Field Multiplet Research Articles

On gravity unification in SL(2N,C) gauge theories

The local SL(2N, C) symmetry is shown to provide, when appropriately constrained, a viable framework for a consistent unification of the known elementary forces, including gravity. Such a covariant constraint implies that an actual gauge field multiplet in the SL(2N, C) theory is ultimately determined by the associated tetrad fields which not only specify the geometric features of spacetime but also govern which local internal symmetries are permissible within it. As a consequence, upon the covariant removal of all “redundant” gauge field components, the entire theory only exhibits the effective SL(2,C)×SU(N) symmetry, comprising SL(2, C) gauge gravity on one hand and SU(N) grand unified theory on the other. Given that all states involved in the SL(2N, C) theories are additionally classified according to their spin values, many potential SU(N) GUTs, including the conventional SU(5) theory, appear to be irrelevant for standard spin 1/2 quarks and leptons. Meanwhile, applying the SL(2N, C) symmetry to the model of composite quarks and leptons with constituent chiral preons in its fundamental representations reveals, under certain natural conditions, that among all accompanying SU(N)L×SU(N)R chiral symmetries of preons and their composites only the SU(8)L×SU(8)R meets the anomaly matching condition ensuring masslessness of these composites at large distances. This, in turn, identifies SL(16, C) with the effective SL(2,C)×SU(8) symmetry, accommodating all three quark-lepton families, as the most likely candidate for hyperunification of the existing elementary forces.

On the Addition of a Large Scalar Multiplet to the Standard Model

Abstract We consider the addition of a single $SU(2)$ multiplet of complex scalar fields to the Standard Model (SM). We explicitly consider the various possible values of the weak isospin J of that multiplet, up to and including $J = 7/2$. We allow the multiplet to have arbitrary weak hypercharge. The scalar fields of the multiplet are assumed to have no vacuum expectation value; the mass differences among the components of the multiplet originate in its coupling, present in the scalar potential (SP), to the Higgs doublet of the SM. We derive exact bounded-from-below and unitarity conditions on the SP, thereby constraining those mass differences. We compare those constraints to the ones that may be derived from the oblique parameters.

Temperature Induced Reversible Switching of the Magnetic Anisotropy in a Neodymium Complex Adsorbed on Graphite.

Controlling the magnetic anisotropy of molecular layers assembled on a surface is one of the challenges that needs to be addressed to create the next-generation spintronic devices. Recently, metal complexes that show a reversible solid-state switch of their magnetic anisotropy in response to physical stimuli, such as temperature and magnetic field, have been discovered. The complex Nd(trensal) (H3trensal=2,2',2''-tris(salicylideneimino)triethylamine) is predicted to exhibit such property. An ultra-thin film of Nd(trensal) is deposited on highly ordered pyrolytic graphite as a proof-of-concept system to show that this property can be retained at the nanoscale on a layered material. By combining single crystal magnetometric measurements and synchrotron X-ray-based absorption techniques, supported by multiplet ligand field simulations based on the trigonal crystal field surrounding the lanthanide centre, it is demonstrated that changing the temperature reverses the magnetic anisotropy of an ordered film of Nd(trensal), thus opening significant perspectives for the realization of a novel family of temperature-controlled molecular spintronic devices.

Tracking Coordination Environment and Reaction Intermediates in Homogeneous and Heterogeneous Epoxidation Catalysts via Ti L2,3-Edge Near-Edge X-ray Absorption Fine Structures.

