Planar Triangular Lattice Research Articles

Shape morphing of 2D lattice structures from localized contra-rotations

The morphing of structure and materials from localized, self-equilibrated actuation loads is limited by Saint-Venant’s principle: Deformations typically decay rapidly from the actuation region, so that changes in shape for the entire structure are negligible. Materials and structures with unusual combinations of elastic properties may induce competitions between different deformation modes over longer decay distances, thereby overcoming this limitation. Here we push this principle to the extreme to generate shape morphing in large 2D lattice structures. We consider planar triangular lattice made of “meta-elements” with unusual combinations of axial, shear and flexural stiffness. We show, using finite element models, that localized contra-rotations on the center nodes can morph the entire structure in bending, provided that adequate combinations of elastic properties are selected. We use the global curvature as a measure of this deformation to establish precise design guidelines for morphing. We finally propose physical embodiments of these meta-elements and lattice structures which we fabricated using laser cutting, and which tested using servo-motors to impose contra-rotations on the two center nodes. The results validate our models and the design guidelines: planar lattice can morph in bending with significant curvatures, especially when the size of the structure is small. In comparison, similar lattice structures made of regular beams show no morphing, with all the deformation localized near the center nodes. These findings may lead to new strategies to actuate morphing materials and structures, with applications in aerospace or robotics.

Planar triangular lattice of the LuMgGaO4: Clustered site-occupancy and the upconversion luminescence of the co-doped Er,Yb ions

The ordered and stable structure of inorganic lattice is the basis of constructing high-efficiency rare earth activated fluorescence, solid-state laser or other optical materials. The mixed sensitized and activated rare earth ions usually keeps a uniform space-occupying and the energy transfer depends much on the doping concentration, while the aggregation of rare earth dopants in order is rare. In this work, a series of LuMgGaO4 phosphors were synthesized and the detail lattice parameters are analyzed through Vietveld refinement and the new CIF file is provided. The site-occupancy of Er3+, Yb3+ shows clustered features and the Er–Yb sublattice structure with various Yb/Er ratios were constructed on the basis of planar triangular lattice. The long-distance excitation energy migration to lattice or defects can be effectively inhibited in case of the hexagonal circle Er-6Yb sublattice, in which the most intense green/red UCL was obtained. All the results demonstrate the novelty of regulating ordered site-occupancy of rare earth ions on a compact planar triangular lattice with higher efficiency of energy migration, which will pave a way for developing phosphor-converted materials or laser materials with better performance.

Pressure-induced superconductivity in triangular lattice spin liquid candidate NaYbSe<sub>2</sub>

Quantum spin liquid is an exotic state without magnetic order down to zero-temperature due to spin frustration, which is closely related to high temperature superconductivity. Therefore, an important issue arises whether the quantum spin liquid can be adjusted into a superconductor, even high-<i>T</i><sub>c</sub> superconductor, by using pressure or chemical doping. Rear-earth chalcogenides NaYbCh<sub>2</sub> (Ch = O, S, Se), consisting of planar triangular lattice, exhibit no long-range magnetic order down to the lowest measured temperatures in specific heat, nuclear magnetic resonance, and neutron scattering, and are considered as a quantum spin liquid candidate. Here we investigate the electrical transport properties of NaYbCh<sub>2</sub> (Ch = O, S, Se) under high pressures. For NaYbSe<sub>2</sub>, zero-resistance behavior is observed at 26.9 GPa, showing that the superconductivity comes into being. The superconducting transition temperature (<i>T</i><sub>c</sub>) is around 5.6 K at 26.9 GPa and robust against pressure till 45 GPa. The phase diagram of <i>T</i><sub>c</sub> versus pressure for NaYbSe<sub>2</sub> is constructed. For NaYbS<sub>2</sub>, the room temperature resistance decreases from the order of 10<sup>11</sup> Ω at 10 GPa to 10 Ω at 67 GPa. However, neither superconductivity nor insulator-metal transition is observed. Additionally, the NaYbO<sub>2</sub> keeps insulating and the resistance is too large to be detected in a pressure range of 0–60 GPa.

