Quadrupole Research Articles

Quadrupole partial orders and triple-q states on the face-centered cubic lattice

We study ${\mathrm{\ensuremath{\Gamma}}}_{3}$ quadrupole orders in a face-centered cubic lattice. The ${\mathrm{\ensuremath{\Gamma}}}_{3}$ quadrupole moments under cubic symmetry possess a unique cubic invariant in their free energy in the uniform ($\mathbf{q}=\mathbit{0}$) sector and the triple-$\mathbf{q}$ sector for the $X$ points $\mathbf{q}=(2\ensuremath{\pi},0,0),(0,2\ensuremath{\pi},0)$, and $(0,0,2\ensuremath{\pi})$. Competition between this cubic anisotropy and anisotropic quadrupole-quadrupole interactions causes a drastic impact on the phase diagram both in the ground state and at finite temperatures. We show details about the model construction and its properties, the phase diagram, and the mechanism of the various triple-$\mathbf{q}$ quadrupole orders reported in our preceding letter [J. Phys. Soc. Jpn. 90, 043701 (2021)]. By using a mean-field approach, we analyze a quadrupole exchange model that consists of a crystalline-electric field scheme with the ground-state ${\mathrm{\ensuremath{\Gamma}}}_{3}$ non-Kramers doublet and the excited singlet ${\mathrm{\ensuremath{\Gamma}}}_{1}$ state. We have found various triple-$\mathbf{q}$ orders in the four-sublattice mean-field approximation. A few partially ordered phases are stabilized in a wide range of parameter space and they have a higher transition temperature than single-$\mathbf{q}$ orders. With lowering temperature, there occur transitions from these partially ordered phases into further symmetry broken phases in which previously disordered sites acquire nonvanishing quadrupole moments. The identified phases in the mean-field approximation are further analyzed by a phenomenological Landau theory. This analysis reveals results qualitatively consistent with the mean-field results and also shows that the cubic invariant plays an important role for stabilizing the triple-$\mathbf{q}$ states. The present mechanism for the triple-$\mathbf{q}$ states also takes effect in systems with different types of quadrupoles, and we discuss its implications for recent experiments in a few $f$- and $d$-electron compounds.

Measurements of the L-shell X-ray emission of fluorine-like europium

Measurements of the L-shell X-ray emission of fluorine-like europium ions (Eu54+) were made under controlled laboratory conditions on the EBIT-I electron beam ion trap at Livermore using an X-ray calorimeter, extending such measurements to the middle of the rare earth elements. Comparing the calorimeter spectra with atomic data from the flexible atomic code, we have identified and analyzed several prominent n = 3 → n = 2 transitions, including one two-electron, one-photon core changing transition and one electric quadrupole transition. We find that the measured energies are typically up to several eV higher than predicted.

Cubic water clusters as building blocks for self-assembly

The processes of self-organization in a system of cubic water clusters of D2d and S4 symmetry are studied. In the course of modeling, using the AMOEBA force field, a tendency to the formation of ice nanotubes and spatial nanostructures formed by tubular fragments is found. It was established that the quadrupole moments of the cubic isomers D2d and S4 are linear. However, the quadrupole–quadrupole interaction becomes decisive only at a great distance. It is very small in magnitude and therefore of little use. The structure of ice nanotubes obtained by combining D2d and S4 isomers has been studied. It is shown that these nanotubes significantly exceed all other configurations of square ice nanotubes in the stabilization energy. An atlas of the most probable structures with the number of cubes from 2 to 4 is presented. The methods of joining nanotubes and some peculiarities of their growth are discussed.

Study of S, Cl and Ar isotopes with $$N \ge Z$$ using microscopic effective sd-shell interactions

In the present work, newly developed microscopic effective $sd$-valence shell interactions such as chiral next-to-next-to-next-to-leading order (N3LO), $J$-matrix inverse scattering potential (JISP16), Daejeon16 (DJ16), and monopole-modified DJ16 (DJ16A) are employed to study the nuclear structural properties of sulphur, chlorine, and argon isotopes with $N \geq Z$. These interactions are derived using the \textit{ab initio} no-core shell-model and the OLS unitary transformation method. We calculate energy spectra and electromagnetic properties to test the predictive strength of the effective interactions for these heavier $sd$-shell nuclei. For a complete systematic study, we compare the microscopic results with the phenomenological USDB results and experimental data. By looking at the excitation energies of these nuclei, the DJ16A interaction is found to be {the} most suitable for these $sd$-shell nuclei among all microscopic interactions. The electric quadrupole transition strength and excitation energy of the first $2^+$ state data of even-even sulphur isotopes indicate the presence of the $N=20$ shell closure. Quadrupole moment predictions are also made using these interactions where experimental data are unknown. Magnetic moments are in excellent agreement with the experimental values. The root-mean-square deviations are also calculated to provide an idea of how accurate the interactions are.

