Next-nearest Neighbor Interactions Research Articles

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.

Crystal chemistry of the hydrothermally synthesized Na2(Mn1-xFex2+)2Fe3+(PO4)3 alluaudite-type solid solution

Several compounds of the Na 2 (Mn 1 - x Fe 2 + x ) 2 Fe 3 + (PO 4 ) 3 solid solution have been hydrothermally synthesized at 400 °C and 1 kbar; pure alluaudite-like compounds have been obtained for x = 0.00, 0.25, 0.50, 0.75, and 1.00. Rietveld refinements of the powder X-ray diffraction patterns indicate the presence of Na + at the A1 and A2' sites, Mn 2 + and Fe 2 + at the M1 site, and Mn 2 + , Fe 2 + , and Fe 3 + at the M2 site. The presence of small amounts of Na + at the M1 site and Mn 2 + at the Al site indicates a partially disordered distribution of these cations. An excellent linear correlation has been established between the M1-M2 distance and the energy of the infrared band attributed to the M 2 + -O vibrations. The Mossbauer spectra, measured between 85 and 295 K, were analyzed in terms of a model which includes the next-nearest neighbor interactions at the M2 and Ml crystallographic sites. Fe 2 + and Fe 3 + isomer shifts are typical of the alluaudite structure and exhibit the expected second-order Doppler shift. The derived iron vibrating masses and Mossbauer lattice temperatures are within the range of values expected for iron cations in an octahedral environment. The Fe 2 + and Fe 3 + quadrupole splittings are typical of the alluaudite structure, and the temperature dependence of the Fe 2 + quadrupole splitting was fit with the Ingalls model, which yielded a ground state orbital splitting of ca. 460 to 735 cm - 1 for the Fe 2 + sites. The isomer shifts and quadrupole splittings of Fe 2 + at the Ml site are larger than those of Fe 2 + at M2, indicating that the Ml site is both larger and more distorted than the M2 site.

Simulation of cellular-dendritic solidification structures of binary alloys in three-dimensional growth using a multiparticle diffusion-limited aggregation model

Abstract Solidification in binary alloy melts was simulated with two different three-dimensional models, that differ in the way the role of the solid/liquid interface energy on the solidification is expressed: either surface rearrangement or a surface curvature-dependent attachment probability was applied. In the melt, the simultaneous diffusion of all diffusing particles (atoms) was taken into account. Cellular–dendritic growth modes, as observed in practice, could be well simulated. The surface rearrangement model is essential for exhibiting details (as facetting) and the effect of the next-nearest neighbour interaction.

Superconductivity and Density Wave in the Quasi-One-dimensional Systems: Renormalization Group Study

The anisotropic superconductivity and the density wave have been investigated by applying the Kadanoff-Wilson renormalization group technique to the quasi-one-dimensional system with finite-range interactions. It is found that a temperature (T) dependence of response functions is proportional to exp(1/T) in a wide region of temperature even within the one-loop approximation. Transition temperatures are calculated to obtain the phase diagram of the quasi-one-dimensional system, which is compared with that of the pure-one-dimensional system. Next-nearest neighbor interactions (V_2) induce large charge fluctuations, which suppress the d_{x^2 -y^2}-wave singlet superconducting (dSS) state and enhance the f-wave triplet superconducting (fTS) state. From this effect, the transition temperature of fTS becomes comparable to that of dSS for large V_2, so that field-induced f-wave triplet pairing could be possible. These features are discussed to comprehend the experiments on the (TMTSF)_2PF_6 salt.

Order by Disorder, without Order, in a Two-Dimensional Spin System with O(2) Symmetry

We present a rigorous proof of an ordering transition for a two-component two-dimensional antiferromagnet with nearest and next-nearest neighbor interactions. The low-temperature phase contains two states distinguished by local among columns or, respectively, rows. Overall, there is no magnetic in accord with the classic Mermin-Wagner theorem. The method of proof employs a rigorous version of order by disorder, whereby a high degeneracy among the ground states is lifted according to the differences in their associated spin-wave spectra.

COMPENSATION TEMPERATURE OF A MIXED SPIN-1 AND SPIN-1/2 HEISENBERG FERRIMAGNETIC MODEL

The behavior of the compensation of a mixed spin-1 and spin-1/2 Heisenberg ferrimagnetic system on a square lattice is investigated theoretically by a two-time Green-function technique which takes into account the quantum nature of Heisenberg spins. The model includes the nearest and next-nearest neighbor interactions between spins, a crystal field and an external magnetic field. This model can be relevant for understanding the magnetic behavior of bimetallic molecular ferrimagnets that are currently being synthesized by several experimental groups. We study the spin-wave spectra of the ground state and investigate the effects of the next-nearest neighbor interactions, a crystal field and an external magnetic field on the compensation temperature. It is found that a compensation point appears and it is basically unchanged when the next-nearest-neighbor interaction between spin-1/2 is taken into account and exceeds a minimum value for other values in Hamiltonian fixed. The compensation temperature is influenced by the next-nearest-neighbor interaction between spin-1 and the external magnetic field and it is disappearing as these parameters exceed the trivial values.