Spin-wave dynamics in the KCeS2 delafossite: A theoretical description of powder inelastic neutron-scattering data

Layered rare-earth delafossites $ARX_2$ with $R$ = Yb(III) or Ce(III) have received a lot of interest as potential hosts for a quantum spin-liquid ground state. Some systems of this family that show no long-range order down to the lowest measured temperatures, such as NaYbO$_2$, NaYbS$_2$, and NaYbSe$_2$, are presumed to be in a quantum spin-liquid state. However, other isostructural compounds are known to order antiferromagnetically at subkelvin temperatures. Among them, KCeS$_2$ exhibits stripe-$yz$ magnetic order in the triangular-lattice planes that sets in below 400 mK. Here we investigate the spin-wave spectrum of this ordered phase with powder inelastic neutron scattering and describe it using a model Hamiltonian obtained from first-principles calculations based on the complete $|J,m_J\rangle$ multiplet description of the Ce sites with an anisotropic nearest-neighbor exchange interaction. Combing the current understanding of the exchange interaction in the systems with the effects of texturing in the powder, we have been able to model the inelastic neutron scattering spectrum with high fidelity.

Finite Element Modeling of Internally Actuated Triangular Lattice and Its Variants for Modular Active Cell Robots (MACROs)

Modular Active Cell Robots (MACROs) is an approach for modular robot hardware that leverages simple components such as actuators and compliant joints to make large deformable robotic structures. In this letter, we consider the planar triangular lattice and its sparser variants as the candidate mesh topologies for MACROs. Through Finite Element (FE) simulations, we quantify the deformations obtained for different choices of edges being actuated in the MACRO mesh. Further, we use this data to identify optimal actuation strategies for a target deformation. We demonstrate a trade-off between passive stiffness and actuation energy and thereafter, we refine the triangular lattice by removing edges to reduce the actuation energy without a significant reduction in stiffness. We also identify the refined meshes optimal for desired specifications.

Electronic properties of the topological kagome metals YV6Sn6 and GdV6Sn6

The synthesis and characterization of vanadium-based kagome metals ${\mathrm{YV}}_{6}{\mathrm{Sn}}_{6}$ and ${\mathrm{GdV}}_{6}{\mathrm{Sn}}_{6}$ are presented. X-ray diffraction, magnetization, magnetotransport, and heat capacity measurements reveal an ideal kagome network of V ions coordinated by Sn and separated by triangular lattice planes of rare-earth ions. The onset of low-temperature magnetic order of Gd spins is detected in ${\mathrm{GdV}}_{6}{\mathrm{Sn}}_{6}$ and is suggested to be noncollinear, while V ions in both compounds remain nonmagnetic. Density functional theory calculations are presented modeling the band structures of both compounds, which can be classified as ${\mathbb{Z}}_{2}$ topological metals in the paramagnetic state. Both compounds exhibit high mobility, multiband transport and present an interesting platform for controlling the interplay between magnetic order associated with the $R$-site sublattice and nontrivial band topology associated with the V-based kagome network. Our results invite future exploration of other $R{\mathrm{V}}_{6}{\mathrm{Sn}}_{6}$ ($R$ = rare earth) variants where this interplay can be tuned via $R$-site substitution.

Probing the effect of magnetic field on charge order in the quasi-two-dimensional Mott insulator κ−(ET)2Hg(SCN)2Cl

Molecular-based quasi-two-dimensional charge-ordered Mott insulators can possess both spin $S=1/2$ and an electric dipole degree of freedom residing on each ${(\mathrm{BEDT}\text{\ensuremath{-}}\mathrm{TTF})}_{2}$ lattice site. There exists a theoretical proposal for a magnetoelectric effect in such a material, which can manifest itself as a sensitivity of charge distribution on ${(\mathrm{BEDT}\text{\ensuremath{-}}\mathrm{TTF})}_{2}$ dimers to the magnetic field. In this work, we used Raman scattering spectroscopy in the magnetic field up to 31 T applied perpendicular to the two-dimensional triangular lattice planes to probe a magnetoelectric effect in $\ensuremath{\kappa}\text{\ensuremath{-}}{(\mathrm{ET})}_{2}\mathrm{Hg}{(\mathrm{SCN})}_{2}\mathrm{Cl}$. This is a model compound, which shows charge order and antiferromagnetic correlations at temperatures below 30 K. We discuss possible reasons for the absence of an observable magnetoelectric effect in the probed temperature and magnetic field ranges.

