Next-nearest Neighbor Interactions Research Articles

Magnetic Properties of a Mixed Spin-3/2 and Spin-1/2 Ising Nanowire with Nearest and Next-Nearest Neighbour Interactions

The magnetic properties and the hysteresis behaviours of a mixed spin-3/2 and spin-1/2 cubic Ising nanowire have been studied by the use of the Monte Carlo simulations. To investigate the effects of the exchange interaction (J A), the crystal field (ΔA) and the nanowire size (N), we have plotted the variation of the magnetizations (m A and m B) of the two sublattices and the total magnetization (M T) with temperature for different values of J A, ΔA and N. The corresponding phase diagrams and the hysteresis loops behaviour are also presented and discussed.

Magnon-phonon coupling effects on the indirect K -edge resonant inelastic x-ray scattering spectrum of a two-dimensional Heisenberg antiferromagnet

We compute the effects of magnon-phonon coupling on the indirect K-edge bimagnon resonant inelastic x-ray scattering (RIXS) intensity spectrum of a square lattice Heisenberg antiferromagnet. We analyze the effects of competing nearest and next--nearest magnetic and magnon-phonon coupling interaction in the RIXS spectrum, for both the antiferromagnetic (AF) and the collinear antiferromagnetic (CAF) phases of the model. Utilizing the Dyson-Maleev representation of spin operators, the Bethe-Salpeter ladder approximation scheme for the bimagnon interacting channel, and considering the lowest order magnon-phonon-magnon scattering interaction we highlight distinct features in the X-ray spectrum. Considering damping effects, arising due to the presence of phonons, we find that in the AF phase the RIXS intensity spectrum attains a maximum value primarily localized around the K $\left(\pm\frac{\pi}{2}, \pm \frac{\pi}{2}\right)$ - point. For the CAF phase the intensity is broadly distributed with a significant scattering intensity located around the Y $\left(\pm\frac{\pi}{2}, 0\right)$ - point. Furthermore, in the CAF phase for suitable anisotropy, nearest-, and next-nearest neighbor interaction parameters the phonon effects can manifest itself as a distinct peak both below and above the bimagnon peak. Such a feature is in contrast to the antiferromagnetic spectrum where the effect due to the phonon peak was located consistently beyond the bimagnon peak in the high energy end of the spectrum. Additionally, in the CAF phase we find the RIXS bimagnon-phonon spectrum to be more sensitive to anisotropy compared to its antiferromagnetic counterpart. We conclude that the ultimate effect of magnon-phonon effects in the indirect K-edge RIXS spectrum, in both the antiferromagnetic and the collinear antiferromagnetic phase, is an observable effect.

Effects of interactions on dynamic correlations of hard-core bosons at finite temperatures

We investigate how dynamic correlations of hard-core bosonic excitation at finite temperature are affected by additional interactions besides the hard-core repulsion which prevents them from occupying the same site. We focus especially on dimerized spin systems, where these additional interactions between the elementary excitations, triplons, lead to the formation of bound states, relevant for the correct description of scattering processes. In order to include these effects quantitatively we extend the previously developed Br\"uckner approach to include also nearest-neighbor (NN) and next-nearest neighbor (NNN) interactions correctly in a low-temperature expansion. This leads to the extension of the scalar Bethe-Salpeter equation to a matrix-valued equation. Exemplarily, we consider the Heisenberg spin ladder to illustrate the significance of the additional interactions on the spectral functions at finite temperature which are proportional to inelastic neutron scattering rates.

Quantum signature of breathers in 1D ultracold bosons in optical lattices involving next-nearest neighbor interactions

The dynamics and the energy spectrum of an ultracold gas of bosonic atoms in an optical lattice can be described by a Bose–Hubbard model for which the system parameters can be controlled by laser light. We study by means of the perturbation theory in addition to the numerical diagonalization, the energy spectrum and the related features of the band structures of the ultracold bosons in optical lattices containing a few number of quanta interacting with next-nearest neighbor interactions (NNNI) modeled by the Bose–Hubbard Hamiltonian. The energy spectra of such system display the bound states signature, which are analyzed in the first Brillouin zone for different wave numbers. The finding, i.e., quantum breathers, shows that their probabilities’ weight depends on the wave vector. The influence of NNNI on both the probabilities’ amplitude and the correlation function is also realized in case of a system with a small number of sites, respectively.

