Search NASA⌕ Search

SEARCH · Search NASA

Results for “Geometric frustration”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Geometric frustration in the myosin superlattice of vertebrate muscle

Geometric frustration results from an incompatibility between minimum energy arrangements and the geometry of a system, and gives rise to interesting and novel phenomena. Here, we report geometric frustration in a native biological macromolecular system---vertebrate muscle. We analyse the disorder in the myosin filament rotations in the myofibrils of vertebrate striated (skeletal and cardiac) muscle, as seen in thin-section electron micrographs, and show that the distribution of rotations corresponds to an archetypical geometrically frustrated system---the triangular Ising antiferromagnet. Spatial correlations are evident out to at least six lattice spacings. The results demonstrate that geometric frustration can drive the development of structure in complex biological systems, and may have implications for the nature of the actin--myosin interactions involved in muscle contraction. Identification of the distribution of myosin filament rotations with an Ising model allows the extensive results on the latter to be applied to this system. It shows how local interactions (between adjacent myosin filaments) can determine long-range order and, conversely, how observations of long-range order (such as patterns seen in electron micrographs) can be used to estimate the energetics of these local interactions. Furthermore, since diffraction by a disordered system is a function of the second-order statistics, the derived correlations allow more accurate diffraction calculations, which can aid in interpretation of X-ray diffraction data from muscle specimens for structural analysis.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Non-equilibrium dynamics in geometrically frustrated spin glass Bi 2 Fe 3 GaO 9 with a Cairo lattice

We have explored the magnetic relaxation of the spin glass phase in Bi 2 Fe 3 GaO 9 , a geometrically frustrated magnet with a unique Cairo lattice made of pentagonal building blocks. Using dc magnetization measurements, we find the relaxation behavior in single crystals follows the Arrhenius law as a function of temperature but remains relatively constant under different magnetic fields. Through a carefully designed protocol, we observe significant rejuvenation and memory effects, reminiscent of classical dilute spin glasses rather than spin jamming systems. Our finding suggests that Bi 2 Fe 3 GaO 9 is probably located in the crossover between conventional spin glass and perfect spin jam and thus provides an excellent platform for investigating the evolution of underlying magnetic structure, paving the way for further neutron scattering research.

aging↗
DOE OSTI2023

Helfrich-Hurault elastic instabilities driven by geometrical frustration

Here, the Helfrich-Hurault (HH) elastic instability is a well-known mechanism behind patterns that form as a result of strain upon liquid crystal systems with periodic ground states. In the HH model, layered structures undulate and buckle in response to local, geometric incompatibilities in order to maintain the preferred layer spacing. Classic HH systems include cholesteric liquid crystals under electromagnetic field distortions and smectic liquid crystals under mechanical strains, where both materials are confined between rigid substrates. However, richer phenomena are observed when undulation instabilities occur in the presence of deformable interfaces and variable boundary conditions. Understanding how the HH instability is affected by deformable surfaces is imperative for applying the instability to a broader range of materials. In this review, the HH mechanism is reexamined and special focus is given to how the boundary conditions influence the response of lamellar systems to geometrical frustration. Lamellar liquid crystals confined within a spherical shell geometry are used as the model system. Made possible by the relatively recent advances in microfluidics within the past 15 years, liquid crystal shells are composed entirely of fluid interfaces and have boundary conditions that can be dynamically controlled at will. Past and recent work that exemplifies how topological constraints, molecular anchoring conditions, and boundary curvature can trigger the HH mechanism in liquid crystals with periodic ground states is examined. The review ends by identifying similar phenomena across a wide variety of materials, both biological and synthetic. The fact that the HH mechanism is a generic and often overlooked response of periodic materials to geometrical frustration is highlighted.

42 ENGINEERING↗
DOE OSTI2020

Nanoscale degeneracy lifting in a geometrically frustrated antiferromagnet

The local atomic and magnetic structures of the compounds A MnO 2 (A = Na, Cu), which realize a geometrically frustrated, spatially anisotropic triangular lattice of Mn spins, have been investigated by atomic and magnetic pair distribution function analysis of neutron total scattering data. Relief of frustration in CuMnO 2 is accompanied by a conventional cooperative symmetry-lowering lattice distortion driven by Néel order. In NaMnO 2 , however, the distortion has a short-range nature. A cooperative interaction between the locally broken symmetry and short-range magnetic correlations lifts the magnetic degeneracy on a nanometer length scale, enabling long-range magnetic order in the Na derivative. The degree of frustration, mediated by residual disorder, contributes to the rather differing pathways to a single, stable magnetic ground state in these two related compounds. This study demonstrates how nanoscale structural distortions that cause local-scale perturbations can lift the ground-state degeneracy and trigger macroscopic magnetic order.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Geometric frustration of Jahn–Teller order in the infinite-layer lattice