Прогнозування третинної структури білка на двомірній трикутній ґратці гібридним еволюційним алгоритмом

This work discusses the problem of forecasting the tertiary structure of a protein, based on its primary sequence. The problem is that science, with all its computing power and a set of experimental data, has not learned to build models that describe the process of protein molecule coagulation and predict the tertiary structure of a protein, based on its primary structure. However, it is wrong to assume that nothing is happening in this field of science. The regularities of folding (convolution) of the protein are known, methods for its modelling have been developed. Analysis of the current state of research in the field of these problems indicates the presence of shortcomings associated with the accuracy of forecasting and the time necessary to obtain the optimal solution. Consequently, the development of new computational methods, deprived of these shortcomings, seems relevant. In this work, the authors focused on the lattice model, which is a special case of the known hydrophobic-polar dill. protein conformation according to the chosen model, hybrid algorithms of cloning selection, differential are proposed. Since the processes of protein coagulation have not been fully understood, the researchers proposed several simplified models based on the physical properties of molecules and which leads to problems of combinatorial optimization. A hydrophobic-polar simplified model on the planar triangular lattice is chosen as a protein model. From the point of view of the optimization problem, the problem of protein folding comes down to finding a conformation with minimal energy. In lattice models, the conformation is represented as a non-self-cutting pathway. A hybrid artificial immune system in the form of a combination of clonal selection and differential evolution algorithms is proposed to solve this problem. The paper proposes a hybrid method and algorithm to solve the protein folding problem using the HP model on a planar triangular lattice. In this paper, a hybrid method and algorithm for solving the protein folding problem using the HP model on a planar triangular lattice are proposed. The developed hybrid algorithm uses special methods for encoding and decoding individuals, as well as the affinity function, which allows reducing the number of incorrect conformations (self-cutting solutions). Experimental studies on test hp-sequences were conducted to verify the effectiveness of the algorithm. The results of these experiments showed some advantages of the developed algorithm over other known methods. Experiments have been taught to verify the effectiveness of the proposed approach. The results labelled "Best" show the minimum energy values achieved over 30 runs, while the results labelled "Medium" show the robustness of the algorithm to achieve minima. Regarding robustness, the hybrid algorithm also offers an advantage, showing higher results. A comparative analysis of the performance results of the proposed algorithm on test sequences with similar results of other published methods allows us to conclude the high efficiency of the developed method. In particular, the result is more stable, and, in some cases, conformations with lower energy are obtained. Keywords: protein folding; hydrophobic-polar model; clonal selection; differential evolution; artificial immune systems; hydrophobic-polar model.

Stripe-yz magnetic order in the triangular-lattice antiferromagnet KCeS2

Yb- and Ce-based delafossites were recently identified as effective spin-1/2 antiferromagnets on the triangular lattice. Several Yb-based systems, such as NaYbO2, NaYbS2, and NaYbSe2, exhibit no long-range order down to the lowest measured temperatures and therefore serve as putative candidates for the realization of a quantum spin liquid. However, their isostructural Ce-based counterpart KCeS2 exhibits magnetic order below T N = 400 mK, which was so far identified only in thermodynamic measurements. Here we reveal the magnetic structure of this long-range ordered phase using magnetic neutron diffraction. We show that it represents the so-called ‘stripe-yz’ type of antiferromagnetic order with spins lying approximately in the triangular-lattice planes orthogonal to the nearest-neighbor Ce–Ce bonds. No structural lattice distortions are revealed below T N, indicating that the triangular lattice of Ce3+ ions remains geometrically perfect down to the lowest temperatures. We propose an effective Hamiltonian for KCeS2, based on a fit to the results of ab initio calculations, and demonstrate that its magnetic ground state matches the experimental spin structure.

Yb delafossites: Unique exchange frustration of4fspin-12moments on a perfect triangular lattice

While the Heisenberg model for magnetic Mott insulators on planar lattice structures is comparatively well understood in the case of transition metal ions, the intrinsic spin-orbit entanglement of $4f$ magnetic ions on such lattices shows fascinating new physics largely due to corresponding strong anisotropies both in their single-ion and their exchange properties. We show here that the Yb delafossites, containing perfect magnetic ${\mathrm{Yb}}^{3+}$ triangular lattice planes with pseudospin $s=\frac{1}{2}$ at low temperatures, are an ideal platform to study these phenomena. Competing frustrated interactions may lead to an absence of magnetic order associated to a gapless spin liquid ground state with a huge linear specific heat exceeding that of many heavy fermions, whereas the application of a magnetic field induces anisotropic magnetic order with successive transitions into different long-range ordered structures. In this comparative study, we discuss our experimental findings in terms of a unified crystal-field and exchange model. We combine electron paramagnetic resonance (EPR) experiments and results from neutron scattering with measurements of the magnetic susceptibility, isothermal magnetization up to full polarization, and specific heat to determine the relevant model parameters. The impact of the crystal field is discussed as well as the symmetry-compatible form of the exchange tensor, and we give explicit expressions for the anisotropic $g$ factor, the temperature dependence of the susceptibility, the exchange-narrowed EPR linewidth, and the saturation field.

