2D Triangular Lattice Research Articles

Iterated star–triangle transformation on inhomogeneous 2D Ising lattices

We consider infinite or periodic 2D triangular Ising lattices with arbitrary positive or negative nearest-neighbor couplings , where and i indicate the bond position and orientation, respectively. Iterative application of the star–triangle transformation to an initial lattice with a set of couplings generates a sequence of lattices , for n = 1, 2, …, with couplings . When includes sufficiently strongly frustrated plaquettes, complex couplings will appear. We show that, nevertheless, the variables remain confined to the union of the real and the imaginary axis. The same holds for a lattice with free boundaries, provided we distinguish between ‘receding’ and ‘advancing’ boundaries, the latter having degrees of freedom that must be fixed by an appropriately chosen protocol. This study establishes a framework for future analytic and numerical work on such frustrated Ising lattices.

Collective Dynamics in Quasi-One-Dimensional Hard Disk System

We present the results of molecular dynamic studies of collective dynamics in a system of hard disks confined to a narrow quasi-one-dimensional (quasi-1D) channel. The computer simulations have been performed for the specific channel width of 3/2 of disk diameter in which the disk arrangement at close packing resembles zigzag ordering characteristic of a vertically oriented two-dimensional (2D) triangular lattice. In such a quasi-1D system, which is intermediate between 1D and 2D arrays of hard disks, the transverse excitations obey very specific dispersion law typical of the usual optical transverse modes. This is in a sharp contrast both to the 1D case, where transverse excitations are not possible, and to the 2D case, where the regular shear waves with a propagation gap were observed. Other peculiarities of the dispersion of collective excitations as well as some results of disk structuring and thermodynamics of the quasi-1D hard disk system are presented and discussed for a range of hard disk densities typical for fluid and distorted crystal states.

Spin texture induced by non-magnetic doping and spin dynamics in 2D triangular lattice antiferromagnet h-Y(Mn,Al)O3

Novel effects induced by nonmagnetic impurities in frustrated magnets and quantum spin liquid represent a highly nontrivial and interesting problem. A theoretical proposal of extended modulated spin structures induced by doping of such magnets, distinct from the well-known skyrmions has attracted significant interest. Here, we demonstrate that nonmagnetic impurities can produce such extended spin structures in h-YMnO3, a triangular antiferromagnet with noncollinear magnetic order. Using inelastic neutron scattering (INS), we measured the full dynamical structure factor in Al-doped h-YMnO3 and confirmed the presence of magnon damping with a clear momentum dependence. Our theoretical calculations can reproduce the key features of the INS data, supporting the formation of the proposed spin textures. As such, our study provides the first experimental confirmation of the impurity-induced spin textures. It offers new insights and understanding of the impurity effects in a broad class of noncollinear magnetic systems.

A new hybrid genetic algorithm for protein structure prediction on the 2D triangular lattice

The flawless functioning of the protein is essentially related to its three-dimensional structure. Therefore,predicting protein structure from its amino acid sequence is a fundamental problem that draws researchers' attentionin many areas. The protein structure prediction problem (PSP) can be formulated as a combinatorial optimization problem based on simplified lattice models such as the hydrophobic-polar model. In this paper, we propose a new hybridalgorithm that combines three different known heuristic algorithms: the genetic algorithm, the tabu search strategy,and the local search algorithm to solve the PSP problem. Regarding the evaluation of the proposed approach, wepresent an experimental study, where we consider the quality of the product solution as the main assessment criterion.Furthermore, we compared the proposed algorithm with state-of-the-art algorithms using a selection of well-studiedbenchmark instances.

Mechanism of remote vacancy emergence by a supersonic crowdion cluster in a 2D Morse lattice

The supersonic M×N-crowdions are excited in a two-dimensional lattice by giving sufficiently large initial velocity v to the M×N block of atoms along a close-packed direction, where N is the number of neighboring atoms in one close-packed row and M is the number of neighboring rows. In this study, dynamics of a pair of quasi-1D supersonic 1×2-crowdions moving in parallel close- packed atomic rows separated by one non-excited atomic row (middle row) are investigated in 2D triangular Morse lattice by means of molecular dynamics simulations. It is shown that when a certain threshold excitation energy value is exceeded, the motion of these two 1×2-crowdions leads to creation of a remote vacancy in the middle row at a significantly long distance from the initiation point at the moment, when the supersonic stage of the crowdion propagation turns into subsonic one. This distance is directly proportional to the excitation energy of the 1×2-crowdion pair. The mechanism of vacancy formation is related to appearance of a Frenkel pair in the middle row, namely an immobile vacancy and an interstitial atom, which, together with the two interstitials in the outermost rows, forms the stable subsonic 3×1-crowdion cluster. It is concluded that the crowdion propagation can be accompanied by not only mass transfer but also plays a role in the formation of atomic vacancies inside crystal lattices.