The Jahn–Teller effect, in which electronic configurations with energetically degenerate orbitals induce lattice distortions to lift this degeneracy, has a key role in many symmetry-lowering crystal deformations. Lattices of Jahn–Teller ions can induce a cooperative distortion, as exemplified by LaMnO 3 . Although many examples occur in octahedrally or tetrahedrally coordinated transition metal oxides due to their high orbital degeneracy, this effect has yet to be manifested for square-planar anion coordination, as found in infinite-layer copper, nickel, iron and manganese oxides. Here, for this work, we synthesize single-crystal CaCoO 2 thin films by topotactic reduction of the brownmillerite CaCoO 2.5 phase. We observe a markedly distorted infinite-layer structure, with ångström-scale displacements of the cations from their high-symmetry positions. This can be understood to originate from the Jahn–Teller degeneracy of the d xz and d yz orbitals in the d 7 electronic configuration along with substantial ligand–transition metal mixing. A complex pattern of distortions arises in a $2\sqrt2$ x $2\sqrt2$ x $1$ tetragonal supercell, reflecting the competition between an ordered Jahn–Teller effect on the CoO 2 sublattice and the geometric frustration of the associated displacements of the Ca sublattice, which are strongly coupled in the absence of apical oxygen. As a result of this competition, the CaCoO 2 structure forms an extended two-in–two-out type of Co distortion following ‘ice rules’.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Interwoven magnetic kagome metal overcomes geometric frustration

Magnetic kagome materials provide a platform for exploring magneto-transport phenomena, symmetry breaking and charge ordering driven by the intricate interplay among electronic structure, topology and magnetism. Yet geometric frustration in conventional kagome magnets limits their tunability. Here we propose a design strategy for interweaving quasi-one-dimensional magnetic Tb zigzag chains with non-magnetic Ti-based kagome bilayers in TbTi 3 Bi 4 . Comprehensive spectroscopic analyses reveal coexisting elliptical-spiral magnetic and spin-density-wave orders accompanied by a large ~90 meV band-folding gap. The combined magnetic and electronic state leads to a giant anomalous Hall conductivity of 10 5 Ω −1 cm −1 , which exceeds that observed in frustrated kagome analogues. These results establish TbTi 3 Bi 4 as a model system of magnetic kagome metals with strong electron–magnetism interactions and underscore the necessity of interweaving designed magnetic and charge layers separately to achieve tunable transport properties. This design strategy will enable the discovery of emergent quantum states and next-generation electronic materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Geometric Frustration on the Trillium Lattice in a Magnetic Metal-Organic Framework

In the dense metal-organic framework Na [ Mn ( HCOO ) 3 ] , Mn 2 + ions ( S = 5 2 ) occupy the nodes of a “trillium” net. In this work, we show that the system is strongly magnetically frustrated: the Néel transition is suppressed well below the characteristic magnetic interaction strength; short-range magnetic order persists far above the Néel temperature; and the magnetic susceptibility exhibits a pseudo-plateau at 1 3 -saturation magnetization. A simple model of nearest-neighbor Heisenberg antiferromagnetic and dipolar interactions accounts quantitatively for all observations, including an unusual 2- k magnetic ground state. We show that the relative strength of dipolar interactions is crucial to selecting this particular ground state. Geometric frustration within the classical spin liquid regime gives rise to a large magnetocaloric response at low applied fields that is degraded in powder samples as a consequence of the anisotropy of dipolar interactions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Geometrically frustrated interactions drive structural complexity in amorphous calcium carbonate

Amorphous calcium carbonate is an important precursor for biomineralization in marine organisms. Key outstanding problems include understanding the structure of amorphous calcium carbonate and rationalizing its metastability as an amorphous phase. Here we report high-quality atomistic models of amorphous calcium carbonate generated using state-of-the-art interatomic potentials to help guide fits to X-ray total scattering data. Exploiting a recently developed inversion approach, we extract from these models the effective Ca∙∙∙Ca interaction potential governing the structure. This potential contains minima at two competing distances, corresponding to the two different ways that carbonate ions bridge Ca 2+ -ion pairs. We reveal an unexpected mapping to the Lennard-Jones–Gauss model normally studied in the context of computational soft matter. The empirical model parameters for amorphous calcium carbonate take values known to promote structural complexity. We thus show that both the complex structure and its resilience to crystallization are actually encoded in the geometrically frustrated effective interactions between Ca 2+ ions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Magnetic and quadrupole coupling emerging in NdB 4 with geometrically frustrated orthogonal antiferromagnetic dimer

Unusual successive order in NdB 4 with the frustrated Shastry-Sutherland lattice was investigated by means of inelastic neutron scattering. Here, we found that the pseudoquartet with |±5/2⟩ and |±7/2⟩ in the paramagnetic state splits into four levels in the magnetically ordered states. The observed spectra are in good agreement with the 𝑓-electron states obtained from the on-site Hamiltonian with the magnetic interaction ⟨𝐽 𝑥 ⟩ ⁢𝐽 𝑥 , the coupling of 𝐽 𝑥 with quadrupole 𝑂 𝑧⁢𝑥 , and the crystalline electric field potential. The 𝑓-electron states reproduce the temperature dependences of the in-plane moment 𝑚 ⊥ = ⟨𝐽 𝑥 ⟩, which is the primary order parameter, and a weakly induced 𝑚 𝑐 = ⟨𝐽 𝑧 ⟩ as the secondary order parameter. The magnetic-quadrupole coupling emerges and plays an essential role under the geometrical frustration, where the Heisenberg interactions are canceled out.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Cuboidal Liquid Crystal Phases Under Multiaxial Geometrical Frustration.

