Next-nearest Interactions Research Articles

Influence of the relative stiffness of second-neighbor interactions on chaotic discrete breathers in a square lattice

It is known that the modulational instability of a delocalized nonlinear vibrational mode (DNVM) with frequency outside the phonon band can lead to spontaneous energy localization in a nonlinear lattice on chaotic discrete breathers (CDBs). Considering a β-FPUT square lattice with nearest and next-nearest interactions, the appearance of CDBs is analyzed for different stiffnesses of the first- and second-nearest interactions, k1 and k2, keeping the density of the lattice unchanged. There are two DNVMs in the square lattice with frequencies above the phonon spectrum and both are studied. The appearance of CDBs in the lattice is monitored by calculating the time evolution of the energy localization parameter L and the maximum energy of the particles emax. For solid state physics and materials science, the important range of stiffness parameters is k2<k1, since the stiffness of chemical bonds typically decreases with the distance between atoms. It is found that CDBs form in the square lattice when k2>k1/4. This means that they can form in crystals if the stiffness of the second-neighbor bonds is smaller than that of the first-neighbor bonds, but not too small. Depending on the relation between the anharmonicity parameters of the first- and second-neighbor bonds CDBs can have different polarization.

Delocalized nonlinear vibrational modes and discrete breathers in a body centered cubic lattice

Body centered cubic (bcc) lattice with nearest and next-nearest interactions described by the β-FPUT interatomic potential is considered. Exact dynamical solutions in the form of zone-boundary delocalized nonlinear vibrational modes (DNVMs) are analyzed. 31 such solutions are revealed from the analysis of only the symmetry of the bcc lattice. Frequency response of DNVMs for the case of soft- and hard-type anharmonicity is calculated. In the case of hard-type anharmonicity, four DNVMs have frequencies bifurcating from the upper edge of the phonon spectrum and growing with the amplitude. Various quasi-discrete breathers are obtained by superimposing localizing functions upon these DNVMs. Our work demonstrates a practical approach to finding quasi-discrete breathers in higher-dimensional lattices. The obtained spatially localized long-lived vibrational modes inspire the search for various discrete breathers in bcc metals.

Magnetic short-range order in polycrystalline SrGd2O4 and SrNd2O4 studied by reverse Monte Carlo simulations and magnetic pair-distribution function analysis

We present a study combining total-scattering powder neutron diffraction, reverse Monte Carlo simulations, and magnetic pair-distribution function analysis to deduce both the static and dynamic short-range magnetic spin correlations in two compounds of the rare-earth strontium oxides: ${\mathrm{SrGd}}_{2}{\mathrm{O}}_{4}$ and ${\mathrm{SrNd}}_{2}{\mathrm{O}}_{4}$. Both compounds exhibit a distorted honeycomb lattice which forms a set of zigzag ladders along the crystallographic $c$ axis of space group $Pnam$. Each set consists of two one-dimensional chains separated by diagonal rungs forming triangles, thus inducing a large degree of geometrical frustration due to the antiferromagnetic exchange between the magnetic ions. Significant magnetic diffuse scattering was observed well above the respective N\'eel temperatures and analyzed with reverse Monte Carlo techniques in reciprocal space. As a complementary analysis in real space we have derived the magnetic pair-distribution function for both compounds as a function of temperature. Our results clearly indicate that the individual zigzag ladders begin ordering well above ${T}_{\mathrm{N}}$ due to the dominating nearest and next-nearest interactions, long before interladder spin correlations become significant only slightly above ${T}_{\mathrm{N}}$. Additionally, for ${\mathrm{SrNd}}_{2}{\mathrm{O}}_{4}$ we find some qualitative differences between the short-range spin correlations above ${T}_{\mathrm{N}}$ and those observed in the ordered state.

Low-order continualization of an anisotropic membrane lattice with next-nearest interactions. Enhanced prediction of its dynamic behaviour

In this paper, a novel anisotropic membrane lattice with nearest and next-nearest interactions (long-range forces) has been continualized through different standard and non-standard continualization procedures, which enables the development of new non-classical continuum models capable of accurately capturing the scale effects, present in the matter due to its discrete nature. The performance of these continuum models is assessed by means of both dispersion and natural frequencies analyses, where the discrete model is considered as a reference. In addition, the appearance of certain physical inconsistencies in some of the developed models is analysed, concluding that these only appear for those developed with continualizations based on Taylor expansion. Interestingly, the non-standard models suitably capture the dispersive behaviour of the discrete one, without both physical inconsistencies and higher-order spatial derivatives, thus avoiding the need for extra boundary conditions when finite solids are involved.

