Antisymmetrization Effects Research Articles

Experimental Evidence of the Molecular and Macroscopic Origins of Circular Dichroism in Chiral Metal‐Halide Networks

AbstractClockwise or counter‐clockwise spin coating? In the current hot research topic of chiral metal‐halide semiconductors, several investigations have been undertaken in order to reveal their natural optical activity and have reported dissymmetry factors (gabs) for thin films of many hybrid compounds, usually without considering the macroscopic anisotropies inherent to solid‐state samples. Yet, CD in the solid state can be strongly modulated by the co‐existence of linear dichroism (LD) and linear birefringence (LB). Theoretical studies recently revealed the importance of such macroscopic interferences in the CD response of solid‐state samples, often referred as symmetric (sLDLB) and antisymmetric (aLDLB) effects. Based on the newly synthesized one‐dimensional lead‐halide networks of formula (S/R‐HP1A)PbBr3 and (S/R‐HP1A)PbI3, an experimental method to accurately discriminate between CD, sLDLB and aLDLB in chiral metal‐halide networks is here presented. The main experimental conditions influencing sLDLB and aLDLB amplitude are also highlighted, such as the concentration of the precursor solution and the spin‐coating rotation direction, finally providing a complete experimental guide for the forthcoming chiroptical investigations of such important family of chiral hybrid materials.

Exploring antisymmetric tensor effects on black hole shadows and quasinormal frequencies

This study explores the impact of antisymmetric tensor effects on spherically symmetric black holes, investigating photon spheres, shadows, emission rate and quasinormal frequencies in relation to a parameter which triggers the Lorentz symmetry breaking. We examine these configurations without and with the presence of a cosmological constant. In the first scenario, the Lorentz violation parameter, denoted as λ, plays a pivotal role in reducing both the photon sphere and the shadow radius, while also leading to a damping effect on quasinormal frequencies. Conversely, in the second scenario, as the values of the cosmological constant (Λ) increase, we observe an expansion in the shadow radius. Also, we provide the constraints of the shadows based on the analysis observational data obtained from the Event Horizon Telescope (EHT) focusing on Sagittarius A* shadow images. Additionally, with the increasing Λ, the associated gravitational wave frequencies exhibit reduced damping modes.

Multigap superconductivity in centrosymmetric and noncentrosymmetric rhenium-boron superconductors

We report a comprehensive study of the centrosymmetric Re$_3$B and noncentrosymmetric Re$_7$B$_3$ superconductors. At a macroscopic level, their bulk superconductivity (SC), with $T_c$ = 5.1 K (Re$_3$B) and 3.3 K (Re$_7$B$_3$), was characterized via electrical-resistivity, magnetization, and heat-capacity measurements, while their microscopic superconducting properties were investigated by means of muon-spin rotation/relaxation ($\mu$SR). In both Re$_3$B and Re$_7$B$_3$ the low-$T$ zero-field electronic specific heat and the superfluid density (determined via tranverse-field $\mu$SR) suggest a nodeless SC. Both compounds exhibit some features of multigap SC, as evidenced by temperature-dependent upper critical fields $H_\mathrm{c2}(T)$, as well as by electronic band-structure calculations. The absence of spontaneous magnetic fields below the onset of SC, as determined from zero-field $\mu$SR measurements, indicates a preserved time-reversal symmetry in the superconducting state of both Re$_3$B and Re$_7$B$_3$. Our results suggest that a lack of inversion symmetry and the accompanying antisymmetric spin-orbit coupling effects are not essential for the occurrence of multigap SC in these rhenium-boron compounds.