Finite temperature properties and frustrated ferromagnetism in a square lattice Heisenberg model

The spin 1/2 Heisenberg model on a square lattice with antiferromagnetic nearest- and next-nearest neighbour interactions (the $J_1$--$J_2$ model) has long been studied as a paradigm of a two-dimensional frustrated quantum magnet. Only very recently, however, have the first experimental realisations of such systems been synthesized. The newest material, Pb$_2$VO(PO$_4$)$_2$ seems to have mixed ferro-- and antiferromagnetic exchange couplings. In the light of this, we extend the semiclassical treatment of the $J_1$--$J_2$ model to include ferromagnetic interactions, and present an analysis of the finite temperature properties of the model based on the exact diagonalization of 8, 16 and 20 site clusters. We propose that diffuse neutron scattering can be used to resolve the ambiguity inherent in determining the ratio and sign of $J_1$ and $J_2$ from thermodynamic properties alone, and use a finite temperature Lanczos algorithm to make predictions for the relevant high temperature spin-spin correlation functions. The possibility of a spin-liquid phase occurring for ferromagnetic $J_1$ is also briefly discussed.

Surface properties of alkaline earth metal oxides

Structural and energetic surface properties of the alkaline earth metal oxides MgO, CaO, SrO, and BaO are investigated within the density functional theory. In particular, structural distortions (relaxation and rumpling) and surface energies are studied for the (1 0 0) and (1 1 0) surfaces. A different sign of the rumpling is calculated for MgO compared to the other oxides. This difference is carefully examined and discussed in terms of differences in electronic properties, as well as nearest and next-nearest neighbor interactions. The stability of the results is investigated with respect to model approximations, such as the finite number of atomic layers used to describe semi-infinite surfaces, and choice of exchange-correlation energy functional.

Quantifying lateral adsorbate interactions by kinetic Monte-Carlo simulations and density-functional theory: NO dissociation on Rh(100)

The dissociation of NO on Rh(100) surfaces has been modelled by kinetic Monte-Carlo (MC) simulations including nearest neighbour (NN) and next-nearest neighbour (NNN) interactions, and zero-coverage kinetic parameters obtained from experiments. Two approaches were performed to derive the lateral interactions. First, the interactions were quantified by fitting the MC model to the experimental data. All interactions between NO, N and O were found to be repulsive. Nearest-neighbour interactions involving atoms are typically on the order of 20–30 kJ mol−1; between molecules they are below 10 kJ mol−1. All next-nearest neighbour interactions were smaller than 10 kJ mol−1. The simulations show that at higher initial NO coverage, the nitrogen and oxygen atoms were created by dissociation form c(2 × 2) islands, thereby compressing the NO areas and impeding their dissociation. Second, interactions estimated using DFT calculations were significantly higher than the ones estimated from fitting the experiments. Monte-Carlo simulations based on interactions obtained from DFT provide a description that is only qualitatively useful.

The crystal chemistry and FeII–site properties of aluminosilicate garnet solid solutions as revealed by Mössbauer spectroscopy and electronic structure calculations

The three binary garnet solid solutions (Fe3Al2Si3O12)-Al-II-(X3Al2Si3O12)-Al-II (X-II= Mg-II, Mn-II, Ca-II) have been investigated by Fe-57 Mossbauer spectroscopy at 298 and 77 K and by electronic structure calculations in the local spin density approximation. The spectra yield isomer shifts and quadrupole splittings that are typical for Fe-II in the dodecahedral X-site of 222 point symmetry and are similar for each of the three binaries recorded. Conversely, electronic structure calculations based on the experimental crystal structure of the different end-member garnets exhibit pronounced variations in some of the electronic properties of Fe-II that are not reflected in the spectroscopic data. These results are interpreted as indicating that the different X-O bonds in garnet solid solutions retain to a large degree the intrinsic lengths that they possess in their respective end members, and that the Fe-O bond does not change greatly as a function of composition. This is evidence for the state of alternating bonds and not for the virtual crystal approximation in describing the X-O bond types or lengths in aluminosilicate garnet solid solutions. The observed degree and behavior of the Fe-II doublet asymmetry in the Mossbauer spectra for the three solid solution series do not indicate major variations in the anisotropic recoil-free fraction of Fe-II. Variations in doublet asymmetry are more likely a result of complex next-nearest X-site neighbor interactions and/or some degree of short-range cation ordering, though doublets representing different local X-site cation configurations cannot be resolved or fitted to the experimental spectra.

