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We investigate the emergence of magnetic skyrmion crystals with swirling topological spin textures in itinerant magnets with an emphasis on momentum-resolved multi-spin interactions. By performing the simulated annealing for the effective spin model with the two-spin and four-spin interactions on a two-dimensional triangular lattice, we show that various types of four-spin interactions become the microscopic origin of the magnetic skyrmion crystal with the skyrmion numbers of one and two. We find that the four-spin interactions between the different wave vectors lead to the skyrmion crystal with the skyrmion number of one, whereas those at the same wave vectors lead to the skyrmion crystals with the skyrmion number of one and two. Our results indicate that the multi-spin interactions arising from the itinerant nature of electrons provide rich topological spin textures in magnetic metals.

Using the strong coupling diagram technique, we find three phases of the half-filled isotropic Hubbard model on a triangular lattice at finite temperatures. The weak-interaction ( U ≲ 5 t ) and strong-interaction ( U ≳ 9 t ) phases are similar to those obtained by zero-temperature methods—the former is a metal without perceptible spin excitations; the latter is a Mott insulator with the 120 ∘ short-range spin ordering. Zero-temperature approaches predict a nonmagnetic insulating spin-liquid phase sandwiched between these two regions. In our finite-temperature calculations, the Mott gap in the intermediate phase is filled by the Fermi-level peak, which is a manifestation of the bound states of electrons with pronounced spin excitations. We relate the appearance of these excitations at finite temperatures to the Pomeranchuk effect. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Using the unrestricted Hartree-Fock variational method, we study the extended Hubbard model in the triangular lattice at 3/4 filling. Due to the nesting instability of the Fermi surface, various density wave states compatible with the 2 × 2 supercell are found as the ground state by tuning the onsite and nearest neighbor repulsions U and V. Surprisingly, the flux phases with complex bond order parameters are realized in a wide range of the U-V phase diagram. They also acquire nontrivial topological properties due to the spontaneous breaking of the time-reversal symmetry. Our study suggests that the flux phases can be stabilized by the interplay between short-range repulsive interactions in correlated electron systems. [ABSTRACT FROM AUTHOR]

We investigate the emergence of magnetic skyrmion crystals with swirling topological spin textures in itinerant magnets with an emphasis on momentum-resolved multi-spin interactions. By performing the simulated annealing for the effective spin model with the two-spin and four-spin interactions on a two-dimensional triangular lattice, we show that various types of four-spin interactions become the microscopic origin of the magnetic skyrmion crystal with the skyrmion numbers of one and two. We find that the four-spin interactions between the different wave vectors lead to the skyrmion crystal with the skyrmion number of one, whereas those at the same wave vectors lead to the skyrmion crystals with the skyrmion number of one and two. Our results indicate that the multi-spin interactions arising from the itinerant nature of electrons provide rich topological spin textures in magnetic metals. [ABSTRACT FROM AUTHOR]

In this research, the effectiveness of six element uniform circular uniform dipole array is designed. To determine the most productive design for the ISM Band, numerous array antenna topologies are tested in this work. The proposed antenna is appropriate for the ISM, IEEE 802.11, Bluetooth, as well as Zigbee, WiMAX, and WiFi applications. We first set up a 6-element dipole linear array for this, after which we switched to a rectangular array using a combination of triangular and rectangular lattice arrangements. The identical 6-element dipole antenna was then configured in a circular fashion, and the results appear to be excessively good when compared to all previous configurations. The symmetrical arrangement of a uniform circular array design allows the phasing of array antennas to operate azimuthally with little variation in its wavelength and side lobe intensities. There are 6 isotropic components in this uniform circular array design. To adjust the antenna to shifting surroundings, complicated values of the antennas array components are calculated. The correlation effect between various elements were analysed. In this work a return loss of – 35 dB was obtained as a maximum value for circular array configuration at 2.45 GHz. The goal of employing array antennas is to provide increased efficiency and broad band capabilities, allowing for usage in a variety of everyday applications. [ABSTRACT FROM AUTHOR]

The Monte Carlo method is used to perform the simulation of four-component Potts model on a triangular lattice. Systems with linear dimensions of L × L = N and L = 10–160 are considered. Phase transitions in terms of the considered Potts model are studied using fourth-order Binder cumulants and histogram analysis of data. It is shown that, in the four-component Potts model on a triangular lattice, second-order transitions are observed. [ABSTRACT FROM AUTHOR]