Dzyaloshinskii Interaction and Exchange-Relativistic Effects in Orthoferrites

We present an overview of the microscopic theory of the Dzyaloshinskii-Moriya (DM) coupling and related exchange-relativistic effects such as exchange anisotropy, electron-nuclear antisymmetric supertransferred hyperfine interactions, antisymmetric magnetogyrotropic effects, and antisymmetric magnetoelectric coupling in strongly correlated 3$d$ compounds focusing on orthoferrites RFeO$_3$ (R is a rare-earth ion or yttrium Y). % Particular emphasis will be placed on the role of crystal field effects, the sense and direction of the Dzyaloshinskii vector, its dependence on the superexchange bonding geometry, and other subtle features of exchange-relativistic effects. Most attention in the paper centers around the derivation of the Dzyaloshinskii vector, its value, orientation, and sense (sign) under different types of the (super)exchange interaction and crystal field. Microscopically derived expression for the dependence of the Dzyaloshinskii vector on the superexchange geometry allows one to find all the overt and hidden canting angles in orthoferrites RFeO$_3$ as well as corresponding contribution to magnetic anisotropy. Being based on the theoretical predictions regarding the sign of the Dzyaloshinskii vector we have predicted and study in detail a novel magnetic phenomenon, {\it weak ferrimagnetism} in mixed weak ferromagnets with competing signs of the Dzyaloshinskii vectors. The ligand NMR measurements in weak ferromagnets are shown to be an effective tool to inspect the effects of DM coupling in an external magnetic field. Along with orthoferrites RFeO$_3$ and weak ferrimagnets RFe$_{1-x}$Cr$_x$O$_3$, although to a lesser extent, we address such typical weak ferromagnets as $\alpha$-Fe$_2$O$_3$, FeBO$_3$, and FeF$_3$.

Analysis of scattering and breakup reactions of 12,14Be within the microscopic model of optical potential

Analysis of the differential cross sections of scattering of neutron-rich nuclei 12,14Be on 12C at 56 MeV/nucleon and on protons at energy near 700 MeV/nucleon is carried out within the microscopic model of optical potential (OP). The real part of the 12,14Be+12C OP is calculated by using the double-folding procedure accounting for the anti-symmetrization effects, while the imaginary part of OP is obtained in the framework of the high-energy approximation (HEA). As to the 12,14Be+p scattering at relativistic energies, calculations of the both real and imaginary OPs were made within the HEA approach. In this framework, the only free parameters of OP are the depths of its real and imaginary parts obtained by fittingto experimental data. The role of the 12,14Be density models is considered when reproducing the experimental data. A contribution of the inelastic channels with excitations of 2+ and 3− states in 12C when calculating the quasielastic cross sections is analysed. Also, the 14Be cluster model, in which this nucleus consists of a 2n-halo and the 12Be core, is applied to calculate the cross sections of diffraction breakup and stripping reactions in the 14Be+12C collisions at the energy of 56 MeV/nucleon. A good agreement of the theoretical results with the available experimental data of both scattering and breakup processes is obtained.

Resonant and scattering states in the α+α system from the nonlocalized cluster model

The non-localized cluster model provides a new perspective on nuclear cluster effects and has been applied successfully to study cluster structures in various bound states and quasi-bound states (i.e., long-lived resonant states). In this work, we extend the application scope of the non-localized cluster model further to resonant and scattering states. Following the $R$-matrix theory, the configuration space is divided into the interior and exterior regions by a large channel radius such that the nuclear forces and the antisymmetrization effects become negligible between clusters in the exterior region. In the interior region, the picture of non-localized clustering is realized mathematically by adopting the Brink-Tohsaki-Horiuchi-Schuck-R\"opke (Brink-THSR) wave functions as the bases to construct the interior wave functions. The Bloch-Schr\"odinger equation is used to match the interior wave functions continuously with the asymptotic boundary conditions of the resonant and scattering states at the channel radius, which leads eventually to solutions of the problem. As a first test of the formalism, the low-lying resonant states of ${}^{8}$Be and the phase shifts of the $\alpha+\alpha$ elastic scattering are studied. The numerical results agree well with the experimental data, which shows the validity of the theoretical framework.