Kaon B-parameter using overlap fermions

I present first results from an in-progress calculation of B K in quenched approximation using overlap fermions. My particular implementation of the overlap uses a kernel with nearest and next-nearest neighbor interactions and HYP-blocked gauge connections. Matching to the continuum NDR regularization is done perturbatively. I present preliminary results at β = 5.9 and 6.1 (lattice spacings 0.125 and 0.09 fm) for quark masses, pseudoscalar decay constants, and B-parameter− B K (NDR)(μ = 2GeV) ⋍ 0.66(3 − 4).

Monte Carlo simulation of europium telluride under hydrostatic pressure

EuTe is a type II antiferromagnetic semiconductor that exhibits a constant Néel temperature under high pressures with a lattice constant varying between 6.25 and 6.6 Å [I. N. Goncharenko and I. Mirebeau, Phys. Rev. Lett. 80, 1082 (1998); Europhys. Lett. 37, 633 (1997)]. Because mean field theory predicts a Néel temperature that is independent of J1, these results were interpreted to suggest a J2 independent of interstitial distances. Monte Carlo simulations of bulk EuTe with J2 held fixed and J1 varying from −.4(J2) to −.6(J2) using a Metropolis algorithm with a Hamiltonian comprised of nearest neighbor (NN) and next-nearest neighbor (NNN) terms have been performed. The Néel Temperature (TN) is observed to vary by 4% for a 20% change in the strength of J1, suggesting that interpretations of the behavior of EuTe based on mean field theory should be reevaluated. A linear relation between J1 and TN suggests that changes in NN and NNN interactions exactly cancel for EuTe under hydrostatic pressure.

Simulation of solidification structures of binary alloys

Abstract A discussion of the multiparticle diffusaon-limited aggregation model for the simulation of solidification structures from a binary alloy melt under isothermal conditions is presented. The model incorporates simultaneous diffusion of all atoms in the liquid, atoe attachment kinetics at the solid/liquid interface, depending on the local number and nature of bonds formed with the solid, and a surface rearrangement process that mimics the capillary (Gibbs-Thomson) effect. The influence of the local surface energy minimisation on the evolution of dendritic and regular lameldar eutectic structures and on the growth rate of a solidified layer is discussed. The role of the next-nearest neighbour interaction on the energy anisotropy of the internal (solid/solid) and external (solid/liquid) interfaces is identified with respect to the development of dendritic, seaweed and regudar lamellar eutectic structures. In the case that no chemical driving force exists for the incorporation of solute (impurity) atom...

Finite temperature quantum transfer-matrix simulations of the frustrated spin-1/2 chains

Thermodynamical properties of the one-dimensional S=1/2 Heisenberg model with dimerized nearest and uniform next-nearest neighbor interactions, applicable to CuGeO3 and Pb[Cu(SO4)(OH)2] compounds, are studied by the numerically exact quantum transfer-matrix method. The Suzuki–Trotter formula is used to obtain a classical system with spin σ=3/2 and effective interactions between nearest neigbors only. Magnetic specific heat and magnetic susceptibility curves are calculated and compared with experimental results in a wide temperature range giving estimates of the coupling parameters in the model proposed for CuGeO3 and Pb[Cu(SO4)(OH)2].

Mössbauer spectral evidence for next-nearest neighbor interactions within the alluaudite structure of Na1−xLixMnFe2(PO4)3

The Mössbauer spectra of the Na1−xLixMnFe2(PO4)3 compounds, with x=0.00, 0.25, 0.50, and 0.75, have been measured between 90 and 295 K and analyzed in terms of a model which takes into account the next-nearest neighbor interactions within the alluaudite structure. Surprisingly, the spectra reveal an unexpected presence of iron(II) in these compounds; the amount of iron(II) is observed to decrease from 19 to 15 atomic percent of the total iron content with increasing x. The temperature dependence of the Fe2+ and Fe3+ isomer shifts agrees with that expected from a second-order Doppler shift and the resulting iron vibrating masses and Mössbauer lattice temperatures are within the expected range of values for iron cations in an octahedral environment. The temperature dependence of the Fe2+ quadrupole splitting has been fit with the Ingalls' model and the results yield a ground state orbital splitting of ca. 500 cm−1 for the iron(II) sites. The compositional dependence of the isomer shifts and Fe2+ content can be understood in terms of a decrease in the unit-cell volume with increasing substitution of sodium by lithium, a substitution which does not influence the observed quadrupole splittings.