Adsorption time scales of cluster-forming systems.

A microscopic model of adsorption in cluster forming systems with competing interaction is considered. The adsorption process is described by the master equation and modelled by a kinetic Monte Carlo method. The evolution of the particle concentration and interaction energy during the adsorption of particles on a plane triangular lattice is investigated. The simulation results show a diverse behavior of the system time evolution depending on the temperature and chemical potential and finally on the formation of clusters in the system. The characteristic relaxation times of adsorption vary in several orders of magnitude depending on the thermodynamic parameters of the final equilibrium state of the adsorbate. A very fast adsorption of particles is observed for highly ordered adsorbate equilibrium states.

Spin waves in decorated lattices

The XXZ Heisenberg model is used to study the dispersion relation of spin waves propagating in decorated planar square and triangular lattices. A superposition of interpenetrating lattices will be used to generate the composed systems. The decorations are introduced in order to generate systems with more than one atom per unit cell. The formalism applied here allows us to study different types of decorated lattices according to the relative position between each other controlled by the parameters α and β. By using the Holstein–Primakoff transformation we obtained the SW dispersion relation for the decorated lattices considered here. The obtained numerical results show the effects of both (i) the relative position of the interpenetrating lattices and (ii) the intra-lattice and inter-lattice exchange couplings on the spin waves dispersion relation.

Phase diagram of the lattice fluid with SRLA-potential on the plane triangular lattice

The lattice system with competing interactions (repulsive between nearest neighbors and attractive between nextnext-nearest neighbors) on a triangular lattice is studied. The possibility of existence of two types of ordered phases in the system is established. The initial lattice was splitted into a system of four identical triangular sublattices to describe the ordered phases. The geometric order parameter of the system is introduced. Using the order parameter, the critical value of the interaction parameter is determined and the phase diagram of the system is constructed. The dependence of the critical parameter of the model on the ratio of intensity of competing interactions is investigated. The simulation data for the chemical potential are compared with the results of the quasichemical approximation. It is shown that the quasichemical approximation results in an adequate assessment of the equilibrium properties of the model in the range of its applicability.

Densest versus jammed packings of bent-core trimers.

We identify putatively maximally dense packings of tangent-sphere trimers with fixed bond angles (θ=θ_{0}), and contrast them to the disordered jammed states they form under quasistatic and dynamic athermal compression. Incommensurability of θ_{0} with three-dimensional (3D) close packing does not by itself inhibit formation of dense 3D crystals; all θ_{0} allow formation of crystals with ϕ_{max}(θ_{0})>0.97ϕ_{cp}. Trimers are always able to arrange into periodic structures composed of close-packed bilayers or trilayers of triangular-lattice planes, separated by "gap layers" that accommodate the incommensurability. All systems have ϕ_{J} significantly below the monomeric value, indicating that trimers' quenched bond-length and bond-angle constraints always act to promote jamming. ϕ_{J} varies strongly with θ_{0}; straight (θ_{0}=0) trimers minimize ϕ_{J} while closed (θ_{0}=120^{∘}) trimers maximize it. Marginally jammed states of trimers with lower ϕ_{J}(θ_{0}) exhibit quantifiably greater disorder, and the lower ϕ_{J} for small θ_{0} is apparently caused by trimers' decreasing effective configurational freedom as they approach linearity.

Spin-liquid-like state in pure and Mn-doped TbInO3 with a nearly triangular lattice.