Photonic crystal channel drop filters (CDFs) play a vital role in optical communication owing to their ability to drop the desired channel. However, it remains challenging to achieve high-efficiency CDFs. Here, we demonstrate a highly efficient three-channel CDF with both high transmission and high quality (Q) factor based on a novel ring resonator that is in the middle of two waveguides. A dielectric column with a large radius replaces the homogeneously distributed dielectric columns inside the ring cavity to modulate the coupling ratio with a straight waveguide, thereby enhancing the transmission and Q factor. The transmission and Q factor of the single-cavity filter are 99.7% and 12,798.4, respectively. The mean value of the three-channel filter based on the basic unit can reach up to 94.6% and 10,617, respectively, and a crosstalk between −30.16 and −50.61 dB is obtained. The proposed CDFs provide efficient filter capability, which reveals great potential in integrated optoelectronics and optical communication. [ABSTRACT FROM AUTHOR]

In the United States, regions (such as states or counties) are frequently divided into districts for the purpose of electing representatives. How the districts are drawn can have a profound effect on who is elected, and drawing the districts to give an advantage to a certain group is known as gerrymandering. It can be surprisingly difficult to detect when gerrymandering is occurring, but one algorithmic method is to compare a current districting plan to a large number of randomly sampled plans to see whether it is an outlier. Recombination Markov chains are often used to do this random sampling: randomly choose two districts, consider their union, and split this union up in a new way. This approach works well in practice and has been widely used, including in litigation, but the theory behind it remains underdeveloped. For example, it is not known if recombination Markov chains are irreducible, that is, if recombination moves suffice to move from any districting plan to any other. Irreducibility of recombination Markov chains can be formulated as a graph problem: for a planar graph G , is the space of all partitions of G into k connected subgraphs (k districts) connected by recombination moves? While the answer is yes when districts can be as small as one vertex, this is not realistic in real-world settings where districts must have approximately balanced populations. Here we fix district sizes to be k 1 ± 1 vertices, k 2 ± 1 vertices, ... for fixed k 1 , k 2 , ... , a more realistic setting. We prove for arbitrarily large triangular regions in the triangular lattice, when there are three simply connected districts, recombination Markov chains are irreducible. This is the first proof of irreducibility under tight district size constraints for recombination Markov chains beyond small or trivial examples. The triangular lattice is the most natural setting in which to first consider such a question, as graphs representing states/regions are frequently triangulated. The proof uses a sweep-line argument, and there is hope it will generalize to more districts, triangulations satisfying mild additional conditions, and other redistricting Markov chains. [ABSTRACT FROM AUTHOR]

We report our numerical results on the stability of the skyrmion crystal phase in an external magnetic field for both in-plane and out-of-plane directions in a centrosymmetric host. We analyze a spin model with the two-spin symmetric anisotropic exchange interaction that arises from relativistic spin–orbit coupling on a triangular lattice. By performing simulated annealing, we construct magnetic phase diagrams when the magnetic field is tilted from the out-of-plane field direction to the in-plane field direction. We find a different stability tendency of the skyrmion crystal phase according to the directions of the in-plane field, which provides a signal of the two-spin symmetric anisotropic exchange interaction for stabilizing the skyrmion crystal phase. Our results indicate that the mechanism of the skyrmion crystal phase triggered by the two-spin symmetric anisotropic exchange interaction can be experimentally tested by applying the in-plane magnetic field.

We report our numerical results on the stability of the skyrmion crystal phase in an external magnetic field for both in-plane and out-of-plane directions in a centrosymmetric host. We analyze a spin model with the two-spin symmetric anisotropic exchange interaction that arises from relativistic spin–orbit coupling on a triangular lattice. By performing simulated annealing, we construct magnetic phase diagrams when the magnetic field is tilted from the out-of-plane field direction to the in-plane field direction. We find a different stability tendency of the skyrmion crystal phase according to the directions of the in-plane field, which provides a signal of the two-spin symmetric anisotropic exchange interaction for stabilizing the skyrmion crystal phase. Our results indicate that the mechanism of the skyrmion crystal phase triggered by the two-spin symmetric anisotropic exchange interaction can be experimentally tested by applying the in-plane magnetic field. [ABSTRACT FROM AUTHOR]

The current wireless technology adopted 5G (Generation) communication, and more research is analyzed towards 6G too. The switching of various Gs is due to achieving a high data rate speed and effective transmission. The terahertz (THz) band helps achieve a high data transmission rate in Terabit per second (Tbps). This manuscript proposed the THz-based photonic crystal (PhC) antenna and investigated the effect of a line defect. In the PhC triangular substrate, the line defect is implanted in horizontal and vertical directions. The antenna performances like return loss, directivity and voltage standing wave ratio (VSWR) are examined. The simulated results conclude that the horizontally oriented defective PhC antenna provided superior antenna performances than the vertically oriented defective PhC structure. The simulated results of the defected PhC antenna exhibited excellent characteristics like −50.60 dB return loss, 1.00 value of VSWR and directivity of 8.96 dB at 1.58 THz frequency. Hence, the proposed defective PhC antenna is applicable for high-speed wireless transmission in terms of Tbps, various medical applications, etc. [ABSTRACT FROM AUTHOR]