Designing xenes with two-dimensional triangular lattice

Xenes, graphene-like two-dimensional (2D) monoelemental crystals with a honeycomb symmetry, have been the focus of numerous experimental and theoretical studies. In comparison, single-element 2D materials with a triangular lattice symmetry have not received due attention. Here, taking Pb as an example, we investigate the triangular-lattice monolayer made of group-IV atoms employing first-principles density functional theory calculations. The flat Pb monolayer supports a mirror-symmetry-protected spinless nodal line in the absence spin-orbit coupling (SOC). The introduction of an out-of-plane buckling creates a glide mirror, protecting an anisotropic Dirac nodal loop. Both flat and buckled Pb monolayers become topologically trivial after including SOC. A large buckling will make the Pb sheet a 2D semiconductor with symmetry-protected Dirac points below the Fermi level. The electronic structures of other group-IV triangular lattices such as Ge and Sn demonstrate strong similarity to Pb. We further design a quasi-3D crystal PbHfO$_2$ by alternately stacking Pb and 1T-HfO$_2$ monolayers. The new compound PbHfO$_2$ is dynamically stable and retains the properties of Pb monolayer. By applying epitaxial strains to PbHfO$_2$, it is possible to drive an insulator-to-metal transition coupled with an anti-ferroelectric-to-paraelectric phase transition. Our results suggest the potential of the 2D triangular lattice as a complimentary platform to design new type of broadly-defined Xenes.

Exploring Hilbert space on a budget: Novel benchmark set and performance metric for testing electronic structure methods in the regime of strong correlation.

This work explores the ability of classical electronic structure methods to efficiently represent (compress) the information content of full configuration interaction (FCI) wave functions. We introduce a benchmark set of four hydrogen model systems of different dimensionalities and distinctive electronic structures: a 1D chain, a 1D ring, a 2D triangular lattice, and a 3D close-packed pyramid. To assess the ability of a computational method to produce accurate and compact wave functions, we introduce the accuracy volume, a metric that measures the number of variational parameters necessary to achieve a target energy error. Using this metric and the hydrogen models, we examine the performance of three classical deterministic methods: (i) selected configuration interaction (sCI) realized both via an a posteriori (ap-sCI) and variational selection of the most important determinants, (ii) an a posteriori singular value decomposition (SVD) of the FCI tensor (SVD-FCI), and (iii) the matrix product state representation obtained via the density matrix renormalization group (DMRG). We find that the DMRG generally gives the most efficient wave function representation for all systems, particularly in the 1D chain with a localized basis. For the 2D and 3D systems, all methods (except DMRG) perform best with a delocalized basis, and the efficiency of sCI and SVD-FCI is closer to that of DMRG. For larger analogs of the models, the DMRG consistently requires the fewest parameters but still scales exponentially in 2D and 3D systems, and the performance of SVD-FCI is essentially equivalent to that of ap-sCI.

Kosterlitz-Thouless-type caging-uncaging transition in a quasi-one-dimensional hard disk system

Molecular dynamics computer simulations of collective excitations in a system of hard disks confined to a narrow channel of the specific width, that resembles 2D triangular lattice at disk close packing, are performed. We found that transverse excitations, which for hard-disk system are absent in the limit of 1D and are of acoustic nature in the limit of 2D, in the case of q1D hard-disk system emerge in the form of transverse optical excitations and could be considered as a tool to detect the structural transition to a zigzag ordering. By analyzing density evolution of longitudinal static structure factor and pair distribution function we have shown that driving force of zigzag ordering is caging phenomenon that in the case of hard-disk system is governed by excluded volume interaction with first and second neighbors and is of entropic origin.

Supersonic voidions in 2D Morse lattice

Abstract Dynamics of M × 1-crowdion clusters ( M = 1 , 2 or 3) and vacancy clusters is analyzed in 2D triangular lattice with Morse interactions. Topological defects are created in the lattice by kicking three neighboring atoms in the three neighboring close-packed atomic rows along the rows. Initial velocity of the atoms in the inner row, vinn, can be positive or negative, while the velocities of both atoms in the outer rows, vout, are equal and positive. The case of v inn = v out was analysed earlier and it was found that if the initial velocity is sufficiently large then a 3 × 1-crowdion cluster and a three-vacancy are formed. Two major effects are reported in the case of vinn ≠ vout analyzed here. (i) Due to the difference in the initial velocities, topological defects can be produced in the lattice with smaller initial energy than in the case of v inn = v out . (ii) In certain range of the initial velocities, a vacancy can appear at a distance of dozens interatomic distances from the initiation point, moving along the close-packed row with supersonic speed. Such moving vacancy is called voidion and mechanism of its formation and motion is revealed. Our results uncover new mechanisms of mass transfer by solitary waves in nonlinear lattices.

