Triangular Geometry Research Articles

Origin of correlated diffuse scattering in the hexagonal manganites

We use a combination of first-principles density-functional calculations and spin-dynamics simulations to explain the unusual diffuse inelastic neutron scattering in the hexagonal multiferroic yttrium manganite, YMnO3. Using symmetry considerations, we construct a model spin Hamiltonian with parameters derived from our density-functional calculations and show that it captures the measured behavior. We then show that the observed directionality in the structured diffuse scattering in momentum space is a hallmark of the triangular geometry, and that its persistence across a wide range of temperatures, both above and below the Néel temperature TN, is a result of the strong magnetic frustration. We predict that this diffuse scattering exists in a yet-to-be-observed modulated continuum of energies, that its associated spin excitations have distinct in-plane and out-of-plane character, and that vestiges of the magnetic frustration persist into the sub−TN state. Finally, we show that visualizing the magnetic order in terms of composite trimer magnetoelectric monopoles and toroidal moments, rather than individual spins, provides insight into the real-space fluctuations, revealing clusters of emerging order in the paramagnetic state, as well as collective short-range excitations in the ordered antiferromagnetic phase. Our understanding of this directional diffuse scattering in such a wide temperature range, both below and above TN, provides new insight into the magnetic phase transitions in classical frustrated systems. Published by the American Physical Society 2024

On surjectivity in tensor triangular geometry

On surjectivity in tensor triangular geometry

A study for geometrical error in micro-geometries using VAT photopolymerization

A set of specimens was manufactured using VAT photopolymerization to study the relative error caused between different CAD geometries (i.e., Hexagonal, Pentagonal, Quadrangular, Circular, and Triangular) and manufactured workpieces. VAT photopolymerization was studied to understand the causes of errors in processing using ABS Flex White as resin. To accomplish the study of the geometry’s characterization, three replicates were measured and characterized. The manufacturing area was divided into four regions for the characterization, and the test probes were measured dimensionally by comparing the CAD design with the manufactured pieces. According to the results, triangular and circular geometries resulted in a lower relative error for solid and hollow samples, which might be attributed to the over-cured voxels and the angle in these geometries. For geometries produced at the microscale, there must be a match between the variation of the internal angle and, the voxel size and the lamp power density along the platform.

Activity of CeO2(111) supported Mnx(x = 1–6) for electrochemical N2 reduction reaction: Insights from density functional theory

It is challenging to realize an efficient nitrogen reduction reaction (NRR) under mild conditions, which suffers from low ammonia yield and low Faraday efficiency due to the extremely stable NN triple bond of N2 as well as competitive hydrogen evolution reaction. In this work, the NRR reactivity of Mnx(x= 1–6) clusters supported on CeO2(111) (Mnx(x = 1–6)/CeO2(111)) was systematically investigated using density functional theory. A volcanic relationship between the limiting potential of NRR on Mnx(x = 1–6)/CeO2(111) and the atom number of Mnx was found. Mn3/CeO2(111) shows the highest activity for NRR with a limiting potential of -0.36, -0.55 and -0.53 V along distal, alternating and enzymatic reaction pathway, respectively. Its high activity is attributed to the triangular geometry and optimal average number of electrons every Mn transferred from Mn3 to CeO2(111), which leads to the strong N2 activation and the stabilization of nitrogen-containing intermediates. Also, Mn3/CeO2(111) exhibits a high NRR selectivity by hindering H adsorption and a high thermal stability at both 298 and 773 K, suggesting its promising potential as effective NRR catalyst. This work provides new insights into the rational design of single cluster catalysts.

Syntheses, structures and magnetisms of dimethyl phosphate-bridged dinuclear lanthanide complexes with pentadentate macrocyclic ligand

A series of air-stable dinuclear complexes, [HNEt3]2[Ln2(L)2((CH3O)2PO2)4](BPh4)4 (L = 2,14-dimethyl-3,6,10,13,19-pentaazabicyclo[13.3.1]nonadeca1(19), 2,13,15,17-pentene, Ln = Dy, 1-Dy; Tb, 2-Tb; Gd, 3-Gd), has been synthesized and characterized using single-crystal X-ray crystallography and magnetic measurements. The crystal structures disclose that two dimethyl phosphate anions act as bridging ligands, linking two Ln(III) ions. Each Ln(III) ion is eight-coordinated by five nitrogen atoms from a pentadentate Schiff based ligand L and three oxygen atoms from three dimethyl phosphates, forming a triangular dodecahedral coordination geometry. Direct-current magnetic susceptibility measurements indicate an extremely weak antiferromagnetic exchange between Gd(III) ions in 3-Gd. Complex 1-Dy exhibits slow magnetic relaxation with an effective energy barrier (Ueff) of 13 K under an applied field of 1000 Oe, whereas 2-Tb does not exhibit single-molecule magnet behavior. This work presents a novel strategy for constructing polynuclear single-molecular magnets by using a pentadetate macrocycle as magnetic building blocks integrated with replaceable axial ligands.