Microscopic analysis of quasielastic scattering and breakup reactions of the neutron-rich nuclei Be12,14

A microscopic analysis of the optical potentials (OPs) and cross sections of quasielastic scattering of $^{12,14}$Be on $^{12}$C at 56 MeV/nucleon and on protons at energy near 700 MeV is carried out. For lower energy scattering the real part of the OP is calculated by using of double-folding procedure accounting for the anti-symmetrization effects, while the imaginary part is obtained on the base of the high-energy approximation (HEA). The HEA is also applied to the calculations of both real and imaginary OPs when solving the relativistic equation for the high-energy proton-nucleus elastic scattering. The neutron and proton density distributions computed in different microscopic models for $^{12}$Be and $^{14}$Be are used. In the present hybrid model of the optical potential the only free parameters are the depths of the real and imaginary parts of OP obtained by fitting the experimental data. The role of the inelastic scattering channel to the first excited $2^{+}$ and $3^{-}$ states in $^{12}$C when calculating the quasielastic cross sections, as well as the modified density of the $^{12}$C target accounting for the surface effects are studied. In addition, the cluster model, in which $^{14}$Be consists of a $2n$-halo and the $^{12}$Be core, is applied to calculate the cross sections of diffraction breakup and stripping reactions in $^{14}$Be+$^{12}$C scattering and longitudinal momentum distributions of $^{12}$Be fragments at energy of 56 MeV/nucleon. A good agreement of the theoretical results with the available experimental data of both quasielstic scattering and breakup processes is obtained.

Explicit inclusion of the spin-orbit contribution in the Tohsaki-Horiuchi-Schuck-Röpke wave function

The Tohsaki-Horiuchi-Schuck-Roepke (THSR) wave function has been successfully used for the studies of gas-like nature of alpha clusters in various nuclei including the so-called Hoyle state of 12C and four alpha states of 16O. In standard alpha cluster models, however, each alpha cluster wave function has spin zero because of its spatial symmetry and antisymmetrization effect. Thus the non-central interactions do not contribute, and this situation is the same in the THSR wave function. In this work, the spin-orbit contribution, which is found to be quite important at short alpha-alpha distances, is taken into account in the THSR wave function by combing it with antisymmetrized quasi cluster model (AQCM). The application to 12C is presented. The multi-integration in the original THSR wave function is carried out by using Monte Carlo technique, which is called Monte Carlo THSR wave function. For the nucleon-nucleon interaction, the Tohsaki interaction, which contains finite-range three-body terms and simultaneously reproduces the saturation properties of nuclear systems, the alpha-alpha scattering phase shift, and the size and binding energy of 4He, is adopted.

Symmetry protected topological phases in two-orbital SU(4) fermionic atoms

We study one-dimensional systems of two-orbital SU(4) fermionic cold atoms. In particular, we focus on an SU(4) spin model [named SU(4) $e$-$g$ spin model] that is realized in a low-energy state in the Mott insulator phase at the filling $n_g=3, n_e=1$ ($n_g, n_e$: numbers of atoms in ground and excited states, respectively). Our numerical study with the infinite-size density matrix renormalization group shows that the ground state of SU(4) $e$-$g$ spin model is a nontrivial symmetry protected topological (SPT) phase protected by $Z_4 \times Z_4$ symmetry. Specifically, we find that the ground state belongs to an SPT phase with the topological index $2\in\mathbb{Z}_4$ and show sixfold degenerate edge states. This is topologically distinct from SPT phases with the index $1\in\mathbb{Z}_4$ that are realized in the SU(4) bilinear model and the SU(4) Affleck-Kennedy-Lieb-Tasaki (AKLT) model. We explore the phase diagram of SU(4) spin models including $e$-$g$ spin model, bilinear-biquadratic model, and AKLT model, and identify that antisymmetrization effect in neighboring spins (that we quantify with Casimir operators) is the driving force of the phase transitions. Furthermore, we demonstrate by using the matrix product state how the $\mathbb{Z}_4$ SPT state with six edge states appears in the SU(4) $e$-$g$ spin model.