The two dimensional classical anisotropic Heisenberg ferromagnetic model with nearest- and next-nearest neighbor interactions

We use the self-consistent harmonic approximation (SCHA) to study the two-dimensional classical Heisenberg anisotropic (easy-plane) ferromagnetic model including nearest- and next-nearest neighbor exchange interactions. For temperatures much lower than the Kosterlitz-Thouless phase transition temperature T KT , spin waves must be the most relevant excitations in the system and the SCHA must account for its behavior. However, for temperatures near T KT , we should expect vortex pairs to be quite important. The effect of these vortex excitations on the phase transition temperature is included in our theory as a renormalization of the exchange interactions. Then, combining the SCHA theory to the renormalization effect due to vortex pairs, we calculate the dependence of T KT as a function of the easy-plane anisotropies and exchange interactions.

Polytypism and mixed layering in minerals

Polytypes are stacking variations that occur in crystals, forming periodic extended defects, without changing the overall composition. Mineral examples are the different polytypes of micas, kaolinite, talc, graphite. None of the theories that have been proposed to explain the occurrence of short and long period superstructures have met with universal success in explaining their occurrences. Polysomatism is defined as the stacking of compositionally different modules, similar to polytypism. Minerals belonging to a polysomatic series have compositions that are linear combinations of the end members. Structures derived from the bixbyite (Mn2O3) structure are used as examples of a polysomatic series and a number of polysomes in single crystals have been described using HRTEM. The relative stabilities of different polysomes have been modelled with a lattice energy minimization programme. The results show that certain polysomes are significantly more stable than others, and that the contribution of next-nearest neighbour interactions seems to be an important factor in determining polysome stability.

Effects of competing interactions on low-energy characteristics of aspin-1/2 cubic cluster

We consider a simple cubic magnetic cluster with spin-1/2 ions atits eight corners. The superexchange Hamiltonian employed in thispaper involves nearest, next-nearest (nn), and next to next-nearest(nnn) neighbour interactions. These competing exchange interactionsare found to generate a number of phases with ground states:(a) ferromagnetic; (b) nn-neighbour dimers; (c) regularantiferromagnetic; (d) nnn-neighbour dimers; and (e) nnn-neighbourforming triplets. We have also found fully polarized and partiallypolarized lowest spin excitations in the broken symmetry phases. Theeffects of the low-energy characteristics in various phases have beenquantified by computing thermodynamic properties, such asmagnetization and susceptibility.

Effect of nearest- and next-nearest neighbor interactions on the spin-wave velocity of one-dimensional quarter-filled spin-density-wave conductors

We study spin fluctuations in quarter-filled one-dimensional spin-density-wave systems in presence of short-range Coulomb interactions. By applying a path integral method, the spin-wave velocity is calculated as a function of on-site $(U),$ nearest (V) and next-nearest ${(V}_{2})$ neighbor-site interactions. With increasing V or ${V}_{2},$ the pure spin-density-wave state evolves into a state with coexisting spin- and charge-density waves. The spin-wave velocity is reduced when several density waves coexist in the ground state, and may even vanish at large V. The effect of dimerization along the chain is also considered.

Generalized antiferromagnetic Heisenberg spin ladders

We utilize the path-integral technique to derive the non-linear Sigma model (NLσM) for generalized antiferromagnetic spin-ladder systems on the square lattice with diagonal (next-nearest neighbor) interactions in addition to the nearest neighbor interaction. The model Hamiltonian is: H=∑ a=1 n l ∑ i J a S a(i)· S a(i+1)+J a,a+1′ S a(i)· S a+1(i)+K a,a+1 S a(i)· S a+1(i+1)+M a,a+1 S a(i+1)· S a(i) . The topological term of the NLσM is absent for the spin- s ladder with an even number of legs and is equal to 2 πs for the ladder with an odd number of legs. The spin wave velocity is s[∑ a ( J a − M a, a+1 − K a, a+1 )/∑ b, c L b, c −1] 1/2 where L a, b =4 J a + J a, a+1 ′+ J a, a−1 ′− M a, a+1 − M a, a−1 − K a, a+1 − K a, a−1 when a= b, and L a, b = J a, b ′+ K a, b + M a, b , when | a− b|=1. The spin gaps are predicted for spin ladders with an even number of chains. We also consider a two-leg ladder with spin s̃ and s, in which diagonal interactions occur only in the even (or odd) cells. The Berry phase is found to be dependent on the coupling constants. The expressions of the spin-wave velocity and spin gap are also given for even-leg ladders. The operator approach to the generalized spin-ladder problem is also presented. Finally we address the finite-size NLσM treatment of this system.