Ti-based molecules and materials are ubiquitous and play a major role in both homogeneous and heterogeneous catalytic processes. Understanding the electronic structures of their active sites (oxidation state, local symmetry, and ligand environment) is key to developing molecular-level structure-property relationships. In that context, X-ray absorption spectroscopy (XAS) offers a unique combination of elemental selectivity and sensitivity to local symmetry. Commonly, for early transition metals such as Ti, K-edge XAS is applied for in situ characterization and subsequent structural analysis with high sensitivity toward tetrahedral species. Ti L2,3-edge spectroscopy is in principle complementary and offers specific opportunities to interrogate the electronic structure of five-and six-coordinated species. It is, however, much more rarely implemented because the use of soft X-rays implies ultrahigh vacuum conditions. Furthermore, the interpretation of the data can be challenging. Here, we show how Ti L2,3-edge spectroscopy can help to obtain unique information about both homogeneous and heterogeneous epoxidation catalysts and develop a molecular-level relationship between spectroscopic signatures and electronic structures. Toward this goal, we first establish a spectral library of molecular Ti reference compounds, comprising various coordination environments with mono- and dimeric Ti species having O, N, and Cl ligands. We next implemented a computational methodology based on multiplet ligand field theory and maximally localized Wannier orbitals benchmarked on our library to understand Ti L2,3-edge spectroscopic signatures. We finally used this approach to track and predict the spectra of catalytically relevant intermediates, focusing on Ti-based olefin epoxidation catalysts.

Core-to-core X-ray emission spectra from Wannier based multiplet ligand field theory

Recent advances using Density Functional Theory (DFT) to augment Multiplet Ligand Field Theory (MLFT) have led to ab-initio calculations of many formerly empirical parameters. This development makes MLFT more predictive instead of interpretive, thus improving its value for studies of highly correlated 3d, 4d, and f-electron systems. Synchrotron time is always at a premium, and tools that provide predictive capabilities have clear value when it comes to planning studies. Here, we develop a DFT + MLFT based approach for core-to-core Kα x-ray emission spectra (XES) and evaluate its performance for a range of transition metal systems. We find good agreement between theory and experiment, as well as the ability to capture key spectral trends related to spin and oxidation state. We also discuss limitations of the model in the context of the remaining free parameters and suggest directions forward.

Covariant action for conformal higher spin gravity

Conformal higher spin (HS) gravity is a HS extension of Weyl gravity and is a family of local HS theories, which was put forward by Segal and Tseytlin. We propose a manifestly covariant and coordinate-independent action for these theories. The result is based on an interplay between HS symmetries and deformation quantization: a locally equivalent but manifestly background-independent reformulation, known as the parent system, of the off-shell multiplet of conformal HS fields (Fradkin–Tseytlin fields) can be interpreted in terms of Fedosov deformation quantization of the underlying cotangent bundle. This brings into the game the invariant quantum trace, induced by the Feigin–Felder–Shoikhet cocycle of Weyl algebra, which extends Segal’s action into a gauge invariant and globally well-defined action functional on the space of configurations of the parent system. The same action can be understood within the worldline approach as a correlation function in the topological quantum mechanics on the circle.

Electronic Structure of the Complete Series of Gas-Phase Manganese Acetylacetonates by X-ray Absorption Spectroscopy.

Metal centers in transition metal-ligand complexes occur in a variety of oxidation states causing their redox activity and therefore making them relevant for applications in physics and chemistry. The electronic state of these complexes can be studied by X-ray absorption spectroscopy, which is, however, due to the complex spectral signature not always straightforward. Here, we study the electronic structure of gas-phase cationic manganese acetylacetonate complexes Mn(acac)1-3+ using X-ray absorption spectroscopy at the metal center and ligand constituents. The spectra are well reproduced by multiconfigurational wave function theory, time-dependent density functional theory as well as parameterized crystal field and charge transfer multiplet simulations. This enables us to get detailed insights into the electronic structure of ground-state Mn(acac)1-3+ and extract empirical parameters such as crystal field strength and exchange coupling from X-ray excitation at both the metal and ligand sites. By comparison to X-ray absorption spectra of neutral, solvated Mn(acac)2,3 complexes, we also show that the effect of coordination on the L3 excitation energy, routinely used to identify oxidation states, can contribute about 40-50% to the observed shift, which for the current study is 1.9 eV per oxidation state.

