Second-neighbor Interactions Research Articles

Chaotic discrete breathers in bcc lattice: Effect of the first- and second-neighbor interactions

Numerical simulations are performed to investigate the formation of chaotic discrete breathers (DBs) in a bcc lattice using four zone-boundary modes with frequencies exceeding the crystal’s phonon spectrum. The study analyzes the impact of the stiffness of elastic bonds between first and second neighbors and identifies a specific range where the formation of chaotic DBs due to modulational instability of four vibrational modes is possible. The time evolution of the energy localization parameter and the maximum energy of all particles were monitored to control the formation of chaotic DBs. Their spontaneous nucleation was observed in a wide range of stiffness of elastic bonds and depends on the mode’s symmetry. Considering DBs in bcc metals, the paper focuses on the scenario where first-neighbor bonds are stiffer than second-neighbor bonds, as bond stiffness typically decreases with interatomic distance. In all four zone-boundary modes, formation of chaotic DB is observed under this condition.

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.

Modulation instability and modulated wave patterns in a nonlinear electrical transmission line with the next-nearest-neighbor coupling

In this paper, we investigate modulation instability and solitary waves in a one-dimensional nonlinear electrical transmission line with second-neighbor interactions. Through the quasi-discrete multiple scale method, we derive coupled nonlinear Schrödinger equations. To investigate the modulation instability in the structure, we use the linear stability analysis, and an expression for the modulation instability spectrum is derived. From the analytical investigation, we show that the second neighbor coupling affects both the modulation instability growth rate and modulation instability bands. Furthermore, we show via single and coupled mode excitation that bright and dark solitary waves can propagate at the lower and upper cutoff frequencies. To evaluate the robustness of the analytical investigation, we use a direct numerical simulation of the continuous wave. We conclude that the second-neighbor couplings generate rogue waves in the structure during the long-time evolution of the plane wave. We also demonstrate that with a variation of the excitation wave number, the nonlinear electrical transmission line can support new objects as wave molecules for high values of the wave number. This feature is not yet observed in nonlinear electrical transmission lines and will be useful in many fields of physics.

Calculation of some thermodynamic quantities for the Ising model on a [formula omitted]th order Cayley tree

This paper focuses on the Ising model with first- and second-neighbor interactions on a kth order Cayley tree (k≥2). We generalize the Ising-Vannimenus model’s Gibbs measures on a Cayley tree with any order by means of Kolmogorov consistency condition. We classify the fixed points of the dynamical system associated with the model under given conditions. We demonstrate how the chaoticity of the corresponding system is influenced by the Cayley tree’s order. Depending on the number k, we obtain a new formula to calculate the free energy of the model on Cayley tree of any order under given boundary conditions. We determine the system’s entropy, which is the derivative of the free energy function with respect to temperature T.

Localization phenomena in a one-dimensional phononic lattice with finite mass modulation: Beyond nearest-neighbor interaction

One-dimensional phononic systems beyond conventional nearest-neighbor interaction have not been well explored, to the best of our knowledge. In this work, we critically investigate the localization properties of a 1D phononic lattice in presence of second-neighbor interaction along with the nearest-neighbor one. A finite modulation in masses is incorporated following the well known Aubry-Andre-Harper (AAH) form to make the system a correlated disordered one. Solving the motion equations we determine the phonon frequency spectrum, and characterize the localization properties of the individual phononic states by calculating inverse participation ratio (IPR). The key aspect of our analysis is that, in the presence of second-neighbor interaction, the phonon eigenstates exhibit frequency dependent transition from sliding to the pinned phase upon the variation of the modulation strength, exhibiting a mobility edge. This is completely in contrast to the nearest-neighbor interaction case, where all the states get localized beyond a particular modulation strength, and thus, no mobility edge appears. Our analysis can be utilized in many aspects to regulate phonon transmission through similar kind of aperiodic lattices that are described beyond the usual nearest-neighbor interaction.