Localized dopant motion across the 2D Ising phase transition

I investigate the motion of a single hole in 2D spin lattices with square and triangular geometries. While the spins have nearest neighbor Ising spin couplings JJ, the hole is allowed to move only in 1D along a single line in the 2D lattice with nearest neighbor hopping amplitude tt. The non-equilibrium hole dynamics is initialized by suddenly removing a single spin from the thermal Ising spin lattice. I find that for any nonzero spin coupling and temperature, the hole is localized. This is an extension of the thermally induced localization phenomenon [Phys. Rev. Res. 6, 023325 (2024)] to the case, where there is a phase transition to a long-range ordered ferromagnetic phase. The dynamics depends only on the ratio of the temperature to the spin coupling, k_BT / |J|kBT/|J|, and on the ratio of the spin coupling to the hopping J/tJ/t. I characterize these dependencies in great detail. In particular, I find universal behavior at high temperatures, common features for the square and triangular lattices across the Curie temperatures for ferromagnetic interactions, and highly distinct behaviors for the two geometries in the presence of antiferromagnetic interactions due geometric frustration in the triangular lattice.

Steady-state semi-analytical solutions for assessing the two-dimensional groundwater hydraulic head depletion induced by river dam removal

Dams are pervasive features of the world’s river systems. The reservoir associated with the dam modifies the distribution of the hydraulic head in the aquifer and the natural groundwater flow. However, such modifications must be defined to forecast their environmental, economic and/or social impacts. Based on the method of fundamental solutions (MFS), steady-state semi-analytical solutions are proposed for evaluating the long-term spatial distribution of the rise or decline of the hydraulic head in an aquifer caused by a dam reservoir on a watercourse or its removal. MFS was chosen because of its ability to account for different boundary conditions along the banks of the watercourse. The dam reservoir can have a triangular or rectilinear geometry. The aquifer is assumed unconfined, homogeneous, inclined and finite. The solutions take into account both the reservoir-aquifer interaction and those between the stream and the aquifer up- and downstream of the reservoir. The reservoir-stream system fully penetrates the aquifer, and is separated from the aquifer by semi-pervious banks (Robin condition). Analysis of the semi-analytical solution included sensitivity tests, and assessment of the influence of several parameters: reservoir leakance parameter, width of the reservoir and width of the aquifer. The results show that the reservoir and river leakage parameters up- and downstream of the reservoir, as well as the geometry of the reservoir dam, are the main determining parameters of the extent of the induced groundwater mound. They show that low aquifer-river exchanges in the river upstream and downstream of the reservoir increases the spatial extension of the mound. The degree of error introduced by the method of linearization used to solve the governing partial differential equation is also discussed. A solution has been also developed with a pumping well, particularly to assess what the depletion of the water level at the well location might be if the dam is removed. The proposed solutions were applied at two field sites, giving satisfactory results.These semi-analytical solutions will be useful applications for assessing the long-term spatial impact on the aquifer of the emplacement, removal or leveling of a reservoir dam.

Modulating Magnetic Performance in DyIII Single Ion Magnets With N5O2 Ligands

ABSTRACT[Dy (LMe)(H2O)]CF3SO3·0.25H2O (1·0.25H2O), where H2LMe is the reported ligand 2,2′‐(((pyridine‐2,6‐diylbis (methylene))bis((pyridin‐2‐ylmethyl)azanediyl))bis (methylene))bis(4‐methylphenol), shows the DyIII ion in an N5O3 environment, with triangular dodecahedral geometry (D2d symmetry). 1·0.25H2O is a single ion magnet (SIM) with an energy barrier for spin reversal of 510 K, and open hysteresis loops up to 8 K. The magnetostructural comparison of 1·0.25H2O with some closely related complexes and with other eight‐coordinated SIMs with high energy barriers (> 300 K) allows to draw some conclusions to enhance the magnetic performance in these nanomagnets with non‐purely axial geometries. Ab initio calculations complement and support the experimental results.