A decorated ferrimagnetic mixed triangular system was studied using the molecular mean-field approximation. The outcomes of the investigation were examined using the Blume-Capel Ising model. The study paper investigates the influence of crystal and external magnetic fields on ferrimagnetic devices decorated with mixed spin-2 and spin-7/2 of a triangular lattice. It is noteworthy that spin-2 ions are located at the nodal points, whereas six additional spin-7/2 ions surround the proposed lattice. Altering the exchange interactions through the specific crystal and external magnetic fields induces superparamagnetic behaviours. New characteristics reveal that mixed spin triangular decorated ferrimagnets exhibit superparamagnetic behaviour at DA∕|J2|=-2.5, with J1 = -0.5 and J2 = -1.0 in the range (15 ≤ KBT /|J2| ≤ 18). It is important to note that the total magnetization changes with the external magnetic field and affects the superparamagnetism phenomenon of a decorated mixed spin ferrimagnet when DA/|J2| = 8, and DB/|J2|=-11, J1 = -0.5 and J2 = 1, for KBT/|J2| = 2, 2.5, 3, 3.5, and 4 Ko respectively.

We study the low-field ground-state (GS) properties of the antiferromagnetic transverse-field Ising model with long-range interactions (afLRTFIM) on the triangular lattice. We use the method of perturbative continuous unitary transformations (pCUT) to derive an effective model for the degenerate GS space of the antiferromagnetic nearest-neighbour (NN) Ising model on a finite system, by treating the transverse-field (TF) and the long-range interactions (LRI) as a perturbation. We determine a level-crossing between the gapped plain stripe phase at small TF and the gapped clock-ordered phase at intermediate TF at hc≅0.129 for α=6, N=36 spins in order three perturbation theory on the finite system. We discuss the qualitative layout of the quantum phase diagram of the afLRTFIM on the triangular lattice.

To address the issues of superconducting and charge properties in hydrated sodium cobalt, we investigate an extended ionic Hubbard model on the triangular lattice, which includes off-site attractions between sites with minor charges. Our quantum Monte Carlo simulations show that close to quarter filling, the off-site attractions induce a significant enhancement of d-wave and extended s-wave pairing correlations. Simultaneously, they render an increase of the charge structure factor at most of wave vectors. A combination with charge correlations in real space indicates the development of short-range finite-q charge density waves on the sites with minor charges. Our findings provide a new perspective on the superconducting mechanism in hydrated sodium cobalt based on the electronic structure which explicitly takes the effect of sodium atoms into account.

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.

Photonic crystal channel drop filters (CDFs) play a vital role in optical communication owing to their ability to drop the desired channel. However, it remains challenging to achieve high-efficiency CDFs. Here, we demonstrate a highly efficient three-channel CDF with both high transmission and high quality (Q) factor based on a novel ring resonator that is in the middle of two waveguides. A dielectric column with a large radius replaces the homogeneously distributed dielectric columns inside the ring cavity to modulate the coupling ratio with a straight waveguide, thereby enhancing the transmission and Q factor. The transmission and Q factor of the single-cavity filter are 99.7% and 12,798.4, respectively. The mean value of the three-channel filter based on the basic unit can reach up to 94.6% and 10,617, respectively, and a crosstalk between −30.16 and −50.61 dB is obtained. The proposed CDFs provide efficient filter capability, which reveals great potential in integrated optoelectronics and optical communication.

This paper presents investigations on reflectarray antennas using non-periodic element distributions. The study involves the analysis and design of two reflectarrays based on quasi-periodic lattices with rectangular and pentagonal profiles, whose performance is compared with equivalent reflectarrays comprised of regular grids of elements. The characterization of these antennas is performed using a tailored analysis technique for reflectarrays with periodical and quasi-periodical grids. The proposed technique uses the Method of Moments under local periodicity conditions (MoM-LP) to compute the field on the surface of each cell and then the far field radiated by the aperture. In both aperture profiles, the quasi-periodic lattices are designed to provide an optimal adjustment, with the edge of the reflectarray maintaining an inter-element spacing similar to the regular grids of elements. This is particularly useful in non-canonical profile apertures, where the regular lattices do not adjust properly with the shape of the reflectarray and therefore exhibit less control of the reflected field in the aperture. The reflectarrays comprised of quasi-regular lattices achieve similar performance in terms of beam shaping, SLL and crosspolar discrimination to those based on regular grids. However, they show an improvement in fractional bandwidth between 7.4% and 11.3%.