New low-order continuum models for the dynamics of a Timoshenko beam lattice with next-nearest interactions

In this paper, the dynamic behaviour of a novel Timoshenko beam lattice with long-range interactions, accounting for both bending and shear deformations, is investigated. Several new non-classical continuum models are developed with the aim of capturing its dispersive behaviour with a lower computational cost. For this, innovative continualization procedures are used, comparing them with techniques commonly used in lattices continualization, as well as with advanced ones. Moreover, low-order continuum governing equations are pursued, thus avoiding the need for extra boundary conditions, whose physical meaning is unclear. A comprehensive analysis of the transition frequency, which initiates the shear propagation spectrum, has been performed here for the first time for this lattice and the corresponding continuum models. The capability of these continuum models in capturing the behaviour of the lattice is assessed by conducting both dispersion and natural frequency analyses, for the latter providing an original method to treat the edges for the three possible boundary conditions in Timoshenko beam lattices. The influence of long-range interactions is analysed, and the way shear effect affects the shape vibration modes of the discrete model is interestingly illustrated, finally concluding that some of the new developed continuum models accurately capture the behaviour of the lattice.

Ionic liquids in conducting nanoslits: how important is the range of the screened electrostatic interactions?

Analytical models for capacitive energy storage in nanopores attract growing interest as they can provide in-depth analytical insights into charging mechanisms. So far, such approaches have been limited to models with nearest-neighbor interactions. This assumption is seemingly justified due to a strong screening of inter-ionic interactions in narrow conducting pores. However, how important is the extent of these interactions? Does it affect the energy storage and phase behavior of confined ionic liquids? Herein, we address these questions using a two-dimensional lattice model with next-nearest and further neighbor interactions developed to describe ionic liquids in conducting slit confinements. With simulations and analytical calculations, we find that next-nearest interactions enhance capacitance and stored energy densities and may considerably affect the phase behavior. In particular, in some range of voltages, we reveal the emergence of large-scale mesophases that have not been reported before but may play an important role in energy storage.

Modulation of topological phase transitions and topological quantum states in one-dimensional superconducting transmission line cavities lattice

We propose a theoretical scheme for a one-dimensional lattice based on a superconducting quantum circuit system consisting of two types of superconducting microwave cavities, the interaction between nearest-neighbor and next-nearest-neighbor unit cells that can be adjusted by the magnetic flux, the system can obtain the collective dynamic evolution and study the topological properties of the system.First, we investigate the energy spectrum and edge states of the odd-even lattice size and find that the odd-even lattice number affects the topological properties of the system. Furthermore, considering the next-nearest interactions, it is found that there are constraints on the next-nearest interactions, which can be tuned to study the topological phase transitions of the system and the transfer of topological quantum states.In addition, considering the influence of defects on topological properties, it is found that the defect potential energy is small, the system energy band is stable, the edge states remain unchanged, and the energy spectrum fluctuation is small and distinguishable. Conversely, the energy band distribution is destroyed, it will become disordered and chaotic. The research results can design some new quantum devices for quantum optics and quantum information processing.

Novel Enriched Kinetic Energy continuum model for the enhanced prediction of a 1D lattice with next-nearest interactions

In this paper, a novel Enriched Kinetic Energy model is proposed for an enhanced prediction of the dynamic behaviour of a one-dimensional lattice with next-nearest interactions playing an important role. The lattice system here considered is made up of a chain formed by particles equally spaced and connected with nearest and next-nearest neighbours, through linear springs with different stiffness. The ability of the novel model proposed in this work in capturing the dynamic behaviour of the lattice system is compared with that of others presented in the literature, concluding that it is the one that shows the best performance around the limit of the Irreducible Brillouin Zone (small wavelengths) when next-nearest interactions are relevant. For this purpose, natural frequencies provided by the continuum models for the finite solid are compared with those provided by the discrete system, considered as a reference. Moreover, the novel Enriched Kinetic Energy model does not present physical inconsistencies, nor higher-order spatial derivatives in its governing equation, so it does not need non-classical boundary conditions to be solved when finite solids are treated.