(Invited) Magnetism of Tb3N@C80 Endofullerenes

Tb3N@C80 was one of the first trimetallic endofullerenes to be studied in view of its magnetization where the microscopic picture of 3 Tb magnetic moments non-collinearly aligned by the ligand field of the central nitrogen ion was proposed [1]. The triangular geometry results in a net molecular magnetization of two Tb3+ ions or 18 μB. Today, this is confirmed with 23 possible pseudospin arrangements of the 3 Tb magnetic moments, resulting in a frustrated magnetic ground state with fluctuating pseudospins [2]. This picture does not include coherent tunneling of the magnetization, which is predicted within an 8-dimensional Hamiltonian and can be tested with low temperature magnetization measurements. Experimentally, we find a low temperature hysteresis that identifies Tb3N@C80 as a single molecule magnet. More surprisingly, we observe room temperature ferromagnetism in cubic single crystallites of the molecules using SQUID magnetometry. Since the magnetic interaction between adjacent carbon cages is expected to be dipolar it is neglected in the explanation of magnetic order above 3 K [3] and it is challenging to explain this finding with endofullerene magnetism. We present a series of analytical chamistry results of samples with and without room temperature ferromagnetism.[1] M. Wolf et al. Angew. Chem. Int. Ed. 44, 3306 (2005).[2] R. Westerström et al. Phys. Rev. B, 89, 060406(R) (2014).[3] A. Kostanyan et al. Phys. Rev. B, 101, 134429 (2020).

Synthesis, Crystal Structure, Fluorescence and Theoretical Calculations of Three Zn(II)/Cd(II) Complexes with Bis-dentate N,N-Quinoline Schiff Base.

Three d10 metal complexes, ZnL(OAc)2 (1), CdL(OAc)2 (2) and [CdL2(NO3)2]·CH3CN (3) were synthesized using the ligand (E)-N-(3-methoxy-4-methylphenyl)-1-(quinolin-2-yl)methanimine (L) and characterized by FT-IR spectra, NMR spectra, and CHN elemental analysis. Single-crystal X-ray diffraction analysis revealed that complexes 1 and 2 are isostructural, with the central metal adopting a hexacoordinate octahedral geometry, while complex 3 adopts a triangular dodecahedron geometry. Thermal gravimetric analysis showed that these complexes exhibit good thermal stability. Solid-state fluorescence spectroscopy measurements demonstrated that complexes 1-3 exhibit bright yellow-green fluorescence (λem = 564nm for 1; 524nm for 2; 542nm for 3), suggesting their potential as photoluminescent materials. Furthermore, DFT calculations, including frontier molecular orbitals, energy levels, and surface electrostatic potential, provided insights into the structural and electronic spectral properties of complexes 1-3.

Spin–Orbit Coupling Free Nonlinear Spin Hall Effect in a Triangle-Unit Collinear Antiferromagnet with Magnetic Toroidal Dipole

We investigate emergent conductive phenomena triggered by collinear antiferromagnetic orderings. We show that an up-down-zero spin configuration in a triangle cluster leads to linear and nonlinear spin conductivities even without the relativistic spin–orbit coupling; the linear spin conductivity is Drude-type, while the nonlinear spin conductivity has Hall-type characterization. We demonstrate the emergence of both spin conductivities in a breathing kagome system consisting of a triangle cluster. The nonlinear spin conductivity becomes larger than the linear one when the Fermi level lies near the region where a small partial band gap opens. Our results indicate that collinear antiferromagnets with triangular geometry give rise to rich spin conductive phenomena.

A New Approach in Part Design for Friction Stir Welding of 3D-Printed Parts with Different Infill Ratios and Colors.

Parts produced using a 3D printer are combined with friction stir welding (FSW). In the FSW processing of parts with a low infill ratio, welding errors occur due to a lack of material. In this study, plates were created using two different-colored PLA Plus filaments with different infill ratios in the weld area (20%, 60%, and 100%). Triangular pin geometry, different feed rates (20, 40, and 60 mm/min), and different tool rotation speeds (1250, 1750, and 2250 rpm) were used as FSW process parameters. Tensile testing was performed to determine weld strength and hardness measurements, and visual inspections were performed. Color measurements were made on the test samples before and after the welding process, and the relationship between welding performance and color was evaluated. The best welding strength was obtained as 17.83 ± 0.68 MPa at a feed rate of 20 mm/min, a tool rotation speed of 1750 rpm, and a part with a 60% infill ratio in the welding zone. In the sample with the best weld strength, the temperature was measured as 198.97 °C. Color changes in the weld area of parts with 60% and 100% infill ratios were measured between 78.9-82.2 and 79.1-84.5, respectively. It was determined that the color change decreases as the weld strength increases in these parts. The results show that with the proposed new part design, the FSW method can be used at low infill ratios, and the weld strength can be evaluated based on the color changes in the weld zone.

