Spin Multiplets Research Articles

Towards a quantum field theory of primitive string fields

We denote generating functions of massless even higher spin fields "primitive string fields" (PSF's). In an introduction we present the necessary definitions and derive propagators and currents of these PDF's on flat space. Their off-shell cubic interaction can be derived after all off-shell cubic interactions of triplets of higher spin fields have become known [2],[3]. Then we discuss four-point functions of any quartet of PSF's. In subsequent sections we exploit the fact that higher spin field theories in $AdS_{d+1}$ are determined by AdS/CFT correspondence from universality classes of critical systems in $d$ dimensional flat spaces. The O(N) invariant sectors of the O(N) vector models for $1\leq N \leq \infty$ play for us the role of "standard models", for varying $N$, they contain e.g. the Ising model for N=1 and the spherical model for $N=\infty$. A formula for the masses squared that break gauge symmetry for these O(N) classes is presented for d = 3. For the PSF on $AdS$ space it is shown that it can be derived by lifting the PSF on flat space by a simple kernel which contains the sum over all spins. Finally we use an algorithm to derive all symmetric tensor higher spin fields. They arise from monomials of scalar fields by derivation and selection of conformal (quasiprimary) fields. Typically one monomial produces a multiplet of spin $s$ conformal higher spin fields for all $s \geq 4$, they are distinguished by their anomalous dimensions (in $CFT_3$) or by their mass (in $AdS_4$). We sum over these multiplets and the spins to obtain "string type fields", one for each such monomial.

Surface hopping trajectory simulations with spin-orbit and dynamical couplings

In this paper we consider the inclusion of the spin-orbit interaction in surface hopping molecular dynamics simulations to take into account spin forbidden transitions. Two alternative approaches are examined. The spin-diabatic one makes use of eigenstates of the spin-free electronic Hamiltonian and of Ŝ(2) and is commonly applied when the spin-orbit coupling is weak. We point out some inconsistencies of this approach, especially important when more than two spin multiplets are coupled. The spin-adiabatic approach is based on the eigenstates of the total electronic Hamiltonian including the spin-orbit coupling. Advantages and drawbacks of both strategies are discussed and illustrated with the help of two model systems.

Condensation of a Nickel Tetranuclear Cubane into a Heptanuclear Single-Molecule Magnet

A tetranuclear complex, [Ni(4)], with a cubane-like structure synthesized from hexafluoroacetylacetone gives, after drying at high temperature and treatment with pyridine, a heptanuclear nickel(II) complex, [Ni(7)]. The crystal structures of both compounds have been determined by single-crystal X-ray diffraction. Their magnetic properties have been studied by SQUID and μ-SQUID magnetometry as well as by high-frequency EPR spectroscopy (HF-EPR). For [Ni(4)], the temperature dependence of the magnetic susceptibility can be fitted by taking into account strong Ni···Ni ferromagnetic interactions which lead to an S = 4 ground-state spin, in good agreement with the HF-EPR study. For [Ni(7)], the temperature dependence of the magnetic susceptibility shows that the Ni···Ni ferromagnetic interactions are kept within the metal core. However, it was not possible to fit this with a clear set of parameters, and the ground-state spin was undetermined. The field dependence of the magnetization indicates an S = 7 ground-state spin at high field. In contrast, the temperature dependence of the magnetic susceptibility indicates a ground-state spin of S = 6 or even S = 5. These results agree with complicated high-frequency EPR spectra which have been ascribed to the superposition of signals from the ground spin multiplet and from an excited spin multiplet very close in energy, with the excited state having a larger S value than the ground state. Very low temperature studies show that only the heptanuclear complex behaves as a single-molecule magnet.