Low order nonstandard continualization of a beam lattice with next-nearest interactions: Enhanced prediction of the dynamic behavior

In this work, a one-dimensional beam lattice composed of masses and rotational springs with nearest and next-nearest interactions is proposed, applying to it several nonstandard continalization procedures. The reliability of nonclassical continuum models to capture the dynamic behavior of the lattice – considered as a reference –, is evaluated through dispersion and natural frequency analyses. A detailed boundary conditions treatment is presented and the existence of physical inconsistencies in the new continuum models is examined. The novel enriched kinetic energy model proposed shows the best performance, its governing equation being of low order, thus, avoiding the use of extra boundary conditions.

Half-auxetic effect and ferroelasticity in a two-dimensional monolayer TiSe

Two-dimensional (2D) materials with both auxetic effect and ferroelasticity are rare, however, have great application potential in next generation microelectromechanical and nanoelectronic devices. Here, we report the findings of an extraordinary combination half-auxetic effect and ferroelasticity in a single p2mm-type TiSe monolayer by performing first-principles calculations. The unique half-auxetic effect, namely the material expand laterally under both uniaxial tensile strain, and compressive strain, is reported and explained by considering both the nearest and the next-nearest interactions. The ferroelasticity is stemming from the degeneracy breaking of the 3d-orbitals of Ti atoms in a distorted tetrahedron crystal field, or the so-called Jahn–Teller effect. The results provide a guideline for the future design of novel 2D multiple functional materials at the nanoscale.

Nonstandard continualization of 1D lattice with next-nearest interactions. Low order ODEs and enhanced prediction of the dispersive behavior

In this article, different standard and nonstandard continualization techniques are applied to a one-dimensional solid consisting in a chain of masses interacting with nearest and next-nearest neighbors through linear springs. The study focuses on the reliability of the different continua in capturing the dispersive behavior of the discrete, on the order of the continuous governing equation because of its effect on the need for including nonclassical boundary conditions, as well as on the physical inconsistencies that appear for short wavelengths. The Regularization method, used by Bacigalupo and Gambarotta for a lattice with nearest interactions, presents advantages over the others.

Mapping of Critical Anisotropy on Spin Dynamics in a Frustrated Antiferromagnet

An influence of the critical anisotropy field (Dc) as a function of next-nearest neighbors interaction is observed from the behavior of the dynamical structure factor and continuum spin conductivity, which thus relates the influence of the quantum phase transition on spin dynamics. The spin excitation becomes gapless around Dc = 0 and this have a direct effect on the dynamics behavior.

Synclinic-anticlinic symmetry in the structure of multilayer polar liquid crystals

A large number of smectic phases can have the same energy when short-range interlayer interactions (interaction of nearest layers and frustrating next-nearest layer interaction) are taken into account. In this situation even weak long-range interactions become important. They lift the degeneracy and lead to the appearance of a manifold of polar structures with multilayer periodicity. We analyze the reasons for the appearance of six-layer structures observed in experiments. Due to specific symmetry of interlayer interactions each antiferroelectric structure corresponds to a ferrielectric one in which synclinic orientations of molecules in nearest layers are replaced by anticlinic and vice versa. It is shown how different long-range interlayer interactions transform the degeneracy and induce different stable and metastable structures.

Magnetic dimerization in the frustrated spin ladder Li2Cu2O(SO4)2

The magnetic properties of ${\mathrm{Li}}_{2}{\mathrm{Cu}}_{2}\mathrm{O}{({\mathrm{SO}}_{4})}_{2}$ are investigated in the framework of density functional theory. In its high-temperature tetragonal structure, this compound appears as a rare material realization of a frustrated spin-1/2 two-leg ladder, where magnetic frustration arises from competing nearest and next-nearest interactions along the legs. Through a large magnetoelastic coupling, the triclinic distortion occurring around 125 K is shown to induce the formation of a staggered dimer structure, lifting most of the magnetic frustration.