Diluting a triangular-lattice spin liquid: Synthesis and characterization of NaYb1−xLuxS2 single crystals

Yb-based magnets, with a perfect triangular lattice of pseudospin-$\frac{1}{2}\phantom{\rule{4pt}{0ex}}{\mathrm{Yb}}^{3+}$ ions, have emerged as candidates for realizing a quantum spin-liquid state, with ${\mathrm{NaYbS}}_{2}$ being a prominent example. Here, we present the solid-solution series ${\mathrm{NaYb}}_{1\ensuremath{-}x}{\mathrm{Lu}}_{x}{\mathrm{S}}_{2}$ with well-defined single crystals over the entire substitution range $0\ensuremath{\le}x\ensuremath{\le}1$. Chemical and structural analysis indicate a statistically homogeneous replacement of ${\mathrm{Yb}}^{3+}$ by ${\mathrm{Lu}}^{3+}$ ions. We magnetically characterize the relatively small single crystals using electron spin resonance (ESR). Below $30\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, the ESR intensity can be well described by a Curie-Weiss function for all $x$, with a decreasing Weiss temperature with increasing Lu content. This reduction of the average magnetic interaction upon Lu substitution is also supported by magnetization measurements. Importantly, no signs of magnetic or spin-glass order are detected down to $2\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ for any $x$. For $x&gt;0.5$, the ESR linewidth strongly increases, indicating the breakup of the magnetic system into disconnected clusters, as expected from percolation physics. The experimental magnetization data are found to be in good agreement for all $x$ with results of classical Monte Carlo simulations for a triangular-lattice Heisenberg model, amended with a small second-neighbor interaction. Taken together, our results establish ${\mathrm{NaYb}}_{1\ensuremath{-}x}{\mathrm{Lu}}_{x}{\mathrm{S}}_{2}$ as a family of diluted triangular-lattice spin liquids.

Backward- and forward-wave soliton coexistence due to second-neighbor coupling in a left-handed transmission line

We study analytically and numerically the impact of the second-neighbor interactions on the propagation of an initial wave-packet through a coupled nonlinear left-handed transmission line. We start with a detailed analysis of the dispersion curve and group velocity. We then use the quasi-discrete approximation with respect to long wavelength transverse perturbations to reduce the nonlinear discrete model of the lattice to a nonlinear Schrödinger equation. A detailed analysis of the product of the group velocity dispersion (P) and the nonlinear term (Q) is presented with respect to the relevant parameters of the system. Here we see the important role of the second-neighbor coupling, which makes the dispersion curve non-monotonic. Thus, for a given frequency, the group velocity can be both positive and negative, while for each choice the product, PQ, can be either positive or negative. Our numerical results confirm that for sufficiently strong second-neighbor coupling, bright backward-wave pulses and dark solitons can coexist at a common frequency, and these travel in opposite directions through the lattice.

Role of frustration in a weakly disordered checkerboard lattice

Quenched disorder effects on frustrated systems are explored by considering random fluctuations on the antiferromagnetic (AF) interactions between spins on the checkerboard lattice. The replica framework is adopted within a cluster mean-field approach, resulting in an effective single-cluster model. This effective model is treated within a one-step replica symmetry breaking (RSB) approach with exact evaluations for all intracluster interactions. Competing interactions are introduced by tuning the ratio J2/J1 (where J1 and J2 are first-neighbor and second-neighbor interactions, respectively), which can lead to a highly frustrated scenario when J2/J1→1, where a phase transition between AF orders takes place in the absence of disorder. In particular, the AF order appears at lower values of J2/J1, with the Néel temperature decreasing as the frustration increases. However, quenched disorder changes this description, introducing a RSB spin-glass phase for strong enough disorder intensity J. In fact, for low levels of disorder, a RSB solution with staggered magnetization (mixed phase) emerges from the maximum frustration region. It suggests that, in the presence of weak quenched disorder, systems with competing interactions are prone to present a glassy behavior instead of conventional orders.