Spinor formalism for massive fields with half-integral spin

In this article, we extend the %Weyl-van der Waerden spinor technique for calculating helicity amplitudes to general massive fields of half-integer spins. We find that the little group generators can be represented as first-order differential operators in the spinor formalism. We use the spinor forms of the generators to get the explicit form of the massive fields of any spin and any helicity. We also deal with the three-particle S-matrix by these spinor form generators, and find that we are able to extend the explicit form of the three-particle vertex obtained by Benincasa and Cachazo to the massive case. We present the explicit expressions for the amplitudes with external particles of the lowest helicities up to -3/2. Group theory, in the form of raising operators of the little group, then dictates other amplitudes with higher helicity in the same spin multiplets. The formalism allows, in principle, to determine the electromagnetic form-factors of charged particles of arbitrary helicities, without additional assumptions about the underlying lagrangian. We find that restrictions which follow from gauge and Lorentz invariance are nearly as restrictive as in the massless case.

Considerations on describing non-singlet spin states in variational second order density matrix methods

Despite the importance of non-singlet molecules in chemistry, most variational second order density matrix calculations have focused on singlet states. Ensuring that a second order density matrix is derivable from a proper N-electron spin state is a difficult problem because the second order density matrix only describes one- and two-particle interactions. In pursuit of a consistent description of spin in second order density matrix theory, we propose and evaluate two main approaches: we consider constraints derived from a pure spin state and from an ensemble of spin states. This paper makes a comparative assessment of the different approaches by applying them to potential energy surfaces for different spin states of the oxygen and carbon dimer. We observe two major shortcomings of the applied spin constraints: they are not size consistent and they do not reproduce the degeneracy of the different states in a spin multiplet. First of all, the spin constraints are less strong when applied to a dissociated molecule than when they are applied to the dissociation products separately. Although they impose correct spin expectation values on the dissociated molecule, the dissociation products do not have correct spin expectation values. Secondly, both under "pure spin state conditions" and under "ensemble spin state" conditions is the energy a convex function of the spin projection. Potential energy surfaces for different spin projections of the same spin state may give a completely different picture of the molecule's bonding. The maximal spin projection always gives the most strongly constrained energy, but is also significantly more expensive to compute than a spin-averaged ensemble. In the dissociation limit, both the problem of nondegeneracy of equivalent spin projections, size-inconsistency and unphysical dissociation can be corrected by means of subspace energy constraints.

Density‐functional‐based prediction of a spin‐ordered open‐shell singlet in an unpassivated graphene nanofilm

AbstractI briefly review some of the methods, developed at the Naval Research Laboratory, that were used in a variety of collaborations with the Frauenheim group. To aid experimental understanding at that time, we attempted to predict equilibrium structures and also provide calculated vibrational spectra for direct comparison to experimental measurements. Most of our work was on carbon‐based systems with a heavy focus on fullerenes and diamond. More recently another pure carbon compound, graphene, has received much attention. In this paper, I present applications of density‐functional‐based spectroscopic techniques to a single graphene nanofilm and confirm that spin polarization can occur at the edge states. However, antiferromagnetic ordering is preferred over ferromagnetic ordering. By extracting a Heisenberg Hamiltonian from the calculations the energy of the various spin multiplets can be estimated through diagonalization of this Hamiltonian. The Perdew–Burke–Ernzerhof–density‐functional theory (PBE‐DFT) results indicate that both antiferromagnetic and ferromagnetic graphene structures are vibrationally stable but that the lowest‐energy eigenstate of the system is an open‐shell singlet with a gap of approximately 14 cm−1 to the open‐shell triplet state. Consistent with recent work that stabilizes graphene nanofilms via adsorption onto metal surfaces the density functional results presented here show that small graphene nanofilms, while vibrationally stable, will exothermically form previously identified fullerene structures. Vibrational excitation spectra for the 54‐atom graphene and fullerene structures are calculated to provide spectroscopic means for distinguishing between the two structures.