Two-dimensional Kβ-Kα fluorescence spectrum by nonlinear resonant inelastic X-ray scattering

High sensitivity of the Kβ fluorescence spectrum to electronic state is widely used to investigate spin and oxidation state of first-row transition-metal compounds. However, the complex electronic structure results in overlapping spectral features, and the interpretation may be hampered by ambiguity in resolving the spectrum into components representing different electronic states. Here, we tackle this difficulty with a nonlinear resonant inelastic X-ray scattering (RIXS) scheme, where we leverage sequential two-photon absorption to realize an inverse process of the Kβ emission, and measure the successive Kα emission. The nonlinear RIXS reveals two-dimensional (2D) Kβ-Kα fluorescence spectrum of copper metal, leading to better understanding of the spectral feature. We isolate 3d-related satellite peaks in the 2D spectrum, and find good agreement with our multiplet ligand field calculation. Our work not only advances the fluorescence spectroscopy, but opens the door to extend RIXS into the nonlinear regime.

Noncommutative $$SO(2,3)_{\star }$$ gauge theory of gravity

Topological gravity (in the sense that it is metric-independent) in a 2n-dimensional spacetime can be formulated as a gauge field theory for the AdS gauge group $$SO(2,2n-1)$$ by adding a multiplet of scalar fields. These scalars can break the gauge invariance of the topological gravity action, thus making a connection with Einstein’s gravity. This review is about a noncommutative (NC) star-product deformation of the four-dimensional AdS gauge theory of gravity, including Dirac spinors and the Yang–Mills field. In general, NC actions can be expanded in powers of the canonical noncommutativity parameter $$\theta$$ using the Seiberg–Witten map. The leading-order term of the expansion is the classical action, while the higher-order $$\theta$$ -dependent terms are interpreted as new types of coupling between classical fields due to spacetime noncommutativity. We study how these perturbative NC corrections affect the field equations of motion and derive some phenomenological consequences, such as NC-deformed Landau levels of an electron. Finally, we discuss how topological gravity in four dimensions (both classical and noncommutative) appears as a low-energy sector of five-dimensional Chern–Simons gauge theory in the sense of Kaluza–Klein reduction.

Large Orbital Magnetic Moment in VI3.

The existence of the V3+-ion orbital moment is an open issue of the nature of magnetism in the van der Waals ferromagnet VI3. The huge magnetocrystalline anisotropy in conjunction with the significantly reduced ordered magnetic moment compared to the spin-only value provides strong but indirect evidence of a large V orbital moment. We used the unique capability of X-ray magnetic circular dichroism to determine the orbital component of the total magnetic moment and provide a direct proof of an exceptionally sizable orbital moment of the V3+ ion in VI3. Our ligand field multiplet simulations of the XMCD spectra in synergy with the results of DFT calculations agree with the existence of two V sites with different orbital occupations and OM magnitudes in the ground state.

Stoichiometry driven tuning of physical properties in epitaxial Fe3-xCrxO4 thin films

Tuning magnetic and electronic transport properties in spinel oxides requires a faithful description between chemical composition and cation site-occupation. Here this challenge is addressed using Fe3-xCrxO4 thin films grown by oxygen-assisted molecular-beam epitaxy within a wide range of composition (0.0 ≤ x ≤ 1.2). Spectroscopic measurements (e.g., X-ray magnetic circular dichroism), refined by theoretical simulations (e.g., crystal field multiplet), are performed to establish a quantitative link between chromium content, Fe2+/Fe3+ site-occupation and macroscopic physical properties of the layers. It is found that Fe3-xCrxO4 thin films (i) delay the transition from inverse to normal spinel configuration with increasing chromium content and (ii) promote collinear spin structure, at odds with bulk material. As a result, strong antiferromagnetic interactions are preserved between spins in tetrahedral and octahedral spinel sublattices, so that chromium-rich thin films exhibit Curie temperatures above room temperature and higher magnetization. Electron hopping is also favored by this singular cation distribution and electronic band gap is smaller than expected for these thin films. The cation site-occupation is therefore a key feature to consider for applications of Fe3-xCrxO4 thin films in spintronics and photocatalysis, as it enables manipulation of magnetic properties (Curie temperature and magnetization) and band gap engineering.

The electronic structure of novel high-pressure and high-temperature phases of Mn2O3: exploring perovskite and ilmenite-type structures

The electronic structures of novel phases of manganese synthesized under high-pressure and high-temperature conditions are analysed using X-ray absorption and X-ray emission spectroscopy together with multiplet ligand field theory.