Structure and magnetism of a new hexagonal polymorph of Ba3Tb(BO3)3 with a quasi-2D triangular lattice

This article reports the structural and magnetic characterisation of a new hexagonal (P63cm) low-temperature phase of Ba3Tb(BO3)3, isostructural with the heavier lanthanide borates with formula Ba3Ln(BO3)3 (Ln ​= ​Dy–Lu). The crystal structure contains a quasi-two-dimensional (2D) triangular lattice of Tb3+ ions and is predicted to display unusual magnetic behaviour as a result of the low dimensionality. Magnetic susceptibility χ(T) shows antiferromagnetic interactions (θCW=−7.15 K) and no sharp ordering transition at T≥2 K, but analysis of χ’(T), isothermal magnetisation and heat capacity suggests the possibility of short-range ordering at T≈10 K. The material exhibits an inverse magnetocaloric effect at T<4 K.

Suppression of long-range ordering and multiferroicity in Sr-substituted Ba3−xSrxMnNb2O9 (x = 1 and 3)

Effects of Sr substitution at A-site in ordered perovskite Ba3−xSrxMnNb2O9 (x = 1 and 3) have been investigated using X-ray diffraction, magnetization, dielectric/magnetodielectric and neutron diffraction measurements. The parent compound Ba3MnNb2O9 having a large spin (S = 5/2) is known to exhibit type-II multiferroic properties with quasi 2D triangular lattice antiferromagnetic ground state. A slight perturbation in exchange interaction due to substitution of smaller size isovalent ion at the A-site in Ba3−xSrxMnNb2O9 (x = 1 and 3) has been found to alter the ground states drastically and hence the multiferroicity. The crucial role of various fluctuations (quantum and/or thermal), weak lattice distortion induced by Sr substitution and slight imbalance between different fluctuations in determining the ground states and the multiferroicity is discussed and compared with the results of smaller spin compounds (S = 1/2 or 1).

Existence of second spectrums of Timoshenko beam and Mindlin–Herrmann rod theories on the basis of atomistic studies

This paper considers a single-layer 2D triangular lattice system as an ideal higher-order rod and/or beam. The objective is to compare the solutions of these continuum models with the standard atomistic solutions. The accuracy of these higher-order rod and beam theories, in modeling several nano-systems, depends on the frequency of vibration. The existence of a second spectrum associated with these higher-order continuum theories and its contribution to the continuum solutions are studied on the basis of molecular dynamics (MD) results. It is shown that the second spectrum of a Timoshenko beam is less accurate with respect to the MD results but cannot be disregarded totally. Also, the existence of a second propagating mode associated with a Mindlin–Herrmann rod is substantiated by MD simulation results. The accuracy of these higher order rod and beam theories deteriorates beyond their cut-on frequencies. However, the use of higher-order rod and beam theories in several high-frequency dynamic and multiscale analyses is still justifiable.

Optically Controlled Orbitronics on a Triangular Lattice.

The propagation of electrons in an orbital multiplet dispersing on a lattice can support anomalous transport phenomena deriving from an orbitally induced Berry curvature. In striking contrast to the related situation in graphene, we find that anomalous transport for an L=1 multiplet on the primitive 2D triangular lattice is activated by easily implemented on site and optically tunable potentials. We demonstrate this for dynamics in a Bloch band where point degeneracies carrying opposite winding numbers are generically offset in energy, allowing both an anomalous charge Hall conductance with the sign selected by off-resonance coupling to circularly polarized light and a related anomalous orbital Hall conductance activated by layer buckling.

Metamaterials with engineered failure load and stiffness

Architected materials or metamaterials have proved to be a very effective way of making materials with unusual mechanical properties. For example, by designing the mesoscale geometry of architected materials, it is possible to obtain extremely high stiffness-to-weight ratio or unusual Poisson's ratio. However, much of this work has focused on designing properties like stiffness and density, and much remains unknown about the critical load to failure. This is the focus of the current work. We show that the addition of local internal prestress in selected regions of architected materials enables the design of materials where the critical load to failure can be optimized independently from the density and/or quasistatic stiffness. We propose a method to optimize the specific load to failure and specific stiffness using sensitivity analysis and derive the maximum bounds on the attainable properties. We demonstrate the method in a 2D triangular lattice and a 3D octahedral truss, showing excellent agreement between experimental and theoretical results. The method can be used to design materials with predetermined fracture load, failure location, and fracture paths.