Inelastic neutron scattering studies in single crystals of TbInO3 and TbIn0.95Mn0.05O3 with nearly triangular antiferromagnetic lattice are reported. At low energies, a broad and apparently gapless continuum of magnetic excitations, located at the triangular lattice (TL) Brillouin zone boundary, is observed. The data are well described by the uncorrelated nearest-neighbor valence bonds model. At higher energies, a broad excitation branch dispersing from the TL zone boundary is observed. No signs of static magnetic order are found down to the temperatures two orders of magnitude smaller than the effective interaction energy. The fluctuating magnetic moment exceeds two-thirds of the Tb3+ free-ion value and is confined to the TL plane. These observations are consistent with a TL-based spin liquid state in TbInO3.

Anisotropic magnetic properties of the triangular plane lattice material TmMgGaO4

The crystal growth, structure, and basic magnetic properties of TmMgGaO4 are reported. The Tm ions are located in a planar triangular lattice consisting of distorted TmO6 octahedra, while the Mg and Ga atoms randomly occupy intermediary bilayers of M-O triangular bipyramids. The Tm ions are positionally disordered. The material displays an antiferromagnetic Curie Weiss theta of ∼−20 −25 K, with no clear ordering visible in the magnetic susceptibility down to 1.8 K; the structure and magnetic properties suggest that ordering of the magnetic moments is frustrated by both structural disorder and the triangular magnetic motif. Single crystal magnetization measurements indicate that the magnetic properties are highly anisotropic, with large moments measured perpendicular to the triangular planes. At 2 K, a broad step-like feature is seen in the field-dependent magnetization perpendicular to the plane on applied field near 2 T.

Rich magnetoelectric phase diagrams of multiferroic single-crystal α−NaFeO2

The magnetic and dielectric properties of the multiferroic triangular lattice magnet compound alpha-NaFeO2 were studied by magnetization, specific heat, dielectric permittivity, and pyroelectric current measurements and by neutron diffraction experiments using single crystals grown by a hydrothermal synthesis method. This work produced magnetic field (in the monoclinic ab-plane, B_ab, and along the c*-axis, B_c) versus temperature magnetic phase diagrams, including five and six magnetically ordered phases in B_ab and along B_c, respectively. Comparing the polarization direction to the magnetic structures in the different ferroelectric phases, we conclude that the extended inverse Dzyaloshinskii-Moriya mechanism expressed by the orthogonal components p1 ~ rij x (Si x Sj ) and p2 ~ Si x Sj can explain the polarization directions. Based on calculations incorporating exchange interactions up to fourth-nearest-neighbor (NN) couplings, we infer that competition among antiferromagnetic second NN interactions in the triangular lattice plane, as well as weak interplane antiferromagnetic interactions, are responsible for the rich phase diagrams of alpha-NaFeO2.

Magnetism in the KBaRE(BO3)2 (RE = Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu) series: materials with a triangular rare earth lattice

We report the magnetic properties of compounds in the KBaRE(BO3)2 family (RE = Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb), materials with a planar triangular lattice composed of rare earth ions. The samples were analyzed by x-ray diffraction and crystallize in the space group R-3m. Physical property measurements indicate the compounds display predominantly antiferromagnetic interactions between spins without any signs of magnetic ordering above 1.8 K. The ideal 2D rare earth triangular layers in this structure type make it a potential model system for investigating magnetic frustration in rare-earth-based materials.

Boundary rules and breaking of self-organized criticality in 2D frozen percolation

We study frozen percolation on the (planar) triangular lattice, where connected components stop growing (freeze) as soon as their becomes at least N, for some parameter N ≥ 1. The size of a connected component can be measured in several natural ways, and we consider the two particular cases of diameter and volume (i.e. number of sites). Diameter-frozen and volume-frozen percolation have been studied in previous works ([25, 11] and [27, 26], resp.), and they display radically different behaviors. These works adopt the rule that the of a frozen cluster stays vacant forever, and we investigate the influence of these boundary conditions in the present paper. We prove the (somewhat surprising) result that they strongly matter in the diameter case, and we discuss briefly the volume case.

Kagome lattices for ultracold atoms induced by additional lightfields

We propose a novel method for the realization of an optical Kagome lattice due to the Raman processes driven by additional light fields applied to the ultracold atoms of two hyperfine internal states trapped in a planar optical triangular lattice. The tunneling between the different internal states of the nearest-neighbor atoms in Kagome lattices can be adjusted by the additional light fields independently of the on-site interaction. This optical lattice protocol can be used to investigate the magnetic quantum phenomena and the nearest-neighbor magnetic coupling becomes strong enough by increasing the intensities of the additional light fields.