Triangular graphene nanosheets, structures with extraordinary bending behavior.

Sometimes, manipulating the geometry or creating a defect can help the engineering of the nanostructured properties, such as increasing the frequency sensitivity of graphene nanosheets as a mass sensor by changing the geometry of the structure in a triangular shape and also by creating a vacancy or making nanodiodes in a triangular shape, which restricts the flow of heat in one direction and expands it in another direction. Then, the mechanical properties of the triangular geometry of graphene nanosheets have an excellent value for future devices. The results of the molecular dynamics study can illustrate the mechanical properties of graphene sheets well, which is particularly important. In this study, using molecular dynamics (MD) simulation, the bending stiffness of triangular graphene sheets was investigated to present a broader view of engineering applications of graphene sheets. Analyzing stress-displacement results of triangular graphene sheets in both zigzag and armchair directions under bending load reveals the effect of the directions of sheets on their bending stiffness. Also, comparing the bending stiffness of pristine and defective sheets showed that bending stiffness was decreased when an atom was removed from the middle of a sheet and made a single vacancy defected sheet. Obtained results suggest that triangular graphene nanosheets with higher bending stiffness, compared to rectangular sheets with the same number of atoms, are better for applications requiring higher bending properties, such as nanoelectromechanical devices. The reported results of this work provide an overall viewpoint concerning the geometry and defect effects on the graphene nanosheets' mechanical properties. The bending stiffness of triangular sheets was 20 and 10 times that of intrinsic and defective rectangular sheets, respectively.

Novel Co(II), Cu(II) and Fe(II) Pentadentate Schiff base complexes: Synthesis, characterization, antimicrobial, antioxidant, and molecular docking studies

The compound H2L, which is a ligand with five coordinating atoms, consisting of three nitrogen atoms and two sulfur atoms (N3S2), was reacted with Fe(OAc)2, Cu(OAc)2.H2O, and Co(OAc)2·4H2O to form the corresponding metal complexes ([FeL], [CuL], [CoL]). Many techniques, including NMR (for ligand), FT-IR, UV–Vis, elemental analysis, and molar conductivity, were used to characterize the synthesized compounds. According to the spectrum of data, complex molecule structures have a distorted triangular bipyramidal geometry with five coordination locations. The compounds that exhibit non-electrolyte behavior in solution do not possess any conductivity features. Evaluation was performed to determine the antioxidant activity of the synthesized compounds in comparison to the stable free radical DPPH. The ligand and its metal complexes were evaluated for antibacterial activity against several Gram-positive and Gram-negative bacteria, as well as a yeast strain. In comparison to the common antibiotic Amoxycillin/Clavulanic Acid (AMC-30), the Schiff base ligand (H2L) and its Cu(II) metal complex showed noticeably larger inhibitory zones against S. aureus. All the compounds showed a high negative binding affinity for S. aureus amino acid molecules when they were docked. The results indicated that the metal complexes, particularly the cobalt complex, exhibited a higher affinity for binding compared to the free ligand.

PARTS—A 2D Self-Reconfigurable Programmable Mechanical Structure

Modular self-reconfigurable robots hold the promise of being capable of performing a wide variety of tasks. However, many systems fall short of either delivering this promised functionality due to constraints in system architecture or validating it on functional hardware prototypes. This paper demonstrates the functional capabilities of the Planar Adaptive Robot with Triangular Structure (PARTS) and documents the versatility of this robot system using a holistic approach that combines simulations and hardware demonstrations on a prototype with nine fabricated modules. PARTS is a two-dimensional modular robot consisting of modules with a shape-shifting triangular geometry capable of forming adaptable space-covering structures. Meta-modules and mesh restructuring techniques are presented as methods for achieving topological self-reconfiguration. The feasibility of these methods is demonstrated by applying them on a simulated reconfiguration example of 62 modules. The paper showcases the versatility of PARTS on the hardware prototype using task-specific configurations, including locomotion using a meta-module and a walker configuration, module-module interaction by establishing a bridge between two separated module clusters, and interaction with the environment using a gripper and supporting structure configuration. The results validate the versatility and emphasize the potential of the system’s design concept, motivating the transfer of the hardware architecture to the third dimension.