Coexistence of strong and weak Majorana zero modes in an anisotropic XY spin chain with second-neighbor interactions

We theoretically investigate Majorana zero modes emerging in an anisotropic XY spin chain with second neighbor interactions. The spin chain is mathematically equivalent to the Kitaev chain composing of spinless fermions if only nearest-neighbor interactions are considered. Recent studies on the Kitaev chain with long-ranged interactions, have presented coexistence of several Majorana zero modes. Investigating the topological phase diagram of the anisotropic XY spin chain with second neighbor interactions, we find coexistence of several Majorana zero modes similar to the Kitaev chain. However, we confirm that one of zero modes is restricted into a Hilbert subspace. The mode is regarded as a so-called weak zero mode that should exhibit thermodynamical properties different from a (strong) zero mode appearing in the whole Hilbert space. Since the quantum statistics of spin is the same as a hard-core boson, we expect an experimental realization of the weak mode in not only quantum spin materials but also optical lattices for cold atom systems.

Electronic spectrum of Kekulé patterned graphene considering second neighbor-interactions

The effects of second-neighbor interactions in Kekulé-Y patterned graphene electronic properties are studied starting from a tight-binding Hamiltonian. Thereafter, a low-energy effective Hamiltonian is obtained by projecting the high energy bands at the Γ point into the subspace defined by the Kekulé wave vector. The spectrum of the low energy Hamiltonian is in excellent agreement with the one obtained from a numerical diagonalization of the full tight-binding Hamiltonian. The main effect of the second-neighbour interaction is that a set of bands gains an effective mass and a shift in energy, thus lifting the degeneracy of the conduction bands at the Dirac point. This band structure is akin to a ‘pseudo spin-one Dirac cone’, a result expected for honeycomb lattices with a distinction between one third of the atoms in one sublattice. Finally, we present a study of Kekulé patterned graphene nanoribbons. This shows that the previous effects are enhanced as the width decreases. Moreover, edge states become dispersive, as expected due to second neighbors interaction, but here the Kek-Y bond texture results in an hybridization of both edge states. The present study shows the importance of second neighbors in realistic models of Kekulé patterned graphene, specially at surfaces.

Interaction of solitons with a qubit in an anisotropic Heisenberg spin chain with first and second-neighbor interactions

Solitons provide a promising means to control the state of a spin-qubit in quantum information technology. In this paper, we consider the anisotropic interaction between a soliton, propagating in a ferromagnetic Heisenberg spin chain and a spin- particle (qubit). The spin chain exhibits an on-site anisotropy and spin-spin nearest-neighbor and next-nearest-neighbor interactions. The Bloch sphere picture is employed to investigate the spin- dynamics. We found that increasing the anisotropic and the second neighbor interactions leads to an increase of the deviation of the spin- particle from its initial state.

Extreme Suppression of Antiferromagnetic Order and Critical Scaling in a Two-Dimensional Random Quantum Magnet.

Sr_{2}CuTeO_{6} is a square-lattice Néel antiferromagnet with superexchange between first-neighbor S=1/2 Cu spins mediated by plaquette centered Te ions. Substituting Te by W, the affected impurity plaquettes have predominantly second-neighbor interactions, thus causing local magnetic frustration. Here we report a study of Sr_{2}CuTe_{1-x}W_{x}O_{6} using neutron diffraction and μSR techniques, showing that the Néel order vanishes already at x=0.025±0.005. We explain this extreme order suppression using a two-dimensional Heisenberg spin model, demonstrating that a W-type impurity induces a deformation of the order parameter that decays with distance as 1/r^{2} at temperature T=0. The associated logarithmic singularity leads to loss of order for any x>0. Order for small x>0 and T>0 is induced by weak interplane couplings. In the nonmagnetic phase of Sr_{2}CuTe_{1-x}W_{x}O_{6}, the μSR relaxation rate exhibits quantum critical scaling with a large dynamic exponent, z≈3, consistent with a random-singlet state.