Improved version of a simplified method for including tensor effects in cluster models

The tensor contribution can be directly incorporated in the cluster model in a simplified way. In conventional $\alpha$ cluster models, the contribution of the non-central interactions exactly cancels because of the antisymmetrization effect and spatial symmetry of $\alpha$ clusters. The mixing of breaking components of $\alpha$ clusters to take into account the spin-orbit and tensor effects is needed. Previously we proposed a simplified method to include the spin-orbit effect, and also for the tensor part, a simplified model to directly take into account the contribution of the tensor interaction (called SMT) was introduced; however the contribution of the tensor interaction was quite limited. Here we improve SMT, which is called $i$SMT. Using newly proposed $i$SMT, the contribution of the tensor interaction in $^4$He is more than $-40$ MeV, four times larger than the previous version. The method is applied to four-$\alpha$ cluster structure of $^{16}$O. In $^{16}$O, the tensor contribution is also large, and this is coming from the finite size effect for the distances among $\alpha$ clusters with a tetrahedral configuration.

Nuclear spin of odd-oddαemitters based on the behavior ofα-particle preformation probability

The preformation probabilities of an $\ensuremath{\alpha}$ cluster inside radioactive parent nuclei for both odd-even and odd-odd nuclei are investigated. The calculations cover the isotopic chains from Ir to Ac in the mass regions $166\ensuremath{\le}A\ensuremath{\le}215$ and $77\ensuremath{\le}Z\ensuremath{\le}89$. The calculations are employed in the framework of the density-dependent cluster model. A realistic density-dependent nucleon-nucleon $(NN)$ interaction with a finite-range exchange part is used to calculate the microscopic $\ensuremath{\alpha}$-nucleus potential in the well-established double-folding model. The main effect of antisymmetrization under exchange of nucleons between the $\ensuremath{\alpha}$ and daughter nuclei has been included in the folding model through the finite-range exchange part of the $NN$ interaction. The calculated potential is then implemented to find both the assault frequency and the penetration probability of the $\ensuremath{\alpha}$ particle by means of the Wentzel-Kramers-Brillouin approximation in combination with the Bohr-Sommerfeld quantization condition. The correlation of the $\ensuremath{\alpha}$-particle preformation probability and the neutron and proton level sequences of the parent nucleus as obtained in our previous work is extended to odd-even and odd-odd nuclei to determine the nuclear spin and parities. Two spin coupling rules are used, namely, strong and weak rules to determine the nuclear spin for odd-odd isotopes. This work can be a useful reference for theoretical calculation of undetermined nuclear spin of odd-odd nuclei in the future.

Microscopic theory of Dzyaloshinskii–Moriya coupling and related exchange-relativistic effects

I present a short overview of the results of the microscopic theory of the Dzyaloshinskii–Moriya coupling and other related exchange-relativistic effects such as exchange anisotropy, antisymmetric magnetoelectric coupling, antisymmetric magnetogyrotropic effects, and electron-nuclear antisymmetric supertransferred hyperfine interactions in strongly correlated 3d compounds.

Both piston-like and rotational motions are present in bacterial chemoreceptor signaling.

Bacterial chemotaxis signaling is triggered by binding of chemo-effectors to the membrane-bound chemoreceptor dimers. Though much is known about the structure of the chemoreceptors, details of the receptor dynamics and their effects on signaling are still unclear. Here, by using molecular dynamics simulations and principle component analysis, we study the dynamics of the periplasmic domain of aspartate chemoreceptor Tar dimer and its conformational changes when binding to different ligands (attractant, antagonist, and two attractant molecules). We found two dominant components (modes) in the receptor dynamics: a relative rotation of the two Tar monomers and a piston-like up-and-down sliding movement of the α4 helix. These two modes are highly correlated. Binding of one attractant molecule to the Tar dimer induced both significant piston-like downward movements of the α4 helix and strong relative rotations of the two Tar monomers, while binding of an antagonist or the symmetric binding of two attractant molecules to a Tar dimer suppresses both modes. The anti-symmetric effects of the relative rotation mode also explained the negative cooperativity between the two binding pockets. Our results suggest a mechanism of coupled rotation and piston-like motion for bacterial chemoreceptor signaling.