Triangular lattice magnets have attracted extensive research interest because they are potential hosts for geometrically frustrated magnetism and strong quantum fluctuations. Here, utilizing a laser floating zone technique, we report the first-time successful growth of a DyInO3 sizable crystal, which contains Dy3+-based triangular layers. The fine-tuning of Indium stoichiometry was found to be the key factor in the stabilization of the desired hexagonal phase. The X-ray diffraction study of the crystal structure reveals a non-centrosymmetric P63mc space group. Switchable polarization, i.e., ferroelectricity, and ferroelectric domain configuration are experimentally demonstrated at room temperature. Anisotropic magnetic and thermodynamic measurements unveil antiferromagnetic interactions, the absence of long-range ordering down to 0.1 K, and a possible doublet ground state, indicating a strongly frustrated magnetism. Our findings suggest that the DyInO3 crystal is an excellent platform for studying emergent phenomena and their interplay with coherent topological defects in the quantum realm. [ABSTRACT FROM AUTHOR]

It is well-known that any Lennard–Jones type potential energy must have a periodic ground state given by a triangular lattice in dimension 2. In this paper, we describe a computer-assisted method that rigorously shows such global minimality result among 2-dimensional lattices once the exponents of the potential have been fixed. The method is applied to the widely used classical (12 , 6) Lennard–Jones potential, which is the main result of this work. Furthermore, a new bound on the inverse density (i.e. the co-volume) for which the triangular lattice is minimal is derived, improving those found in (Bétermin and Zhang 2015 Commun. Contemp. Math. 17 1450049) and (Bétermin 2016 SIAM J. Math. Anal. 48 3236–3269). The same results are also shown to hold for other exponents as additional examples and a new conjecture implying the global optimality of a triangular lattice for any parameters is stated. [ABSTRACT FROM AUTHOR]

Mixed-valent Ba2Mn2+Mn23+(SeO3)6 crystallizes in a monoclinic P21/c structure and has honeycomb layers of Mn3+ ions alternating with triangular layers of Mn2+ ions. We established the key parameters governing its magnetic structure by magnetization M and specific heat Cp measurements. The title compound exhibits a close succession of a short-range correlation order at Tcorr = 10.1 ± 0.1 K and a long-range Néel order at TN = 5.7 ± 0.1 K, and exhibits a metamagnetic phase transition at T < TN with hysteresis most pronounced at low temperatures. The causes for these observations were found using the spin exchange parameters evaluated by density functional theory calculations. The title compound represents a unique case in which uniform chains of integer spin Mn3+ (S = 2) ions interact with those of half-integer spin Mn2+ (S = 5/2) ions. [ABSTRACT FROM AUTHOR]

This paper focuses on creation of a technique to derive systems with explicitly defined symmetry protected topological (SPT) phases on a triangular lattice, based on models featuring arbitrary symmetries. It results in emergence of effective edge models, which are massless in nontrivial SPT phases. When applied on non-interacting systems, the technique results in models with a translational invariance, which ensures independence from the local geometry. [ABSTRACT FROM AUTHOR]

Here we report the successful synthesis of large single crystals of triangular frustrated PrMgAl _11 O _19 using the optical floating zone technique. Single crystal x-ray diffraction (XRD) measurements unveiled the presence of quenched disorder within the mirror plane, specifically ~7% of Pr ions deviating from the ideal 2 d site towards the 6 h site. Magnetic susceptibility measurements revealed an Ising anisotropy with the c -axis being the easy axis. Despite a large spin–spin interaction that develops below ~10 K and considerable site disorder, the spins do not order or freeze down to at least 50 mK. The availability of large single crystals offers a distinct opportunity to investigate the exotic magnetic state on a triangular lattice with an easy axis out of the plane.