Magnetic phases in the J1−J2 Heisenberg antiferromagnet on the triangular lattice

We use series expansion methods to investigate the phase diagram of a spin-1/2 Heisenberg antiferromagnet on the triangular lattice with first- and second-neighbor interactions. We find regions of ${120}^{\ensuremath{\circ}}$ and collinear ``stripe'' order, separated by an intermediate nonmagnetic phase, in agreement with results obtained previously using other methods. Magnon excitation spectra in the ordered phases are also obtained, and discussed.

Partial antiferromagnetic helical order in single-crystal Fe3PO4O3

Magnetic frustration in Fe$_3$PO$_4$O$_3$ has been shown to produce to an unusual magnetic state below T$_N = 163$ K, where incommensurate antiferromagnetic order is restricted to nanosized needle-like domains, as inferred from neutron powder diffraction. Here we show using single-crystal neutron diffraction that Fe$_3$PO$_4$O$_3$ does not exhibit a preferred ordering wavevector direction in the $ab$ plane despite having a well-defined ordering wavevector length. This results in the observation of continuous rings of scattering rather than satellite Bragg peaks. The lack of a preferred incommensurate ordering wavevector direction can be understood in terms of an antiferromagnetic Heisenberg model with nearest-neighbor ($J_1$) and second-neighbor ($J_2$) interactions, which produces a quasi-degenerate manifold of ordering wavevectors. This state appears to be similar to the partially ordered phase of MnSi, but in Fe$_3$PO$_4$O$_3$ arises in a frustrated antiferromagnet rather than a chiral ferromagnet.

Magnon spectrum of the Weyl semimetal half-Heusler compound GdPtBi

The compound GdPtBi is known as a material where the non-trivial topology of electronic bands interplays with an antiferromagnetic order, which leads to the emergence of many interesting magnetotransport phenomena. Although the magnetic structure of the compound has previously been reliably determined, the magnetic interactions responsible for this type of order remained controversial. In the present study, we employed time-of-flight inelastic neutron scattering to map out the low-temperature spectrum of spin excitations in single-crystalline GdPtBi. The observed spectra reveal two spectrally sharp dispersive spin-wave modes, which reflects the multi-domain state of the $\mathbf{k} = (\frac{1}{2}\frac{1}{2}\frac{1}{2})$ face-centred cubic antiferromagnet in the absence of a symmetry-breaking magnetic field. The magnon dispersion reaches an energy of $\sim 1.1$~meV and features a gap of $\sim 0.15$~meV. Using linear spin-wave theory, we determined the main magnetic microscopic parameters of the compound that provide good agreement between the simulated spectra and the experimental data. We show that GdPtBi is well within the ($\frac{1}{2}\frac{1}{2}\frac{1}{2}$) phase and is dominated by second-neighbor interactions, thus featuring low frustration.

Global existence and regularity for the dynamics of viscous oriented fluids

We prove global existence of weak solutions to regularized versions of balance equations representing the dynamics over a torus of complex fluids, with microstructure described by a vector field taking values in the unit ball. Regularization is offered by the presence of second-neighbor microstructural interactions and our choice of filtering the balance of macroscopic momentum by inverse Helmholtz operator with unit length scale.

(Cu)tet(Cr2-xSnx)octS4-ySey Spinels: Crystal Structure, Density Functional Theory Calculations, and Magnetic Behavior.