Cuboidal liquid crystal phases - the so-called blue phases - consist of a network of topological defects arranged into a cubic symmetry. They exhibit striking optical properties, including Bragg reflection in the visible range and fast response times. Confining surfaces can interfere with the packing of such a network, leading to structures that have not been explored before. In this work, a Landau-de Gennes free energy formalism for the tensor alignment field Q is used to investigate the behavior of chiral liquid crystals under non-isotropic confinement. The underlying free energy functional is solved by relying on a Monte Carlo method that facilitates efficient exploration of configuration space. The results of simulations are expressed in terms of phase diagrams as a function of chirality and temperature for three families of spheroids: oblate, spherical, and prolate. Upon deformation, blue phases adapt and transform to accommodate the geometrical constraints, thereby resulting in a wider range of thermal stability. For oblate spheroids, confinement interferes with the development of a full blue phase structure, resulting on a combination of half skyrmions. For prolate spheroids, the blue phases are hybridized and exhibit features of blue phases I and II. More generally, it is shown that mechanical deformation provides an effective means to control, manipulate and stabilize blue phases and cholesterics confined in tactoids.

Palacio-Betancur, Viviana↗
DOE OSTI2021

Geometrical Frustration and Defect Formation in Growth of Colloidal Nanoparticle Crystals on a Cylinder: Implications for Assembly of Chiral Nanomaterials

Using a combination of experiment and simulation, we study how two-dimensional (2D) crystals of colloidal nanoparticles grow on cylindrical substrates. The cylindrical geometry allows us to examine growth in the absence of Gaussian curvature but in the presence of a closure constraint - the requirement that a crystal loops back onto itself. In some cases, this constraint results in structures that have been observed previously in theory and nonequilibrium packing experiments: chiral crystals and crystals with linear defects known as "line slips". More generally, though, the structures we see differ from those that have been observed: the line slips are kinked and contain partial vacancies. We show that these structures arise because the cylinder changes how the crystal grows. After a crystal wraps around the cylinder and touches itself, it must grow preferentially along the cylinder axis. As a result, crystals with a chiral line slip tend to trap partial vacancies. Indeed, we find that line slips that are less aligned with the cylinder axis incorporate more partial vacancies on average than the ones that are more aligned. Here, these results show that crystal growth on a cylinder is frustrated by the closure requirement, a finding that may shed some light on the assembly of biological nanosystems such as tobacco mosaic virus and might inform ways to fabricate chiral optical nanomaterials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Geometrical frustration versus Kitaev interactions in BaCo 2 (AsO 4 ) 2

Recently, Co-based honeycomb magnets have been proposed as promising candidate materials to host the Kitaev spin liquid (KSL) state. One of the front-runners is BaCo 2 (AsO 4 ) 2 (BCAO), where it was suggested that the exchange processes between Co 2+ ions via the surrounding edge-sharing oxygen octahedra could give rise to bond-dependent Kitaev interactions. In this work, we present and analyze a comprehensive inelastic neutron scattering (INS) study of BCAO with fields in the honeycomb plane. Combining the constraints from the magnon excitations in the high-field polarized state and the inelastic spin structure factor measured in zero magnetic field, we examine two leading theoretical models: the Kitaev-type JK Γ Γ ′ model and the XXZ - J 1 - J 3 model. We show that the existing experimental data can be consistently accounted for by the XXZ - J 1 - J 3 model but not by the JK Γ Γ ′ model, and we discuss the implications of these results for the realization of a spin liquid phase in BCAO and more generally for the realization of the Kitaev model in cobaltates.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Geometrical frustration and competing orders in the dipolar trimerized triangular lattice

Here, we introduce and explore low-energy configurations in two-dimensional arrays consisting of Ising-type dipolar coupled nanomagnets lithographically defined onto three-nanomagnet vertices arranged in a triangular coordination. Thus, the system is dubbed the trimerized triangular lattice. Employing synchrotron-based photoemission electron microscopy, we perform temperature-dependent magnetic imaging of moment configurations. These states are then characterized in terms of spin correlations and magnetic structure factors. The results reveal a competition between ferromagnetic and vortex dominated orders, which can be controlled by varying the relevant lattice parameter and the corresponding competing interactions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Ground-state degeneracy and complex magnetism of geometrically frustrated Gd 2 Ir 0.97 Si 2.97

We report a new triangular-lattice intermetallic compound Gd 2 Ir 0.97 Si 2.97 was successfully synthesized as single phase by deliberately introducing vacancies. Theoretical analysis suggests that the ground state is competing with several low-energy spin configurations due to magnetic frustration on a nearly ideal triangular lattice. Despite a number of competing magnetic states, the compound exhibits long-range antiferromagnetic order at16K, a long-range ferrimagnetic transition at 6.5 K, and a reentrant cluster-glass transition below T f ~ 3K. The complex magnetism in the compound could be correlated with competing antiferromagnetic and ferrimagnetic structures predicted theoretically.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