Analysis of super-deformed bands in A∼150 mass region: The principal-axis cranking versus the variable moment of inertia

A systematic study of the super-deformed (SD) bands in [Formula: see text] mass region is carried out by using two different approaches, namely, the Principal-axis Cranking (PAC) and the Variable Moment of Inertia (VMI). Both these approaches not only support each other’s results but also their hand-in-hand calculations help us in establishing the prominent features, like the band-head spin, parity, quadrupole moment and excitation energy, of the observed SD bands. Since the rotational frequency in the PAC model depends on angular momentum, parity, and quadrupole moment, by identifying the most common rotational frequency between the calculations and the experimentally observed ones, the band-head spin, and parity are likely to be extracted. On the other hand, the VMI model calculations are quite simple and are capable of predicting the threshold limits of band-head spin, the quadrupole moment, and the excitation energy, which in turn are significantly useful for deciding an appropriate configuration assignment in the PAC model calculations of the existing as well as upcoming SD bands. Further, the VMI model calculations involve the variation of the moment of inertia with angular momentum, which in turn is quite helpful in understanding the mechanism of the observed identical SD bands between a pair of neighboring nuclei.

Influence of molecular anisotropy and quadrupolar moment on evaporation

The molecular interactions of numerous real fluids, like argon, nitrogen, or carbon dioxide, are adequately described by the two-center Lennard-Jones plus quadrupole potential. Applying this model class in molecular dynamics simulations, evaporation is investigated systematically. The influence of the molecular anisotropy and quadrupole as well as the boundary conditions, i.e., bulk liquid temperature and evaporation magnitude, is reported. A method for specifying the evaporation magnitude in terms of hydrodynamic velocity is further developed for that purpose. Analyses show that the largest molar flux and energy flux occur for spherical molecules and that anisotropy and quadrupole influence several quantities. Depending on the bulk liquid temperature, the quadrupole predominantly affects the interface temperature, while the anisotropy of the molecule significantly influences the interface temperature as well as both molar and energy fluxes. In addition, the preferred average orientation of the molecules in the interface region is investigated. The evaporation coefficient is determined, and thermodynamic states traversed during the evaporation process are discussed.

Strain-induced magnetic anisotropy in Heusler alloys studied from first principles

We report the microscopic origin of strain-mediated changes in the magnetocrystalline anisotropy energy of the Co2FeSi, Co2MnSi, and Fe3Si Heusler alloys from the viewpoint of first-principles electron theory. Both Co2FeSi and Co2MnSi have similar anisotropy changes upon induced strain within the (001) plane, where the quadrupole moment due to Co minority-spin states dominates the anisotropy modulation, and, thus, giant magnetoelectric couplings in multiferroic heterointerfaces containing these compounds. In contrast, the strain-induced anisotropy modulation in Fe3Si has mixed contributing factors not limited to the anisotropy term of the orbital magnetic moment and the quadrupole term.

Persistent currents, revival time and effects of rotation on an attractive inverse-square-type potential in a magnetic quadrupole moment system

We study the appearance of an Aharonov–Bohm-type effect around a cylindrical cavity in a magnetic quadrupole moment system in a rotating reference frame. The analogue of the Aharonov–Bohm-type effect of bound states arises from the interaction of the magnetic quadrupole moment of a neutral particle with an induced electric field when the neutral particle is subject to an attractive inverse-square-type potential, which in turn stems from the interaction of the magnetic quadrupole moment of a neutral particle with a magnetic field. We also discuss how the effects of rotation modify the degeneracy of the energy levels in contrast to the case of absence of rotation. Besides this, we calculate the revival time and the persistent currents.