Repulsive Interactions Induced by Specific Adsorption: Anomalous Step Diffusivity and Inadequacy of Nearest-Neighbor Ising Model (Part II Theory)

This is Part II of two closely related papers, where we show that the strong repulsive interaction caused by specifically adsorbed anions leads to a failure of the nearest-neighbor Ising model to describe structures on electrode surfaces. In this part, an analytical form of the step diffusivity is derived in terms of nearest and next-nearest neighbor interactions for steps with a mean direction along 〈110〉 (the close-packed direction). With the help of a further analytical expression for the diffusivity of steps with 〈100〉 mean orientation a simple scheme is developed whereby the nearest and next-nearest interaction energies can be extracted from the experimental values for the diffusivity along the 〈110〉- and 〈100〉-directions. The method is applicable to repulsive and attractive next-nearest neighbor interactions, both for surfaces in vacuum and in contact with an electrolyte. An example is presented in Part I, where we apply our approach to Au(100) in Br--, Cl-- and SO42—containing electrolytes.

Diffuse Scattering on Ising Chain with Competing Interactions

We considered the Ising 1D chain in an external magnetic field taking into account the nearest and next-nearest interactions. By the method of Kramers–Wannier transfer-matrix, the rigorous analytical expression for Fourier-transform of pair spin-spin correlation function was obtained, and the temperature evolution of the scattering was analyzed for various relations of exchange parameters.

Multiferroic properties of S = 1∕2 chain cuprates LiCuVO4: Comparison with LiCu2O2

We propose a microscopic model in order to study the multiferroic (MF) properties of [Formula: see text] (LCVO) taking into account the competing nearest and next-nearest magnetic interactions, frustration and a linear magnetoelectric (ME) coupling. We obtain for [Formula: see text]. The temperature and magnetic field dependence of the polarization [Formula: see text] and [Formula: see text] is observed. It is shown that the dielectric constant [Formula: see text] has a kink near the magnetic phase transition [Formula: see text] K which disappears with increasing of the external magnetic field. Some differences in the MF behavior between [Formula: see text] (LCO) and LCVO are discussed.

Generalized transformation for decorated spin models

Abstract The paper discusses the transformation of decorated Ising models into an effective undecorated spin model, using the most general Hamiltonian for interacting Ising models including a long range and high order interactions. The inverse of a Vandermonde matrix with equidistant nodes [ − s , s ] is used to obtain an analytical expression of the transformation. This kind of transformation is very useful to obtain the partition function of decorated systems. The method presented by Fisher is also extended, in order to obtain the correlation functions of the decorated Ising models transforming into an effective undecorated Ising model. We apply this transformation to a particular mixed spin-(1/2, 1) and (1/2, 2) square lattice with only nearest site interaction. This model could be transformed into an effective uniform spin- S square lattice with nearest and next-nearest interaction, furthermore the effective Hamiltonian also includes combinations of three-body and four-body interactions; in particular we considered spin 1 and 2.

Magnetic ordering in ordered complex Cu perovskite probed by [formula omitted]SR and neutron diffraction

Magnetic properties of antiferromagnetic (AF) B-site-ordered perovskite Ba 2 CuWO 6 have been investigated by μ SR and neutron diffraction. Interesting features of this compound are the magnetic two-dimensionality and seemingly frustrating interactions between the nearest and the next-nearest s = 1 2 spins of Cu 2 + . Zero-field μ SR experiments on a powder sample have shown the oscillating asymmetry below 28 K and the subsequent neutron diffraction experiment has confirmed the three-dimensional AF ordering presumably of the type-II on the face-centered lattice. The results suggest the dominance of the interaction between the next-nearest neighbor spins within the c-plane. Some contradictions, however, again arise to the expectations and explanations based on the seemingly equivalent nearest and next-nearest interaction paths. Nature of the magnetically ordered state is also interesting.

Monte Carlo simulations on a triangular Ising antiferromagnet with nearest and next-nearest interactions

Monte Carlo (MC) simulations on the triangular Ising antiferromagnet with antiferromagnetic next-nearest neighbor interaction points out the existence of a first order phase transition between the low temperature two-sublattice antiferromagnetic phase and the high temperature paramagnetic phase. This scenario differs from that observed when the next-nearest neighbor interaction is ferromagnetic, where a Berezinskii-Kosterlitz-Thouless phase occurs at intermediate temperature between the three-sublattice ferrimagnetic phase at low temperature and the paramagnetic phase at high temperature.