Scale-invariant 3-3-1-1 model with B−L symmetry

Motivated by a possible interplay between the mechanism of dynamical symmetry breaking and the seesaw mechanism for generating fermion masses, we present a scale-invariant model that extends the gauge symmetry of the Standard Model electroweak sector to SU(3)$_L\otimes$U(1)$_X\otimes$U(1)$_N$, with a built-in $B-L$ symmetry. The model is based on the symmetry structure of the known 3-3-1 models and, thus, it relates the number of the three observed fermion generations with the cancellation of gauge anomalies. Symmetry breaking is triggered via the Coleman-Weinberg mechanism taking into account a minimal set of scalar field multiplets. We establish the stability conditions for the tree-level scalar potential imposing the copositivity criteria and use the method of Gildener-Weinberg for computing the one-loop effective potential when one has multiple scalar fields. With the addition of vectorial fermions, getting their mass mainly through the vacuum expectation value of scalar singlets at $10^3$ TeV, the $B-L$ symmetry leads to textures for the fermion mass matrices, allowing seesaw mechanisms for neutrinos and quarks to take place. In particular, these mechanisms could partly explain the mass hierarchies of the quarks. Once the breakdown of the SU(3)$_L$ symmetry is supposed to occur around 10 TeV, the model also predicts new particles with TeV-scale masses, such as a neutral scalar, $H_{1}$, a charged scalar, $H^\pm$, and the gauge bosons $Z^{\prime}$, $W^{\prime\pm}$ and $Y^0$, that could be searched with the high-luminosity LHC.

Re‐Dichalcogenides: Resolving Conflicts of Their Structure–Property Relationship

AbstractReX2 (X = S, Se) remains a copious source of controversies and unanswered questions due to its widely contrasting experimental and theoretical results. With the help of comparative first‐principles electronic structure and phonon calculations, the correct structures for both systems are established, which minimize the apparent divergence of different experimental results. It is demonstrated that ReS2 and ReSe2 are neither iso‐structural nor iso‐electronic. The contributions of the in‐plane and out‐of‐plane orbitals at the band‐edges of the bulk and monolayers are coordinated with their anisotropic optical response. Under moderately high pressure, both of these systems are observed to undergo a semiconductor to metal transition. With the help of a combined full‐potential density functional theory and multiplet ligand field theory (DFT+MLFT) approach, the X‐ray spectral properties of these two systems are analyzed in the light of their intricate differences of optimized structures and electronic correlations.

Energy Levels in Pentacoordinate d5 to d9 Complexes

Energy levels of pentacoordinate d5 to d9 complexes were evaluated according to the generalized crystal field theory at three levels of sophistication for two limiting cases of pentacoordination: trigonal bipyramid and tetragonal pyramid. The electronic crystal field terms involve the interelectron repulsion and the crystal field potential; crystal field multiplets account for the spin–orbit interaction; and magnetic energy levels involve the orbital– and spin–Zeeman interactions with the magnetic field. The crystal field terms are labelled according to the irreducible representations of point groups D3h and C4v using Mulliken notation. The crystal field multiplets are labelled with the Bethe notations for the respective double groups D’3 and C’4. The magnetic functions, such as the temperature dependence of the effective magnetic moment and the field dependence of the magnetization, are evaluated by employing the apparatus of statistical thermodynamics as derivatives of the field-dependent partition function. When appropriate, the formalism of the spin Hamiltonian is applied, giving rise to a set of magnetic parameters, such as the zero-field splitting D and E, magnetogyric ratio tensor, and temperature-independent paramagnetism. The data calculated using GCFT were compared with the ab initio calculations at the CASSCF+NEVPT2 level and those involving the spin–orbit interaction.