All-dielectric metasurface based ultranarrow bandpass filter in optical C-band

Metasurface-based nanophotonics devices can potentially replace traditional bulky optical components such as optical filters, modulators, and switches. In this study, we report a dielectric metasurface-based ultranarrow bandpass filter operating at 1549.8 nm with the ability to tune the central wavelength within the C-band. The proposed tunable filter consists of a 2D periodic array of gallium arsenide blocks placed on top of a quartz substrate. The introduction of a symmetry-breaking defect results in an ultranarrow resonance with an FWHM of 0.31 nm at a 1549.8 nm wavelength when a TE-polarized wave is normally incident. The sharp, high Q factor resonance is understood to be governed by the symmetry-protected bound state in the continuum. The resonant response can be tuned by changing the periodicity, thickness, and asymmetry of the metasurface constituents. The multipolar analysis indicates the excitation of the electric quadrupole mode at the resonance wavelength. Our findings can be useful for the design of compact tunable ultranarrow bandpass filters for optical communications systems.

Axial and triaxial degrees of freedom in 72Zn

The unstable N=42 nucleus 72Zn has been studied using multiple safe Coulomb excitation in inverse kinematics. The experiment was performed at the REX-ISOLDE facility at CERN making first use of the silicon detector array C-REX in combination with the γ-ray spectrometer Miniball. The high angular coverage of C-REX allowed to determine the reduced transition strengths for the decay of the yrast 01+, 21+ and 41+ as well as of the 02+ and 22+ states in 72Zn. The quadrupole moments of the 21+, 41+ and 22+ states were extracted. Using model independent quadrupole invariants, the ground state of 72Zn was found to have an average deformation in the γ degree of freedom close to maximum triaxiality. In comparison to experimental data in zinc isotopes with N<40, the collectivity of the 41+ state in neutron-rich 72Zn is significantly larger, indicating a collective yrast band based on the ground state of 72Zn. In contrast, a low experimental B(E2;02+→21+) strength was determined, indicating a different structure for the 02+ state. Shell-model calculations propose a 02+ state featuring a larger fraction of the (spherical) N=40 closed-shell configuration in its wave function than for the 01+ ground state.The results were also compared with beyond mean field calculations which corroborate the large deformation in the γ degree of freedom, while pointing to a more deformed 02+ state. These experimental and theoretical findings establish the importance of the γ degree of freedom in the ground state of 72Zn, located between the 68,70Ni nuclei that have spherical ground states, and 76Ge, which has a rigid triaxial shape.

Cold Ion-Molecule Chemistry: The Very Different Reactions of He⁺ with CO and NO.

The ion-molecule reactions He+ + CO → He + C+ + O and He+ + NO → He + N+ + O have been measured at collision energies between 0 and kB · 10 K. Strong variations of the rate coefficients are observed below kB · 5 K. The rate of the He+ + CO reaction decreases by ~30% whereas that of the He+ + NO reaction increases by a factor of ~1.5. These observations are interpreted in the realm of an adiabatic-channel capture model as arising from interactions between the ion charge and the dipole and quadrupole moments of CO and NO. We show that the different low-energy behavior of these reactions originates from the closed- vs. open-shell electronic structures of CO and NO.

Electromagnetic scattering by arbitrary-shaped magnetic particles and multipole decomposition: Analytical and numerical approaches

We develop a theoretical approach that makes it possible to analyze the role of multipole contributions in the scattering spectra of arbitrarily shaped magnetic particles with the relative permittivity and permeability given in a general tensor-valued form. The method for calculating the exact multipole moments with the inclusion of induced electric polarization and magnetization is suggested and explicitly applied for dipole and quadrupole terms. The final expressions for the dipole and quadrupole moments are obtained in such a form that they can be easily implemented in numerical solvers. Successful verification of the analytical expressions for multipole moments and the multipole decomposition of the scattered field and scattering cross section is provided by comparing the results obtained for differently shaped magnetic particles using the analytical Mie theory, numerical discrete dipole approximation, and comsol multiphysics software. As a particular example, the manifestation of the Faraday effect for fields scattered by a ferrite sphere is discussed in the framework of the multipole decomposition method with the derived magnetization terms. Accounting for the magnetic properties of particles in the multipole analysis of the electromagnetic scattering significantly expands the method's capabilities for studying and modeling metamaterial properties in the spectral ranges where natural materials can have a relative permeability different from unity.