The Effects of Three Magnons Interactions in the Magnon-Density Waves of Triangular Spin Lattices

We investigate the magnon-density waves proposed as the longitudinal excitations in triangular lattice antiferromagnets by including the cubic and quartic corrections in the large-s expansion. The longitudinal excitation spectra for the two-dimensional (2D) triangular antiferromagnetic model and quasi-one dimensional (quasi-1D) antiferromagnetic materials have been obtained for a general quantum spin number $s$. For the 2D triangular lattice model, we find a significant reduction (about 40 %) in the energy spectra at the zone boundaries due to both the cubic and quartic corrections. For the quasi-1D antiferromagnets, since the cubic term comes from the very weak couplings on the hexagonal planes, they make very little correction to the energy spectra, whereas the major correction contribution comes from the quartic terms in the couplings along the chains with the numerical values for the energy gaps in good agreement with the experimental results as reported earlier (Ref.~41).

Strong quantum fluctuations in a quantum spin liquid candidate with a Co-based triangular lattice

Currently under active study in condensed matter physics, both theoretically and experimentally, are quantum spin liquid (QSL) states, in which no long-range magnetic ordering appears at low temperatures due to strong quantum fluctuations of the magnetic moments. The existing QSL candidates all have their intrinsic disadvantages, however, and solid evidence for quantum fluctuations is scarce. Here, we report a previously unreported compound, [Formula: see text], a geometrically frustrated system with effective spin-1/2 local moments for Co2+ ions on an isotropic 2-dimensional (2D) triangular lattice. Magnetic susceptibility and neutron scattering experiments show no magnetic ordering down to 0.05 K. Thermodynamic measurements show that there is a tremendous amount of magnetic entropy present below 1 K in 0-applied magnetic field. The presence of localized low-energy spin fluctuations is revealed by inelastic neutron measurements. At low applied fields, these spin excitations are confined to low energy and contribute to the anomalously large specific heat. In larger applied fields, the system reverts to normal behavior as evident by both neutron and thermodynamic results. Our experimental characterization thus reveals that this material is an excellent candidate for the experimental realization of a QSL state.

Prediction of intrinsic two-dimensional non-Dirac topological insulators in triangular metal-organic frameworks

Two-dimensional (2D) metal-organic frameworks (MOFs) with topologically nontrivial states have attracted considerable attention recently. Based on ab initio calculations, we demonstrate that Cu(C21N3H15) with a triangular lattice is an intrinsic quantum anomalous Hall insulator. The multiple p (px and py)-like molecular orbitals of the C21N3H15 molecule with C3 symmetry give rise to a degenerate energy point at the Γ point with quadratic non-Dirac band dispersions. When the spin-orbit coupling is included, the bandgap is opened around the non-Dirac Γ point and a topologically nontrivial state is achieved. Quantum spin Hall effects can also be realized in this kind of 2D triangular lattice MOF if the time-reversal symmetry is preserved, as proposed in the Ni(C21N3H15) lattice. The physical mechanism is analyzed through a k · p model built. Our results present that the 2D triangular lattice MOFs are excellent candidates for producing 2D topological insulators and might have promising applications in future microelectronics and spintronics.

REZnAl11O19 (RE = Pr, Nd, Sm–Tb): a new family of ideal 2D triangular lattice frustrated magnets

We report the synthesis, structure and magnetic properties of a new family of rare-earth (RE) based magnetoplumbite-type REZnAl11O19 (RE = Pr–Tb) compounds with space-group P63/mmc.

Principal Chiral Model in Correlated Electron Systems.

We discuss noncollinear magnetic phenomena whose local order parameter is characterized by more than one spin vector. By focusing on the simple cases of 2D triangular and 3D pyrochlore lattices, we demonstrate that their low-energy theories can be described by a one-parametric class of sigma models continuously interpolating between the classical Heisenberg model and the principal chiral model Tr(∂_{a}U∂_{a}U^{†}) for all U∈SU(2). The target space can be viewed as a U(1) fibration over the CP(1) space. The 3D version of our model is further generalized to break spatial and spin rotation symmetry SO(3)×SO(3)→SO(3).

Two-dimensional discrete breathers in hcp titanium

Recently delocalized nonlinear vibrational modes (DNVMs) have been derived for a two-dimensional (2D) triangular lattice and their frequencies as the functions of amplitude have been calculated for a 2D Morse crystal. A 3D hcp lattice is formed by certain stacking of 2D triangular lattices. In the present work, we attempt to excite eight DNVMs with in-plane atomic displacements in a single plane of hcp titanium, modelled using many-body interatomic potentials. It is found that three of eight DNVMs produce long-lived 2D discrete breathers (DBs) in a titanium crystal. A 2D DB is delocalized in two spatial dimensions and localized in the third one, so that atoms of only one atomic plane have large vibrational amplitudes. The fFrequencies of the newly found DBs lie above the small-amplitude phonon spectrum of titanium and grow with increasing amplitude. Thus, we report on three novel 2D DBs in hcp metal. Our results open the route to finding new types of DBs in pure metals.