Detection and characterization of symmetry-broken long-range orders in the spin- 12 triangular Heisenberg model

We present new numerical tools to analyze symmetry-broken phases in the context of $SU(2)$-symmetric translation-invariant matrix product states (MPS) and density-matrix renormalization-group (DMRG) methods for infinite cylinders, and determine the phase diagram of the geometrically-frustrated triangular Heisenberg model with nearest and next-nearest neighbor (NN and NNN) interactions. The appearance of Nambu-Goldstone modes in the excitation spectrum is characterized by "tower of states" levels in the momentum-resolved entanglement spectrum. Symmetry-breaking phase transitions are detected by a combination of the correlation lengths and second and fourth cumulants of the magnetic order parameters (which we call the Binder ratio), even though symmetry implies that the order parameter itself is strictly zero. Using this approach, we have identified $120^{\circ}$ order, a columnar order, and an algebraic spin liquid (specific to width-6 systems), alongside the previously studied topological spin liquid phase. For the latter, we also demonstrate robustness against chiral perturbations.

Low dimensional mixed-spin Ising model with next-nearest neighbor interaction

In this study, the effects of next-nearest neighbor interaction on a one-dimensional mixed spin 3 - spin 3/2 Ising model was investigated using Cellular Automaton (CA). The Ising model hamiltonian contains the antiferromagnetic nearest neighbor interaction (J1), the ferromagnetic next- nearest neighbor interaction (J2) and the external magnetic field (h = H/J1). Magnetization (M) of the mixed spin system was obtained in the interval 0 ≤ R ≤ 1 of the interaction ratio (R = J2/J1) using field cooling (FC) and zero-field cooling (ZFC) processes. Hysteresis curves were drawn for several R values in the interval −0.1 ≤ h ≤ 0.1 using FC results. The functional behavior for coercive field (HC) was determined depending on R. Thus, the mixed spin system became a hard magnetic material and the lattice geometry also changed from one dimensional linear chain to triangular chain with increasing R value.

Truncated Calogero-Sutherland models

A one-dimensional quantum many-body system consisting of particles confined in a harmonic potential and subject to finite-range two-body and three-body inverse-square interactions is introduced. The range of the interactions is set by truncation beyond a number of neighbors and can be tuned to interpolate between the Calogero-Sutherland model and a system with nearest and next-nearest neighbors interactions discussed by Jain and Khare. The model also includes the Tonks-Girardeau gas describing impenetrable bosons as well as a novel extension with truncated interactions. While the ground state wavefunction takes a truncated Bijl-Jastrow form, collective modes of the system are found in terms of multivariable symmetric polynomials. We numerically compute the density profile, one-body reduced density matrix, and momentum distribution of the ground state as a function of the range $r$ and the interaction strength.

Gibbs measures and free energies of Ising–Vannimenus model on the Cayley tree

In this paper, we consider the Ising–Vannimenus model on a Cayley tree for order two with competing nearest-neighbor and prolonged next-nearest neighbor interactions. We stress that the mentioned model was investigated only numerically, without rigorous (mathematical) proofs. One of the main points of this paper is to propose a measure-theoretical approach for the considered model. We find certain conditions for the existence of Gibbs measures corresponding to the model, which allowed to establish the existence of the phase transition. Moreover, the free energies and entropies, associated with translation invariant Gibbs measures, are calculated.

Coupled energy patterns in zigzag molecular chains

The contribution of both longitudinal and transversal nonlinear oscillations to energy localization is investigated in a zigzag molecular chain, which include simultaneously nearest- and next-nearest neighbor interactions. Coupled amplitude equations are found in the form of discrete nonlinear Schrödinger equations, whose plane wave solutions are found to be subjected to some instabilities. They are shown to be very sensitive to transverse and longitudinal couplings, which is confirmed via direct numerical simulations. The two available modes are found to be alternatively responsible for energy localization and transport. Thermal fluctuations effects bring about highly localized modes, along with narrow structures for efficient energy transport.

Ferromagnetic Exchange in Bichloride Bridged Cu(II) Chains: Magnetostructural Correlations between Ordered and Disordered Systems

The synthesis, structure, magnetic properties, and theoretical analysis of a new phase of dichloro(2-chloro-3-methylpyridine)copper(II) (2) and its isomorphous analogue dichloro(2-bromo-3-methylpyridine)copper(II) (3) are reported. Both complexes crystallize in the orthorhombic space group Pbca and present square pyramidal Cu(II) ions bridged into chains by chloride ions with each copper(II) bearing a single pyridine ligand. Variable temperature magnetic susceptibility measurements were well fit by a uniform one-dimensional ferromagnetic chain model with 2, J = 69.0(7) K, C = 0.487 emu-K/mol-Oe; 3, J = 73.9(4) K, C = 0.463 emu-K/mol-Oe (H = -JΣSi·Sj Hamiltonian). The experimental J-values were confirmed via theoretical calculations. Comparison to a known disordered polymorph of dichloro(2-chloro-3-methylpyridine)copper(II), 1, shows marked differences as there are significant antiferromagnetic next-nearest neighbor interactions in 1 in addition to randomness induced by the disorder which provide a distinctly different magnetic response. The differences in magnetic behavior are attributed principally to the structural difference in the Cu(II) coordination sphere, 1 being significantly closer to trigonal-bipyramidal, whose difference changes both the nearest and next-nearest neighbor interactions.