Multipole mixing effects on the angular distribution and polarization of dielectronic hypersatellite lines from highly charged helium-like ions

The angular distribution and the degree of linear polarization of the dielectronic hypersatellite lines of highly charged helium-like ions are studied by using the multiconfiguration Dirac-Fock method and density matrix theory with a focus on the multipole mixing effects. Detailed calculations have been carried out for the emission of characteristic X-rays from the (2s2p)P1,23 and P11 resonant states decay to the (1s2s)S13 state following the KLL dielectronic recombination of initial hydrogen-like ions with atomic nuclear charge from Z=22 to Z=100. It is shown that the mixing of electric dipole (E1) and magnetic quadrupole (M2) radiations significantly alters the angular distribution and the degree of linear polarization, in which the shifts are dependent on the resonant capture states and the atomic nuclear charges. The E1+M2 mixing has opposite effects for the (2s2p)P23 and (2s2p)P11 resonant states, except for the (2s2p)P11 resonance of the heavy ions with Z≳90, where the profile of angular distribution is reversed by strong mixing effects due to the contribution of the M2 term and its interference with the E1 radiative channel. The results should be of particular interest to the diagnosis of anisotropic plasmas and the test of fundamental physics in few-electron heavy ions.

Ion Bridging by Carbon Dioxide Facilitates Electrochemical Energy Storage at Charged Carbon–Ionic–Liquid Interfaces

AbstractSolvent free ionic liquid (IL) electrolytes facilitate high‐voltage supercapacitors with enhanced energy density, but their complex ion arrangement and through that the electrochemical properties, are limited by strong Coulombic ordering in the bulk state and like‐charged ion repulsion at electrified interfaces. Herein, a unique interfacial phenomenon resulting from the presence of carbon dioxide loaded in 1‐Ethyl‐3‐methylimidazoliumtetrafluorborate electrolyte that simultaneously couples to IL ions and nitrogen‐doped carbonaceous electrode is reported. The adsorbed CO2 molecule polarizes and mitigates the electrostatic repulsion among like‐charged ions near the electrified interface, leading to an ion “bridge effect” with increased interfacial ionic density and significantly enhanced charge storage capability. The unpolarized CO2 possessing a large quadrupole moment further reduces ion coupling, resulting in higher conductivity of the bulk IL and improved rate capability of the supercapacitor. This work demonstrates polarization‐controlled like‐charge attraction at IL–electrode–gas three‐phase boundaries, providing insights into manipulating complex interfacial ion ordering with small polar molecule mediators.

Multipole Excitations and Nonlocality in 1d Plasmonic Nanostructures.

Efficient simulation methods for taking nonlocal effects in nanostructures into account have been developed, but they are usually computationally expensive or provide little insight into underlying physics. A multipolar expansion approach, among others, holds promise to properly describe electromagnetic interactions in complex nanosystems. Conventionally, the electric dipole dominates in plasmonic nanostructures, while higher order multipoles, especially the magnetic dipole, electric quadrupole, magnetic quadrupole, and electric octopole, can be responsible for many optical phenomena. The higher order multipoles not only result in specific optical resonances, but they are also involved in the cross-multipole coupling, thus giving rise to new effects. In this work, we introduce a simple yet accurate simulation modeling technique, based on the transfer-matrix method, to compute higher-order nonlocal corrections to the effective permittivity of 1d plasmonic periodic nanostructures. In particular, we show how to specify the material parameters and the arrangement of the nanolayers in order to maximize or minimize various nonlocal corrections. The obtained results provide a framework for guiding and interpreting experiments, as well as for designing metamaterials with desired dielectric and optical properties.

Eu2+/Ce3+-doped NaAlSiO4 selective occupation-induced emission structure unit evolution and its luminescence characteristics

NaAlSiO4: xEu2+,yCe3+ blue-red phosphors were prepared by high-temperature melting-icy quenching-heat treatment. The effects of emission structure unit evolution, microstrain, microcrystalline size and selective occupation on the luminescence characteristics of the prepared phosphor were systematically studied by powder X-ray diffraction pattern (XRD) and photoluminescence spectroscopy (PL). In the structure of NaAlSiO4: 2%Eu2+, 2%Ce3+ hexagonal crystalline sodium nepheline, Eu2+ ions occupy the Na+ (II) position to form a EuNa+(II)2+ luminescent structure unit, and Ce3+ ions occupy the Na+ (I) position to form a CeNa+(I)3+ luminescent structure unit. The NaAlSiO4: 2%Eu2+/NaAlSiO4: 2%Ce3+ emits 555 nm yellow-green light/395 nm blue-violet light under the excitation of 354 nm/298 nm, respectively, which is derived from the 5d-4f transition of Eu2+ and Ce3+. There is energy transfer of Ce3+→Eu2+ in the sodium nepheline matrix, of which the transport pathway is m EuNa+(II)2+ ←O←n CeNa+(I)3+ →O→m EuNa+(II)2+, and the transport mechanism is electric quadrode-electric quadrupole interaction, and the energy transfer efficiency reaches 98.6%. The sodium nepheline NaAlSiO4: 2%Eu2+, 2%Ce3+ phosphor with energy level barrier 0.386 eV, possesses good thermal stability. This single-phase aluminosilicate multicolor phosphor has potential application value for WLED illumination and PDP display.