Skyrmions are prospected as the potential future of data storage due to their topologically protected spin structures. However, traditional ferromagnetic (FM) skyrmions experience deflection when driven with an electric current, hindering their usage in spintronics. Antiferromagnetic (AFM) skyrmions, consisting of two FM solitons coupled antiferromagnetically, are predicted to have zero Magnus force, making them promising candidates for spintronic racetrack memories. Currently, they have been stabilized in synthetic AFM structures, i.e., multilayers hosting FM skyrmions, which couple antiferromagnetically through a non-magnetic spacer, while recent first-principle simulations predict their emergence in an intrinsic form, within a row-wise AFM single monolayer of Cr deposited on a PdFe bilayer grown on Ir (111) surfaces. The latter material forms a triangular lattice, where single and interlinked AFM skyrmions can be stabilized. Here, we explore the minimal Heisenberg model, enabling the occurrence of such AFM solitons and the underlying phase diagrams by accounting for the interplay between the Dzyaloshinskii–Moriya and Heisenberg exchange interactions, as well as the magnetic anisotropy and impact of the magnetic field. By providing the fundamental basis to identify and understand the behavior of intrinsic AFM skyrmions, we anticipate our model to become a powerful tool for exploring and designing new topological magnetic materials to conceptualize devices for AFM spintronics.

Triangular lattice, with each site coordinating with six neighbors, is one most common network in two-dimensional (2D) limit. Manifestations of peculiar properties in the lattice, including magnetic frustration and quantum spin liquid, have been restricted to single-orbital tight-binding (TB) model so far, while the orbital degree of freedom is largely overlooked. Here, by combining TB modeling with first-principles calculations, we demonstrate the rich electronic structures of triangular lattice with multiple (p x , p y , p z) orbitals. Type I/II Dirac point, quadratic nodal point and nodal-loops are observed, and the topological phase diagram is mapped out by manipulating the horizontal mirror symmetry, spin-orbit coupling and energy position of relevant orbitals. Remarkably, we show that large-gap quantum spin Hall phase (∼0.2 eV) can be realized in experimentally achievable systems by growing indium monolayer on a series of semiconducting substrates, such as C/Si/Ge(111) and SiC(0001) surfaces, and the proposed materials capture the TB parameter space well. Our work not only provides physical insights into the orbital physics in 2D lattices, but also sheds light on the integration of novel quantum states with conventional semiconductor technology for potential applications, such as dissipationless interconnects for electronic circuits. [ABSTRACT FROM AUTHOR]

The physical and chemical properties of the nanocrystals are highly shape dependent, and shape control has become very important. The seeded growth method enables seeds to grow in a predetermined way. We have already proposed such a model that can reproduce the granular growth on a triangular lattice and for different growth shapes. In this paper, however, we have introduced a limitation on seed growth up to a certain length. This method can be used when the growth of all seeds have to be limited to the same length, or for a mixture with the different growth limits. The main goal is to investigate how the growing limits affect the values of the percolation threshold and jamming density, and whether large objects significantly affect the percolation threshold. We used growing needle-shaped objects (k-mers) made by a self-avoiding random walk filling the nodes of the triangular lattice. Objects can grow until they reach the growth limit k' defined as the maximum number of lattice nodes belonging to one object. For k' ≥ 10, percolation is reached for all investigated seed densities. We obtained that the values of the percolation threshold and jamming density are identical for k' ≥ 10. Above these values, the percolation threshold and jamming remain unchanged, regardless of the growth limit. Our results also show that when significant growth is allowed, long objects are very rare and do not influence the results. [ABSTRACT FROM AUTHOR]

The influence of magnon bands on entanglement in the antiferromagnetic XXZ model on a triangular lattice, which models the bilayer structure consisting of an antiferromagnetic insulator and normal metal, is investigated. This effect was studied in ferromagnetic as well as antiferromagnetic triangular lattices. Quantum entanglement measures given by the entanglement negativity have been studied, where a magnon current is induced in the antiferromagnet due to interfacial exchange coupling between localized spins in the antiferromagnet and itinerant electrons in a normal metal. Moreover, quantum correlations in other frustrated models, namely the metal-insulation antiferromagnetic bilayer model and the Heisenberg model with biquadratic and bicubic interactions, are analyzed. [ABSTRACT FROM AUTHOR]

A partitioning scheme based on Penrose-inspired subarrays is proposed for wide-scan planar phased arrays. The regular triangular lattice adopted for the arrangement of the antenna elements is organized into irregularly shaped tiles that exploit the properties offered by the Penrose tessellation. The novel array architecture ensures a remarkable reduction of the transmit/receive modules without harming the scan angle range and peak sidelobe level thanks to the optimization based on the Pareto front that is able to tackle conflicting objectives. The performance of the proposed approach is assessed in different scenarios and proves the robustness and flexibility of the new tiling architecture. Moreover, a thorough analysis is carried out to highlight the unique feature of the partition scheme of offering a noteworthy reduction in energy consumption. [ABSTRACT FROM AUTHOR]