Detailed Ab Initio First-Principles Study of the Magnetic Anisotropy in a Family of Trigonal Pyramidal Iron(II) Pyrrolide Complexes

A theoretical, computational, and conceptual framework for the interpretation and prediction of the magnetic anisotropy of transition metal complexes with orbitally degenerate or orbitally nearly degenerate ground states is explored. The treatment is based on complete active space self-consistent field (CASSCF) wave functions in conjunction with N-electron valence perturbation theory (NEVPT2) and quasidegenerate perturbation theory (QDPT) for treatment of magnetic field- and spin-dependent relativistic effects. The methodology is applied to a series of Fe(II) complexes in ligand fields of almost trigonal pyramidal symmetry as provided by several variants of the tris-pyrrolylmethyl amine ligand (tpa). These systems have recently attracted much attention as mononuclear single-molecule magnet (SMM) complexes. This study aims to establish how the ligand field can be fine tuned in order to maximize the magnetic anisotropy barrier. In trigonal ligand fields high-spin Fe(II) complexes adopt an orbitally degenerate (5)E ground state with strong in-state spin-orbit coupling (SOC). We study the competing effects of SOC and the (5)E⊗ε multimode Jahn-Teller effect as a function of the peripheral substituents on the tpa ligand. These subtle distortions were found to have a significant effect on the magnetic anisotropy. Using a rigorous treatment of all spin multiplets arising from the triplet and quintet states in the d(6) configuration the parameters of the effective spin-Hamiltonian (SH) approach were predicted from first principles. Being based on a nonperturbative approach we investigate under which conditions the SH approach is valid and what terms need to be retained. It is demonstrated that already tiny geometric distortions observed in the crystal structures of four structurally and magnetically well-documented systems, reported recently, i.e., [Fe(tpa(R))](-) (R = tert-butyl, Tbu (1), mesityl, Mes (2), phenyl, Ph (3), and 2,6-difluorophenyl, Dfp (4), are enough to lead to five lowest and thermally accessible spin sublevels described sufficiently well by S = 2 SH provided that it is extended with one fourth order anisotropy term. Using this most elementary parametrization that is consistent with the actual physics, the reported magnetization data for the target systems were reinterpreted and found to be in good agreement with the ab initio results. The multiplet energies from the ab initio calculations have been fitted with remarkable consistency using a ligand field (angular overlap) model (ab initio ligand field, AILFT). This allows for determination of bonding parameters and quantitatively demonstrates the correlation between increasingly negative D values and changes in the σ-bond strength induced by the peripheral ligands. In fact, the sigma-bonding capacity (and hence the Lewis basicity) of the ligand decreases along the series 1 > 2 > 3 > 4.

LDA + slave‐boson approach to the correlated electronic structure of the metamagnetic bilayer ruthenate Sr3Ru2O7

AbstractThe combination of the local‐density approximation (LDA) with the rotationally invariant slave‐boson theory (RISB) is used to investigate the realistic correlated electronic structure of Sr3Ru2O7. From Wannier‐downfolding the low‐energy band structure to a three‐band model for the Ru(t2g) states, the interacting problem is solved including intra‐ and inter‐orbital Hubbard terms as well as spin‐flip and pair‐hopping interactions. Therewith it is possible to obtain valuable insight into the orbital occupations, relevant local spin multiplets, and the fermiology with increasing correlation strength. Besides generic correlation‐induced band‐narrowing and ‐shifting, an intriguing quasiparticle structure close to the Fermi level is found in the neighborhood of the notorious γ2 pocket in the Brillouin zone. Along the Γ–X direction in k‐space, that structure appears very sensitive to electronic self‐energy effects. The subtle sensitivity, connected also to its manifest multi‐orbital character, may put this very low‐energy structure in context with the puzzling metamagnetic properties of the compound.

Effects of magnetic anisotropy on the subgap excitations induced by quantum impurities in a superconducting host

We study the magnetic anisotropy effects on the localized subgap excitations induced by quantum impurities coupled to a superconducting host. We establish the ground-state phase diagrams for single-channel and two-channel high-spin Kondo impurities; they unveil surprising complexity that results from the (multistage) Kondo screening in competition with the superconducting correlations and the magnetic anisotropy splitting of the spin multiplets. We discuss the possibility of detecting the Zeeman splitting of the subgap states, which would provide an interesting spectroscopic tool for studying the magnetism on the single-atom level. We also study the problem of two impurities coupled by the Heisenberg exchange interaction, and we follow the evolution of the subgap states for both antiferromagnetic and ferromagnetic coupling. For sufficiently strong antiferromagnetic coupling, the impurities bind into a singlet state that is nonmagnetic, thus the subgap states move to the edge of the gap and can no longer be discerned. For ferromagnetic coupling, some excited states remain present inside the gap.