Investigation of possible correlation betweenα-particle preformation probability and energy levels forαemitters with74≤Z≤83

The preformation probability of an $\ensuremath{\alpha}$ cluster inside radioactive parent nuclei is investigated. The calculations are employed in the framework of the density-dependent cluster model for both even-even and odd-$A$ isotopes with $74\ensuremath{\le}Z\ensuremath{\le}83$. A realistic density-dependent nucleon-nucleon ($NN$) interaction with a finite-range exchange part is used to calculate the microscopic $\ensuremath{\alpha}$-nucleus potential in the well-established double-folding model. The main effect of antisymmetrization under exchange of nucleons between the $\ensuremath{\alpha}$ and daughter nuclei has been included in the folding model through the finite-range exchange part of the $NN$ interaction. The calculated potential is then implemented to find both the assault frequency and the penetration probability of the $\ensuremath{\alpha}$ particle by means of the Wentzel-Kramers-Brillouin approximation in combination with the Bohr-Sommerfeld quantization condition. We investigated the correlation between the $\ensuremath{\alpha}$-particle preformation probability, ${S}_{\ensuremath{\alpha}}$, and the energy levels of the parent nucleus for $\ensuremath{\alpha}$ emitters with atomic number $74\ensuremath{\le}Z\ensuremath{\le}83$. Based on the similarity in the behavior of ${S}_{\ensuremath{\alpha}}$ with the neutron number for two nuclei, we try to predict or confirm the unknown or doubted nuclear spins and parities in this mass region.

Large zero-field splittings of the ground spin state arising from antisymmetric exchange effects in heterometallic triangles.

[Ru2Mn(O)(O2CtBu)6(py)3] has an S=5/2 ground state with a very large zero-field splitting (ZFS) of D=2.9 cm(-1), as characterized by EPR spectroscopy at 4-330 GHz. This is far too large to be due to the Mn(II) ion (D <0.2 cm(-1)), as shown from the {Fe2Mn} analogue, but can be modeled by antisymmetric exchange effects.

Large Zero‐Field Splittings of the Ground Spin State Arising from Antisymmetric Exchange Effects in Heterometallic Triangles

Abstract[Ru2Mn(O)(O2CtBu)6(py)3] has an S=5/2 ground state with a very large zero‐field splitting (ZFS) of D=2.9 cm−1, as characterized by EPR spectroscopy at 4–330 GHz. This is far too large to be due to the MnII ion (D &lt;0.2 cm−1), as shown from the {Fe2Mn} analogue, but can be modeled by antisymmetric exchange effects.

1,2,4-Triazolyl-Carboxylate-Based MOFs Incorporating Triangular Cu(II)-Hydroxo Clusters: Topological Metamorphosis and Magnetism