Resonant inelastic x-ray scattering study of spin-wave excitations in the cuprate parent compound Ca2CuO2Cl2

By means of resonant inelastic x-ray scattering at the Cu L$_3$ edge, we measured the spin wave dispersion along $\langle$100$\rangle$ and $\langle$110$\rangle$ in the undoped cuprate Ca$_2$CuO$_2$Cl$_2$. The data yields a reliable estimate of the superexchange parameter $J$ = 135 $\pm$ 4 meV using a classical spin-1/2 2D Heisenberg model with nearest-neighbor interactions and including quantum fluctuations. Including further exchange interactions increases the estimate to $J$ = 141 meV. The 40 meV dispersion between the magnetic Brillouin zone boundary points (1/2,\,0) and (1/4,\,1/4) indicates that next-nearest neighbor interactions in this compound are intermediate between the values found in La$_{2}$CuO$_4$ and Sr$_2$CuO$_2$Cl$_2$. Owing to the low-$Z$ elements composing Ca$_2$CuO$_2$Cl$_2$, the present results may enable a reliable comparison with the predictions of quantum many-body calculations, which would improve our understanding of the role of magnetic excitations and of electronic correlations in cuprates.

J1x-J1y-J2 square-lattice anisotropic Heisenberg model

The spin one Heisenberg model with an easy-plane single-ion anisotropy and spatially anisotropic nearest-neighbor coupling, frustrated by a next-nearest neighbor interaction, is studied at zero temperature using a SU(3) Schwinger boson formalism (sometimes also referred to as flavor wave theory) in a mean field approximation. The local constraint is enforced by introducing a Lagrange multiplier. The enlarged Hilbert space of S=1 spins lead to a nematic phase that is ubiquitous to S=1 spins with single ion anisotropy. The phase diagram shows two magnetically ordered phase, separated by a quantum paramagnetic (nematic) phase.

Spin transport in the disordered phase of a frustrated antiferromagnet

I analyze the spin transport, in the disordered phase, of the frustrated Heisenberg antiferromagnet with spin S=1 with next and next-nearest neighbor interactions on a square lattice. The spin conductivity is calculated using a SU(3) Schwinger boson formalism and the Kubo theory, within the ladder approximation. The spin conductivity exhibits a nonzero Drude weight at finite temperature.

Crystal Growth of a frustrated J1–J2 chain magnet NaCuMoO4(OH)

In a frustrated J1–J2 chain magnet with ferromagnetic nearest neighbor interactions J1 and antiferromagnetic next-nearest neighbor interactions J2, novel quantum states such as a spin nematic state are theoretically expected to be present. To detect the novel states experimentally, it is required to find a suitable model compound and to obtain its sizeable and high-quality single crystals. Here we report synthesis of a single-crystalline NaCuMoO4(OH), a model compound of frustrated J1–J2 chain magnet, by a hydrothermal method and discuss its magnetic properties. The temperature dependencies of magnetization are almost consistent with those of powder samples at high temperatures, while the peak in heat capacity divided by temperature associated with a magnetic transition becomes sharper and larger in the single crystal. This indicates the improved quality of the single-crystalline sample compared with the powder sample. Single-crystalline NaCuMoO4(OH) should give a new experimental approach to the novel spin-nematic states expected near 26 T.

Phase transition and Gibbs measures of Vannimenus model on semi-infinite Cayley tree of order three

Ising model with competing nearest–neighbors (NN) and prolonged next–nearest–neighbors (NNN) interactions on a Cayley tree has long been studied, but there are still many problems untouched. This paper tackles new Gibbs measures of Ising–Vannimenus model with competing NN and prolonged NNN interactions on a Cayley tree (or Bethe lattice) of order three. By using a new approach, we describe the translation-invariant Gibbs measures (TIGMs) for the model. We show that some of the measures are extreme Gibbs distributions. In this paper, we try to determine when phase transition does occur.

Topological Phases of Spin-1/2 Ferromagnetic–Antiferromagnetic Alternating Heisenberg Chains with Alternating Next-Nearest-Neighbour Interaction

A series of symmetry-protected topological(SPT) and trivial spin-gap phases in the spin-1/2 ferromagnetic--antiferromagnetic alternating Heisenberg chain with alternating next-nearest-neighbour interaction are investigated using two kinds of entanglement spectra defined by different divisions of the whole chain. In the case one of the next-nearest-neighbor interaction vanishes, the model reduces to the $\Delta$-chain in which a series of spin-gap phases are found in J. Phys. Soc. Jpn. 77, 044707 (2008). From the degeneracy of the entanglement spectra, these phases are identified as the SPT and trivial phases. It is found that the ground state phases boundaries are insensitive to the strength of the alternation in next-nearest neighbor interaction. These results are consistent with the analysis based on the nonlinear $\sigma$ model and exact solution on the ferromagnetic-nonmagnetic phase boundary.