Dynamically generated quadrupole polarization using Floquet adiabatic evolution

We investigate the nonequilibrium dynamics of the $S=1$ quantum spin chain subjected to a time-dependent external drive, where the driving frequency is adiabatically decreased as a function of time (``Floquet adiabatic evolution''). We show that when driving the rhombic anisotropy term (known as the ``two-axis countertwisting'' in the context of squeezed spin states) of a N\'eel antiferromagnet, we are able to induce an overall enhancement in the quadrupole polarization, while at the same time suppressing the staggered magnetization order. The system evolves into a new state with a net quadrupole moment and antiferroquadrupolar correlations. This state remains stable at long times once the driving frequency is kept constant. On the other hand, we find that we cannot achieve a quadrupole polarization for the symmetry-protected Haldane phase, which remains robust against such driving.

Engineered pseudo and hybrid anapole states in a silicon nanoresonator metasurface

Significant attention has been devoted to realizing non-radiating states (popularly known as anapole states) in several systems due to the strong localization of electromagnetic fields, which can be attained through destructive interference of various dipole moments, yielding fundamental or higher-order anapole states. Recently, it has been shown that the interference of higher-order excitation also permits light manipulation at the nanoscale and provides additional benefits such as efficient power transfer and enhancement in nonlinearities. In this work, we report discrete electric anapole (pseudo and hybrid) by careful design of an all-dielectric metasurface consisting of a silicon nanodisk such that a higher-order toroidal electric dipole (TD) and quadrupole interfere destructively, producing a hybrid anapole at 815 nm, whereas the pseudo anapole is generated when TD and second-order TD minima occur at the same wavelength of 522 nm. The phase plots confirm the findings of these radiationless states. Such dual and distinct non-radiating current configurations may find applications in spectroscopy, sensing, switching, optical nonlinearity, and optomechanics.

Molecular orientation-dependent energetic shifts in solution-processed non-fullerene acceptors and their impact on organic photovoltaic performance

The non-fullerene acceptors (NFAs) employed in state-of-art organic photovoltaics (OPVs) often exhibit strong quadrupole moments which can strongly impact on material energetics. Herein, we show that changing the orientation of Y6, a prototypical NFA, from face-on to more edge-on by using different processing solvents causes a significant energetic shift of up to 210 meV. The impact of this energetic shift on OPV performance is investigated in both bilayer and bulk-heterojunction (BHJ) devices with PM6 polymer donor. The device electronic bandgap and the rate of non-geminate recombination are found to depend on the Y6 orientation in both bilayer and BHJ devices, attributed to the quadrupole moment-induced band bending. Analogous energetic shifts are also observed in other common polymer/NFA blends, which correlates well with NFA quadrupole moments. This work demonstrates the key impact of NFA quadruple moments and molecular orientation on material energetics and thereby on the efficiency of high-performance OPVs.

Modeling horizon absorption in spinning binary black holes using effective worldline theory

The mass and spin of black holes (BHs) in binary systems may change due to the infall of gravitational-wave (GW) energy down the horizons. For spinning BHs, this effect enters at 2.5 post-Newtonian (PN) order relative to the leading-order energy flux at infinity. There is currently a discrepancy in the literature in the expressions of these horizon fluxes in the test-body limit at 4PN order (relative 1.5PN order). Here, we model the horizon absorption as tidal heating in an effective worldline theory of a spinning particle equipped with tidally-induced quadrupole and octupole moments. We match the tidal response to analytic solutions of the Teukolsky equation in a scattering scenario, and obtain general formulae for the evolution of mass and spin. We then specialize to the case of aligned-spin--quasi-circular binaries, obtaining the corresponding contributions to the GW phasing through 4PN order. Importantly, we find that the number of GW cycles due to horizon fluxes with masses observed by LIGO-Virgo-KAGRA detectors is about 2-3 orders of magnitude smaller than the other contributions to the phasing at the same PN order. Furthermore, in the test-body limit, we find full agreement with results obtained earlier from BH perturbation theory, with a small mass in an equatorial circular orbit treated as a source perturbing the Kerr metric. Thus, we weigh in on one side of the previous discrepancy.