr.

Interface in an Ising model with a spatially varying coupling constant.

We consider the Ising model on square and simple-cubic lattices with a nearest-neighbor coupling constant which varies linearly with position in one direction. In the region where the coupling constant K passes through its critical value there is an interface which separates two regions. In one region K is less than its critical value, and the system is essentially in the disordered phase, while in the other region the system is in an ordered phase. We study the properties of this interface, using both mean-field theory and Monte Carlo simulations. In particular, we investigate simple scaling predictions for the behavior of various quantities near the interface. We are also able to obtain good numerical estimates for the exponent combinations \ensuremath{\beta}/(1+\ensuremath{\nu}) and \ensuremath{\nu}(1-\ensuremath{\eta})/(1+\ensuremath{\nu}). .AE

Antiferromagnetic Ising Model on a Triangular Lattice

An antiferromagnetic Ising system on a triangular lattice is studied by means of a transfer matrix and the phenomenological scaling method. System consists of a semi-infinite strip and helical boundary conditions are imposed at the end of each row. At external magnetic fields h =0 and 6 J , where J is a nearest neighbor coupling constant, a unite residual entropy is obtained at the zero temperature. With a small field, specific heat is found to have two peaks; a high-temperature peak corresponding to the enhanced short-range order, and a low-temperature peak to the appearance of a long-range order. A phase diagram in h - T space is obtained by means of the phenomenological scaling, and agrees fairly well with the one obtained by Monte Carlo simulation. The main deficiency is the finite transition temperature at h =0, which may be due to a crossover to the XY-like phase transition.

Boundary magnetization and spin correlations in inhomogeneous two-dimensional Ising systems

We consider a system of Ising spins on a semi-infinite triangular lattice with nearest-neighbor coupling constants that depend on the distance $m$ from the boundary. An exact technique for calculating the boundary magnetization and the boundary pair correlation function is described. It relies on repeated application of a mapping based on the star-triangle transformation. The case of coupling constants that differ from the bulk coupling by an amount ${\mathrm{Am}}^{\ensuremath{-}y}$ for large $m$ is examined in detail. For $y<1$ the inhomogeneity of the couplings leads to an interesting variety of modifications in the boundary critical behavior. For $y=1$, $A>{A}_{c}$ (${A}_{c}$ being a positive critical value), and for $y<1$, $A>0$, there is a spontaneous surface magnetization at the bulk critical temperature.

Surface critical behavior of the smoothly inhomogeneous Ising model

We consider a semi-infinite two-dimensional Ising model with nearest-neighbor coupling constants that deviate from the bulk coupling by $A{m}^{\ensuremath{-}y}$ for large $m$, $m$ being the distance from the edge. The case $Al0$ of couplings which are weaker near the surface has been discussed by Hilhorst and van Leeuwen. We report exact results for the boundary magnetization and boundary pair-correlation function when $Ag0$. At the bulk critical temperature there is a rich variety of critical behavior in the $A \ensuremath{-}y$ plane with both paramagnetic and ferromagnetic surface phases. Some of our results can be derived and generalized with simple scaling arguments.

Electronic States of a Disordered Polymer

A method introduced by Schmidt to give the vibrational frequency spectrum of an isotopic disordered one-dimensional lattice is generalized and applied to an infinite one-dimensional disordered molecular crystal with nearest-neighbor interactions. Such a model is applicable to a polymer having several molecular species arranged randomly along the polymer axis. Equations are derived which may be solved numerically to give the density of states for the following types of polymer: (1) the general disordered polymer having a random arrangement of several molecular species, the coupling constants between two species being determined by the species being coupled; (2) the glassy polymer having only one molecular species but with the coupling constants distributed randomly according to a continuous probability law. A numerical calculation of the density of states is made for the isotopic disordered polymer both with and without positional correlation between the molecular species and for the glassy polymer. When the energies of the two species in the diatomic isotopic disordered polymer differ by more than the nearest-neighbor coupling constant, the density of states is quite structured. Several of the peaks in this structure are associated with clusters of one or two molecules of one species in a lattice of molecules of the other species. Structure also appears in the density of states for the glassy polymer when there is a finite probability of small values for the nearest-neighbor coupling integrals.