• Ultracompact multiway ultrasonic power splitters based on the phononic crystals with a triangular lattice were constructed. • Such power splitters can effectively divide ultrasonic energy into multiple channels (n ≥ 2) and output them. • The arrow-shaped and star-shaped power splitters were separately discussed in detail as examples. • Displacement field distribution and transmission of these outputs were calculated to evaluate their efficiency. • Power splitters possess promising properties, including ultracompact, high-efficiency, and large bandwidth. We report the ultracompact multiway power splitters based on the phononic crystal with a triangular lattice. Such power splitters can effectively divide ultrasonic energy into multiple channels (n≥2) and output them. The arrow-shaped and star-shaped power splitters were separately discussed in detail based on the finite element method (FEM) as examples. The phononic bandgap in the triangular lattice arrangement and dispersive curves of a single phononic waveguide were analyzed, respectively. Also, the displacement field distribution and transmission efficiency of these outputs were calculated to evaluate the efficiency of the splitters. The results indicate that these splitters possess novel and promising properties, including ultracompact, high-efficiency, and large bandwidth. The perturbations analysis of the power splitter proves that it has good mechanical stability. It is to be expected that these ultracompact splitters will present practical applications in future acoustic wave circuits. [ABSTRACT FROM AUTHOR]

We prepared a layered antiferromagnet KNiB 4 O 6 F 3 1 by hydrothermal synthesis, and characterized its structure and physical properties by X-ray diffraction, magnetization and specific heat measurements as well as thermal stability, FTIR and UV–vis–NIR measurements. 1 consists of layers of composition [NiB 4 O 6 F 3 ]- separated by layers of K+ cations. And Ni2+ ions are arranged in slightly distorted triangular pattern in each [NiB 4 O 6 F 3 ]- layer. The magnetic susceptibility measurements indicate no divergence between the zero-field-cooled and field-cooled curves down to 7.9 K, below which a long-range order takes place as verified by specific heat measurements. The M (H) curve linearly increases when the field is weak (below ∼2 T), confirming that the ground state of 1 is antiferromagnetic. At 7 T, the magnetization of 1 is 1.67 μ B which is lower than the saturation magnetization. A two-dimensional layered magnetic compound KNiB 4 O 6 F 3 with triangular lattice has been hydrothermally synthesized, exhibiting no three-dimensional long-range order until 6.9 K with spin canting behavior may due to moderate spin frustration. [Display omitted] • A two-dimensional layered magnetic compound KNiB 4 O 6 F 3 with triangular spin lattice has been hydrothermally synthesized. • Magnetic susceptibility results show no three-dimensional long-range order until 7.9 K may due to moderate spin frustration. • The magnetic-field dependence of magnetization confirms the antiferromagnetic ground state in KNiB 4 O 6 F 3. • The heat capacity result confirms the magnetic susceptibility results with long-range order at 7.9 K. [ABSTRACT FROM AUTHOR]

Triangular lattice magnets have attracted extensive research interest because they are potential hosts for geometrically frustrated magnetism and strong quantum fluctuations. Here, utilizing a laser floating zone technique, we report the first-time successful growth of a DyInO3 sizable crystal, which contains Dy3+-based triangular layers. The fine-tuning of Indium stoichiometry was found to be the key factor in the stabilization of the desired hexagonal phase. The X-ray diffraction study of the crystal structure reveals a non-centrosymmetric P63mc space group. Switchable polarization, i.e., ferroelectricity, and ferroelectric domain configuration are experimentally demonstrated at room temperature. Anisotropic magnetic and thermodynamic measurements unveil antiferromagnetic interactions, the absence of long-range ordering down to 0.1 K, and a possible doublet ground state, indicating a strongly frustrated magnetism. Our findings suggest that the DyInO3 crystal is an excellent platform for studying emergent phenomena and their interplay with coherent topological defects in the quantum realm.

We adapt the notion of poidge-convexity to subgraphs of the triangular lattice, and investigate the poidge-convexity of graphs belonging to two families of such subgraphs: paths and grid graphs. [ABSTRACT FROM AUTHOR]

The condition number for eigenvector computations is a well-studied quantity. But how small can it possibly be? Specifically, what matrices are perfectly conditioned with respect to eigenvector computations? In this note we answer this question for n × n matrices, giving a solution that is exact to first-order as n → ∞. [ABSTRACT FROM AUTHOR]