Einstein–Yang–Mills-Aether Theory with Nonlinear Axion Field: Decay of Color Aether and the Axionic Dark Matter Production

We establish a nonlinear version of the SU(N)-symmetric theory, which describes self-consistently the interaction between the gravitational, gauge, vector and pseudoscalar (axion) fields. In the context of this theory the SU(N)-symmetric multiplet of vector fields is associated with the color aether, the decay of which in the early Universe produced the canonic dynamic aether and the axionic dark matter. The SU(N)-symmetric Yang–Mills field, associated with the color aether, forms the source, which transfers the energy of the decaying color aether to the axion field. The nonlinear modification of the model uses explicitly the requirement of discrete symmetry, prescribed by the axion field, and is based on the analogy with a nonlinear physical pendulum. We show that in the framework of this nonlinear regular model, the axion field can grow to an arbitrarily large value, thus explaining the abundance of the axionic dark matter in the Universe.

Atomic scale crystal field mapping of polar vortices in oxide superlattices

Polar vortices in oxide superlattices exhibit complex polarization topologies. Using a combination of electron energy loss near-edge structure analysis, crystal field multiplet theory, and first-principles calculations, we probe the electronic structure within such polar vortices in [(PbTiO3)16/(SrTiO3)16] superlattices at the atomic scale. The peaks in Ti L-edge spectra shift systematically depending on the position of the Ti4+ cations within the vortices i.e., the direction and magnitude of the local dipole. First-principles computation of the local projected density of states on the Ti 3d orbitals, together with the simulated crystal field multiplet spectra derived from first principles are in good agreement with the experiments.

Magnetic Hysteresis in a Monolayer of Oriented 6 nm CsNiCr Prussian Blue Analogue Nanocrystals.

Prussian blue analogue nanocrystals of the CsINiII[CrIII(CN)6] cubic network with 6 nm size were assembled as a single monolayer on highly organized pyrolytic graphite (HOPG). X-ray magnetic circular dichroism (XMCD) studies, at the Ni and Cr L2,3 edges, reveal the presence of an easy plane of magnetization evidenced by an opening of the magnetic hysteresis loop (coercive field of ≈200 Oe) when the magnetic field, B, is at 60° relative to the normal to the substrate. The angular dependence of the X-ray natural linear dichroism (XNLD) reveals both an orientation of the nanocrystals on the substrate and an anisotropy of the electronic cloud of the NiII and CrIII coordination sphere species belonging to the nanocrystals' surface. Ligand field multiplet (LFM) calculations that reproduce the experimental data are consistent with an elongated tetragonal distortion of surface NiII coordination sphere responsible for the magnetic behavior of monolayer.

Extraction of the local coordination and electronic structures of FeO6 octahedra using crystal field multiplet calculations combined with STEM-EELS

The material properties of metal oxides are sensitive to even low levels of cation doping, and the local atomic structures around such trace elements in a crystal will differ from the bulk structure due to the different ionic size and electron configuration. The present work explores the extraction of the local structure of a minority component contained in an atomic column by analyzing the Fe L2,3 energy-loss near-edge structure of atomic-resolution monochromated electron energy-loss spectra, using crystal field multiplet calculations. The crystal field splitting of the Fe 3d state and the local coordination structure of FeO6 octahedra in iron oxides in real space with known structures were determined. The results closely agreed with structures obtained from neutron diffraction and the Fe 3d DOS generated by density functional theory calculations. The previously unknown local structure of FeO6 octahedra present at octahedral sites as a minor component (14.4%) in the brownmillerite structure of Ca2Fe1.07Mn0.93O5 was determined. This structure was found to be unique and differed from the results obtained using neutron diffraction, which reflect those of mainly MnO6 octahedra. The present method is evidently an effective means of investigating the local structures around trace elements.

Scotogenic neutrino mass with large SU(2)_L multiplet fields

We construct a scotogenic neutrino mass model introducing large SU(2)_L multiplet fields without adding an extra symmetry. We have introduced extra scalar fields such as a septet, quintet and quartet where we make the vacuum expectation value of quartet scalar to be zero while septet and quintet develop non-zero ones. Then the neutrino mass is generated at one-loop level by introducing quintet fermion. We analyze the neutrino mass matrix taking constraints from lepton flavor violation into account and discuss collider physics regarding charged fermions from large multiplet fields. We have analysed the production and the decays of the quintet fermions, as well as the discovery reach at 14 TeV and 27 TeV LHC.