Quantum soliton in 1D Heisenberg spin chains with Dzyaloshinsky-Moriya and next-nearest-neighbor interactions.

We report in this work, an analytical study of quantum soliton in 1D Heisenberg spin chains with Dzyaloshinsky-Moriya Interaction (DMI) and Next-Nearest-Neighbor Interactions (NNNI). By means of the time-dependent Hartree approximation and the semi-discrete multiple-scale method, the equation of motion for the single-boson wave function is reduced to the nonlinear Schrödinger equation. It comes from this present study that the spectrum of the frequencies increases, its periodicity changes, in the presence of NNNI. The antisymmetric feature of the DMI was probed from the dispersion curve while changing the sign of the parameter controlling it. Five regions were identified in the dispersion spectrum, when the NNNI are taken into account instead of three as in the opposite case. In each of these regions, the quantum model can exhibit quantum stationary localized and stable bright or dark soliton solutions. In each region, we could set up quantum localized n-boson Hartree states as well as the analytical expression of their energy level, respectively. The accuracy of the analytical studies is confirmed by the excellent agreement with the numerical calculations, and it certifies the stability of the stationary quantum localized solitons solutions exhibited in each region. In addition, we found that the intensity of the localization of quantum localized n-boson Hartree states increases when the NNNI are considered. We also realized that the intensity of Hartree n-boson states corresponding to quantum discrete soliton states depend on the wave vector.

Phase diagram of the ferrimagnetic mixed-spin Blume-Capel model with four-spin and next-nearest neighbor interactions

A finite cluster approximation based on a single cluster theory is developed for a ferrimagnetic mixed spin-1/2 and spin-1 Blume-Capel model with four-spin interaction J4 and next-nearest neighbor couplings J’. The state equations are derived for the two-dimensional square lattice and the phase diagram is explored. We found that the system can exhibits both critical and tricritical behavior according to appropriate values of J’, D and J4.

Phase transitions and critical properties in the antiferromagnetic Ising model on a layered triangular lattice with allowance for intralayer next-nearest-neighbor interactions

The phase transitions (PTs) and critical properties of the antiferromagnetic Ising model on a layered (stacked) triangular lattice have been studied by the Monte Carlo method using a replica algorithm with allowance for the next-nearest-neighbor interactions. The character of PTs is analyzed using the histogram technique and the method of Binder cumulants. It is established that the transition from the disordered to paramagnetic phase in the adopted model is a second-order PT. Static critical exponents of the heat capacity (α), susceptibility (γ), order parameter (β), and correlation radius (ν) and the Fischer exponent η are calculated using the finite-size scaling theory. It is shown that (i) the antiferromagnetic Ising model on a layered triangular lattice belongs to the XY universality class of critical behavior and (ii) allowance for the intralayer interactions of next-nearest neighbors in the adopted model leads to a change in the universality class of critical behavior.

Structure and Magnetic Behavior of Layered Honeycomb Tellurates, BiM(III)TeO6 (M = Cr, Mn, Fe).

New layered honeycomb tellurates, BiM(III)TeO6 (M = Cr, Mn, Fe) were synthesized and characterized. BiM(III)TeO6 (M = Cr, Fe) species crystallize in a trigonal space group, P3̅1c (No. 163), of edge-sharing M3+/Te6+O6 octahedra, which form honeycomb-like double layers in the ab plane with Bi3+ cations located between the layers. Interestingly, the structure of BiMnTeO6 is similar to those of the Cr/Fe analogues, but with monoclinic space group, P21/c (No. 14), attributed to the strong Jahn-Teller distortion of Mn3+ cations. The crystal structure of BiM(III)TeO6 is a superstructure of PbSb2O6-related materials (ABB'O6). The Cr3+ and Fe3+ cations are ordered 80% and 90%, respectively, while the Mn3+ ions are completely ordered on the B-site of the ABB'O6 structure. BiCrTeO6 shows a broad antiferromagnetic transition (AFM) at ∼17 K with a Weiss temperature (θ) of -59.85 K, while BiFeTeO6 and BiMnTeO6 show sharp AFM transitions at ∼11 K with θ of -27.56 K and at ∼9.5 K with θ of -17.57 K, respectively. These differences in the magnetic behavior are ascribed to the different concentration of magnetic nearest versus next-nearest neighbor interactions of magnetic cations due to the relative differences in the extent of M/Te ordering.