This article presents a dual-polarized frequency-scaled ultra-wide spectrum element (FUSE) array on a triangular lattice, precision-machined from an Aluminum block as a self-supporting structure, similar to all-metal Vivaldi arrays reported by the authors in past work. Whereas dual-polarized FUSE arrays normally consist of offset radiator pairs conforming to the ubiquitous square-lattice egg-crate configuration and capacitively coupled at the ends to achieve ultra-wideband operational frequency ranges, this work is novel in that it uses conventional manufacturing to directly machine the dual-polarized FUSE array on a triangular lattice instead. Triangular lattices for dual-polarized wideband arrays are uncommon in the literature and have the benefit of 15.5% reduction in element counts over a square lattice aperture of the same footprint and upper frequency of operation, making this a useful development for applications requiring minimum element counts, i.e., reduced cost/weight. In this article, embedded element performance predictions for the dual-polarized triangular-lattice FUSE array are presented and validated with measurements of a hardware prototype. Results show similar overall grating-lobe-free performance to a square lattice FUSE array of the same footprint and operational frequencies reported in earlier work. The asymmetries of the triangular lattice result in relative performance degradation versus square lattice FUSE arrays as a trade-off to the benefit of reduced element counts for apertures of similar size. [ABSTRACT FROM AUTHOR]

We consider the Helmholtz equation (Δd + k2)u = f on the triangular lattice, where Δd is the discrete Laplacian, f has finite support, and wave number k belongs to the pass‐band. Using the limiting absorption principle, we derive the discrete analogue of the Sommerfeld radiation condition for all values of k∈(0,3)\{22}. It turns out that this condition is anisotropic and depends on the value of k. We introduce the notion of a radiating solution and prove the unique solvability result. [ABSTRACT FROM AUTHOR]

The influence of magnon bands on entanglement in the antiferromagnetic XXZ model on a triangular lattice, which models the bilayer structure consisting of an antiferromagnetic insulator and normal metal, is investigated. This effect was studied in ferromagnetic as well as antiferromagnetic triangular lattices. Quantum entanglement measures given by the entanglement negativity have been studied, where a magnon current is induced in the antiferromagnet due to interfacial exchange coupling between localized spins in the antiferromagnet and itinerant electrons in a normal metal. Moreover, quantum correlations in other frustrated models, namely the metal-insulation antiferromagnetic bilayer model and the Heisenberg model with biquadratic and bicubic interactions, are analyzed.

A compact wideband and wide-scanning planar triangular-lattice phased array is proposed. The proposed element is a U-slot microstrip antenna surrounded by a substrate-integrated cavity (SIC) structure fed by a 50 $\Omega$ coaxial cable. The scan blindness is effectively shifted out of the operation band as the SIC structure obstructs the surface wave and mutual coupling. The proposed array is arranged in a triangular lattice with fewer elements than a rectangular one. A $4\times 8$ planar array prototype is fabricated and measured over $X$ -band. The antenna provides a bandwidth of over 30% frequency range under ±60° scanning in all azimuth planes. [ABSTRACT FROM AUTHOR]

We study the low-field ground-state (GS) properties of the antiferromagnetic transverse-field Ising model with long-range interactions (afLRTFIM) on the triangular lattice. We use the method of perturbative continuous unitary transformations (pCUT) to derive an effective model for the degenerate GS space of the antiferromagnetic nearest-neighbour (NN) Ising model on a finite system, by treating the transverse-field (TF) and the long-range interactions (LRI) as a perturbation. We determine a level-crossing between the gapped plain stripe phase at small TF and the gapped clock-ordered phase at intermediate TF at h c ≅ 0. 129 for α = 6 , N = 36 spins in order three perturbation theory on the finite system. We discuss the qualitative layout of the quantum phase diagram of the afLRTFIM on the triangular lattice. • Exploration of the antiferromagnetic long-range transverse-field Ising model on the triangular lattice. • Nearest-neighbour order-by-disorder competes with long-range interactions. • Utilisation of perturbative continuous unitary transformations to derive an effective model. [ABSTRACT FROM AUTHOR]

To address the issues of superconducting and charge properties in hydrated sodium cobalt, we investigate an extended ionic Hubbard model on the triangular lattice, which includes off-site attractions between sites with minor charges. Our quantum Monte Carlo simulations show that close to quarter filling, the off-site attractions induce a significant enhancement of d -wave and extended s -wave pairing correlations. Simultaneously, they render an increase of the charge structure factor at most of wave vectors. A combination with charge correlations in real space indicates the development of short-range finite- q charge density waves on the sites with minor charges. Our findings provide a new perspective on the superconducting mechanism in hydrated sodium cobalt based on the electronic structure which explicitly takes the effect of sodium atoms into account. • The hydrated sodium cobalt is studied based on an extended ionic Hubbard model. • Unconventional superconductivity is enhanced by the off-site attractions. • Short-range charge density wave is induced by the off-site attractions. [ABSTRACT FROM AUTHOR]