Assembly-inspired multiferroicity with nontrivial Chern insulating phase from exohedral metallofullerenes.

Fullerene-assembled low-dimensional materials have been experimentally realized in polymorphic forms and have attracted significant interest very recently. Here, we predict a two-dimensional (2D) honeycomb lattice material TM2(C60)3 (TM = Cr, Mo, and W) assembled from exohedral metallofullerene clusters TM(C60)3 that could exhibit planar triangular geometries. According to first-principles calculations combined with Monte Carlo simulations, we suggest that these 2D assembled materials exhibit various exotic physical properties, including ferromagnetism, ferroelectricity, and quantum anomalous Hall effect. Interestingly, mechanical strains could effectively tune their magnetic moments and switch the conducting spin channel of the Dirac bands at the Fermi level. Our work provides a new cluster-assembly design strategy toward cluster-assembled 2D materials based on fullerene characters.

Observation of Nagaoka polarons in a Fermi-Hubbard quantum simulator.

Quantum interference can deeply alter the nature of many-body phases of matter1. In the case of the Hubbard model, Nagaoka proved that introducing a single itinerant charge can transform a paramagnetic insulator into a ferromagnet through path interference2-4. However, amicroscopic observation of this kinetic magnetism induced by individually imaged dopants has been so far elusive. Here we demonstrate the emergence of Nagaoka polarons in a Hubbard system realized with strongly interacting fermions in a triangular optical lattice5,6. Using quantum gas microscopy, we image these polarons asextended ferromagnetic bubbles around particle dopants arising from the local interplay of coherent dopant motion and spin exchange. By contrast, kinetic frustration due to the triangular geometry promotes antiferromagnetic polarons around hole dopants7. Our work augurs the exploration of exotic quantum phases driven by charge motion in strongly correlated systems and over sizes that are challenging for numerical simulation8-10.

Superfluid fraction tensor of a two-dimensional supersolid

We investigate the superfluid fraction of crystalline stationary states within the framework of mean-field Gross–Pitaevskii theory. Our primary focus is on a two-dimensional Bose–Einstein condensate with a non-local soft-core interaction, where the superfluid fraction is described by a rank-2 tensor. We then calculate the superfluid fraction tensor for crystalline states exhibiting triangular, square, and stripe geometries across a broad range of interaction parameters. Factors leading to an anisotropic superfluid fraction tensor are also considered. We also refine the Leggett bounds for the superfluid fraction of the 2D system. We systematically compare these bounds to our full numerical results, and other results in the literature. This work is of direct relevance to other supersolid systems of current interest, such as supersolids produced using dipolar Bose–Einstein condensates.

Modulating the Magnetic Dynamics of Five‐Coordinate DyIII Single‐Molecule Magnets by the Substitution Effect on the Axial Ligand

AbstractTwo five‐coordinate mononuclear DyIII single‐molecule magnets [(TrapenTMS)Dy(L)] (Trapen=tris(2‐aminobenzyl) amine; TMS=SiMe3; L=OPMe3 1, OPEt3 2) have been synthesized by the reaction of [(TrapenTMS)Dy(THF)] and OPMe3, OPEt3, respectively. The molecular structures of 1 and 2 were fully established by single crystal X‐ray diffraction. The centre DyIII ions of both complexes exhibit distorted triangular bipyramid geometries, varying with different neutral ligands L on the apex. The TrapenTMS ligand forms the pyramid base of the trigonal bipyramid. Subtle structural modifications of the axial O‐ligand terminal substituent result in different dynamic magnetic behaviors. Magnetic data analysis reveals that 1 and 2 exhibit the characteristic behavior of SMM without a dc field, accompanying an unambiguous quantum tunneling of the magnetization. Field‐induced slow magnetic relaxation was observed for 1 and 2 under an applied bias dc field of 1000 Oe, the relaxation energy barriers are 107 K and 88 K for 1 and 2, respectively. We have investigated the differences in magnetism and magnetic anisotropy between the two complexes by ab initio calculations.

Tensor-Triangular Geometry and Interactions

The workshop brought together experts in a rapidly growing field of tensor triangular geometry highlighting applications to and techniques coming from homotopy theory, algebraic geometry, modular representation theory, motivic homotopy theory and noncommutative algebra.