Bifunctional 1,2,4-triazole-carboxylate ligands, an achiral 1,2,4-triazol-4-yl-acetic acid (trgly-H) and a chiral (d)-2-(1,2,4-triazol-4-yl)-propionic acid (d-trala-H), derived from the corresponding α-amino acid precursors revealed unique binding abilities in the construction of Cu(II)-coordination polymers composing discrete triangular [Cu3(μ3-OH)] clusters. A related series of MOFs, [Cu3(μ3-OH)(trgly)3(SO4)]·2H2O (1a), [Cu3(μ3-OH)(trgly)3(H2O)3]SO4·16H2O (1b), Cu3(μ3-OH)(d-trala)3(ClO4)0.5](ClO4)1.5·1.5H2O (2), was prepared, and their crystal structures were determined by means of X-ray diffraction. Being singly deprotonated, the organic ligands act as multidentate μ3- or μ4-donors using tr and -COO(-) moieties. The generated [Cu3(μ3-OH)(tr)3] cluster core is primarily supported by three [-N-N-] triazole heterocycles in a basal plane and tripodal-assisted μ3-anions (SO4(2-): 1a; ClO4(-): 2) capping the axial faces. The carboxylate groups join the units into either two-dimensional (2D) layer (1a, 2) or 3D zeolite-like networks (1b). Compound 1b represents the topology of α-Po (pcu: 4(12).6(3)) and crystallizes in the noncentrosymmetric space group I4̅3m, in which the six-connected [Cu3(μ3-OH)] clusters and trgly self-assemble in an open-channel cubic array possessing ∼56% solvent-accessible volume. Upon slight thermal treatment (∼60 °C), the structure irreversibly shrinks to the nonporous 2D motif 1a that belongs to a uninodal (3,6) network type. In structure 2 (space group R32), due to the [-N-N-] triazole and 1,3-bidentate carboxylate binding mode, each organic ligand bridges three metal clusters affording cross-linking of two adjacent layers with the same (3,6) topology. The resultant 3,9-c net is novel and can be categorized as two-nodal with point symbol {4(18).6(18)}{4(2).6}3. Spin frustration and antisymmetric exchange effects, resulting in abnormally low g values in the S = 1/2 states, were observed in the magnetic properties and the EPR spectra.

Point Contact Andreev Reflection from Erbium: The role of external magnetic field and the sign of the spin polarization

Point Contact Andreev Reflection has established itself as a technique of choice for the measurement of Fermi level spin polarization in a variety of metallic and degenerate semiconducting materials. So far, the methodology has been limited to determination of the absolute value of the spin polarization in zero or small magnetic field. Here an experimental account is presented of the existence of magnetic field and current antisymmetric effects in the PCAR spectra of some Nb/Er contacts. This is hoped to bridge the gap to the neighboring Tedrow-Meservey technique and help in the determination of correct sign and magnitude of the polarization in new and novel materials. The spin polarization of erbium has been determined to be P = +0.58(2).

Two-neutron overlap functions for 6He from a microscopic structure model

A fully antisymmetrized microscopic model is developed for light two-neutron halo nuclei using a hyper-spherical basis to describe halo regions. The many-body wavefunction is optimized variationally. The model is applied to 6He bound by semi realistic Minnesota nucleon–nucleon forces. The two-neutron separation energy and the radius of the halo are reproduced in agreement with experiment. Antisymmetrization effects between 4He and halo neutrons are found to be crucial for binding of 6He. We also properly extract two-neutron overlap functions and find that there is a significant increase of 30%–70% in their normalization due to microscopic effects as compared to the results of three-body models.

Structure-related frustrated magnetism of nanosized polyoxometalates: aesthetics and properties in harmony

The structural versatility characterizing polyoxometalate chemistry, in combination with the option to deliberately use well-defined building blocks, serves as the foundation for the generation of a large family of magnetic clusters, frequently comprising highly symmetric spin arrays. If the spin centers are coupled by antiferromagnetic exchange, some of these systems exhibit spin frustration, which can result in novel magnetic properties of purely molecular origins. We discuss here the magnetic properties of selected nanosized polyoxometalate clusters featuring spin triangles as their magnetic 'building blocks' or fragments. This includes unique porous Keplerate clusters of the type {(Mo)Mo(5)}(12)M(30) (M = Fe(III), Cr(III), V(IV)) with the spin centers defining a regular icosidodecahedron and the {V(15)As(6)}-type cluster sphere containing a single equilateral spin triangle; these species are widely discussed and studied in the literature for their role in materials science as molecular representations of Kagomé lattices and in relation to quantum computing, respectively. Exhibiting fascinating and unique structural features, these magnetic molecules allow the study of the implications of frustrated spin ordering. Furthermore, this perspective covers the impact of spin frustration on the degeneracy of the ground state and related problems, namely strong magnetic anisotropy and the interplay of antisymmetric exchange and structural Jahn-Teller effects.