We investigated the effect of Ni doping in a recently proposed quantum spin liquid (QSL) candidate Li 4 CuTeO 6. We performed a comprehensive study on the structural and magnetic properties. We find that the anti-site disorder between Li + and Cu 2 + persists until 50% Ni doping in which Ni and Cu occupy different crystallographic sites. As a result, while Cu sits in both triangular and honeycomb layers in Li 4 CuTeO 6 , Ni forms only honeycomb layer in Li 4 NiTeO 6 and Li 4 Cu 0.5 Ni 0.5 TeO 6. Our magnetic susceptibility measurements show that the Weiss temperature decreases from -145.68 K in Li 4 CuTeO 6 to -6.15 K in Li 4 NiTeO 6 as Ni doping increases, and find no hint of magnetic ordering or freezing down to 1.8 K. Our analysis implies the existence of abundant low energy excitations in these materials. • Triangular-lattice antiferromagnets hosting possible quantum spin liquids (QSL). • Unavoidable anti-site disorder between Li + and Cu 2 + ions on triangular networks. • Comprehensive study of the crystal and magnetic properties in Li 4 Cu 1 − x Ni x TeO 6. [ABSTRACT FROM AUTHOR]

This article presents a dual-polarized Vivaldi array on a triangular lattice. The all-metal ultrawideband Vivaldi features offset radiator pairs that are precision-machined from aluminum stock as a modular tile, similar to earlier reports on more typical all-metal square-lattice Vivaldi arrays. The intent of this work is to validate the embedded element performance of the dual-polarized triangular-lattice Vivaldi, comparing one-to-one with results for a similarly sized dual-polarized all-metal Vivaldi array on a square (egg-crate) lattice, reported previously. The triangular-lattice Vivaldi array is optimally sampled for grating-lobe-free scans with a potential 15.5% reduction in element count compared to a corresponding optimally sampled square-lattice array of similar size. As such, the footprint of the manufactured triangular-lattice Vivaldi array is roughly 8% larger than the square-lattice array, yet has 7% fewer elements. Infinite array predictions are presented and shown to compare favorably with previous findings for the square-lattice Vivaldi array, noting minor performance compromises. Wideband and wide-scan simulations are validated with measurements of prototype hardware, demonstrating that embedded element performance of the triangular-lattice array correlates well with modeling predictions. All told, the triangular-lattice array has similar capability to the square-lattice Vivaldi array in a more efficiently sampled aperture. [ABSTRACT FROM AUTHOR]

Vortex beams carrying orbital angular momentum (OAM) are widely applied in various electromagnetic, optical, and quantum systems. A tailored OAM spectrum composed of several specific modes as expected holds a promise for expanding the degrees of freedom of the systems. However, such a broadband high‐purity tailored spectrum is difficult to be achieved by the present devices, where the broadband amplitude manipulation is not explored yet. In this work, inspired by the envelope‐modulation theory, an elegant and universal way to manipulate the OAM spectrum in wide bandwidth is proposed by using a shape‐tailored metasurface. First, the rotating meta‐atoms on a triangular lattice are proved to have smaller coupling distortion than that on a square lattice, and this behavior is critical for high‐purity vortex spectrum generation by the Pancharatnam–Berry‐based metasurfaces. Second, a universal modulation relation is established between the spatial arrangement of metasurfaces and the generated vortex beams. Finally, the broadband‐modulated OAM spectra and the comb‐like OAM spectra are theoretically and experimentally demonstrated by the shape‐tailored metasurfaces. The proposed amplitude‐modulation scheme offers a novel concept and engineering route to manipulate the OAM spectrum in wide bandwidth, which can promote the development of OAM‐based applications. [ABSTRACT FROM AUTHOR]

Summary: Nowadays, the wireless communication is improved in numerous ranges, and the use of the high speed of data rate in the communication systems is needed. The standing problem of high‐performance planar antenna is reduced by the recently developed artificial dielectric called photonic crystal, which is used to control and manipulate the optical property of light. This paper addresses the slotted tube antenna structure, and the investigation is done by the concept of triangular lattice structure based on the photonic crystal. This utility enhances the return loss of −57.81 dB and the voltage standing wave ratio (VSWR) of 1.002 at 2.37 THz operating frequencies. The increase in hole radius provides the shifting in zero dispersion point towards the shorter wavelength that helps for faster data rate transmission applications. Further, to characterize the model of the proposed antenna, the optimal value of the air hole, lattice constant value between holes and the thickness of the slot are found and the related parameters of such antenna are studied with the support of simulation software CST microwave studio. [ABSTRACT FROM AUTHOR]