A new series of (Cu)tet[Cr2-xSnx]octS4-ySey compounds was prepared by solid-state reaction at high temperature. Determination of the crystal structures by single-crystal X-ray diffraction revealed that CuCr1.0Sn1.0S2.1Se1.9, CuCr1.2Sn0.8S2.1Se1.9, CuCr1.3Sn0.7S2.2Se1.8, and CuCr1.5Sn0.5S2.2Se1.8 crystallize in a normal spinel-type structure (cubic Fd3m space group). The powder X-ray diffraction patterns and Rietveld refinements of nominal CuCr2-xSnxS2Se2 (x = 0.2, 0.4, 0.6, 0.8, and 1.0) were consistent with single-crystal X-ray diffraction data. Raman scattering analysis revealed that the A1g, Eg, and three F2g vibrational modes were observed in the spectra. The signal at ∼382 cm-1, corresponding to the A1g mode, is attributed to symmetrical stretching of the chalcogen bond with respect to the tetrahedral metal. The samples with x = 0.2 and 0.4 exhibited ferromagnetic behavior, characterized by large positive θ values of +261 and +189 K, respectively. In contrast, antiferromagnetic (AF) behavior was observed for CuCrSnS2Se2 with a Néel temperature (TN) of 18.8 K and a θ value of -36.0 K. Density functional theory (DFT) and effective magnetic moments (μeff/μtheo) experimentally measured showed that the Sn ion is in oxidation state of 4+, i.e., diamagnetic behavior. DFT calculations revealed that the most stable magnetic state of CuCr1.0Sn1.0S2Se2 was AF with exchange constants for first- and second-neighbor interactions of J1 = 56.22 cm-1 and J2 = -33.88 cm-1. Thus, the AF interactions between ferromagnetic chains in CuCr1.0Sn1.0S2Se2 originate from the presence of diamagnetic Sn cations.

Embedded solitons in the double sine-Gordon lattice with next-neighbor interactions.

Topological solitons can propagate without radiation in discrete media. These solutions are known as embedded solitons (ES). They come as isolated solutions and exist despite their resonance with the linear spectrum of the respective lattices. In this paper the properties of embedded solitons in the discrete double sine-Gordon equation with next-neighbor and second-neighbor interactions are investigated. Depending on the sign of these interactions they can be either destructive or favorable for the ES creation. The ES existence area depends on the width of the linear spectrum: narrowing of the spectrum widens the ES existence range and vice versa. The application to the Josephson junction arrays is discussed.

Thermal Hall signatures of non-Kitaev spin liquids in honeycomb Kitaev materials

Motivated by the recent surge of field-driven phenomena discussed for Kitaev materials, in particular the experimental observation of a finite thermal Hall effect and theoretical proposals for the emergence of additional spin liquid phases beyond the conventional Kitaev spin liquid, we develop a theoretical understanding of the thermal Hall effect in honeycomb Kitaev materials in magnetic fields. Our focus is on gapless U(1) spin liquids with a spinon Fermi surface, which have been shown to arise as field-induced phases. We demonstrate that in the presence of symmetry-allowed, second-neighbor Dzyaloshinskii-Moriya interactions these spin liquids give rise to a finite, non-quantized, thermal Hall conductance in a magnetic field. The microscopic origin of this thermal Hall effect can be traced back to an interplay of Dzyaloshinskii-Moriya interaction and Zeeman coupling, which generates an internal U(1) gauge flux that twists the motion of the emergent spinons. We argue that such a non-quantized thermal Hall effect is a generic response in Kitaev models for a range of couplings.

Robustness of entropy plateaus: A case study of triangular Ising antiferromagnets

Residual entropy is a key feature associated with emergence in many-body systems. From a variety of frustrated magnets to the onset of spin-charge separation in Hubbard models and fermion-$Z_2$-flux variables in Kitaev models, the freezing of one set of degrees of freedom and establishment of local constraints are marked by a plateau in entropy as a function of temperature. Yet, with the exception of rare-earth pyrochlore family of spin-ice materials, evidence for such plateaus is rarely seen in real materials, raising questions about their robustness. Following recent experimental findings of the absence of such plateaus in triangular-lattice Ising antiferromagnet (TIAF) TmMgGaO$_4$ by Li et al, we explore in detail the existence and rounding of entropy plateaus in TIAF. We use a transfer matrix method to numerically calculate the properties of the system at different temperatures and magnetic fields, with further neighbor interactions and disorder. We find that temperature windows of entropy plateaus exist only when second-neighbor interactions are no more than a couple of percent of the nearest-neighbor ones, and they are also easily destroyed by disorder in the nearest-neighbor exchange variable, thereby explaining the challenge in observing such effects.