Postprocessing and sparse blind source separation of positive and partially overlapped data

We study sparse blind source separation (BSS) for a class of positive and partially overlapped signals. The signals are only allowed to have nonoverlapping at certain locations, while they could overlap with each other elsewhere. For nonnegative data, a novel approach has been proposed by Naanaa and Nuzillard (NN) assuming that nonoverlapping exists for each source signal at some location of acquisition variable. However, the NN method introduces errors (spurious peaks) in the output when their nonoverlapping condition is not satisfied. To resolve this problem and improve robustness of separation, postprocessing techniques are developed in two aspects. One is to detect coherent and uncertain components from NN outputs by using multiple mixture data, then removing the uncertain portion to enhance signals. The other is to find better estimation of mixing matrix by leveraging reliable source peak structures in NN output. Numerical results on examples including NMR spectra of a 13C-1-acetylated carbohydrate with overlapping proton spin multiplets show satisfactory performance of the postprocessed sparse BSS and offer promise to resolve complex spectra without using multidimensional NMR methods.

Search for low-spin identical bands in light Xe-Gd nuclei

The excitation energies of ground and gamma bands belonging to F0 spin multiplets of Xe-Gd nuclei are found to be constant. The pair conjugates nuclei with the same F-spin and ?F0 values also have identical NpNn values. The smooth dependence of moment of inertia and function of valence proton and neutron number [f(NpNn)] give the existence of low-spin identical bands in this region. A correlation ansatz to identify such nuclei based on the concepts of NpNn and F-spin is also discussed.

N=4, 3D supersymmetric quantum mechanics in a non-Abelian monopole background

Using the harmonic superspace approach, we construct the three-dimensional N=4 supersymmetric quantum mechanics of the supermultiplet (3,4,1) coupled to an external SU(2) gauge field. The off-shell N=4 supersymmetry requires the gauge field to be a static form of the 't Hooft ansatz for the 4D self-dual SU(2) gauge fields, that is a particular solution of Bogomolny equations for BPS monopoles. We present the explicit form of the corresponding superfield and component actions, as well as of the quantum Hamiltonian and N=4 supercharges. The latter can be used to describe a more general N=4 mechanics system, with an arbitrary BPS monopole background and on-shell N=4 supersymmetry. The essential feature of our construction is the use of semi-dynamical spin (4,4,0) multiplet with the Wess-Zumino type action.

High-Frequency Electron-Spin-Resonance Study of the Octanuclear Ferric Wheel CsFe8

High-frequency (f = 190 GHz) electron paramagnetic resonance (EPR) at magnetic fields up to 12 T and Q-band (f = 34.1 GHz) EPR were performed on single crystals of the molecular wheel CsFe(8). In this molecule, eight Fe(III) ions, which are coupled by nearest-neighbor antiferromagnetic (AF) Heisenberg exchange interactions, form a nearly perfect ring. The angle-dependent EPR data allow for the accurate determination of the spin Hamiltonian parameters of the lowest spin multiplets with S ≤ 4. Furthermore, the data can be well reproduced by a dimer model with a uniaxial anisotropy term, with only two free parameters J and D. A fit to the dimer model yields J = -15(2) cm(-1) and D = -0.3940(8) cm(-1). A rhombic anisotropy term is found to be negligibly small, E = 0.000(2) cm(-1). The results are in excellent agreement with previous inelastic neutron scattering and high-field torque measurements. They confirm that the CsFe(8) molecule is an excellent experimental model of an AF Heisenberg ring. These findings are also important within the scope of further investigations on this molecule such as the exploration of recently observed magnetoelastic instabilities.

Quasiparticle excitations in Bose-Fermi mixtures

We analyze the excitation spectrum of a three-dimensional Bose-Fermi mixture with tunable resonant interaction parameters and high hyperfine spin multiplets. We focus on a three-particle vertex describing fermionic and bosonic atoms which can scatter to create fermionic molecules or disassociate. For a single molecular level, in analogy to the single magnetic impurity problem we argue that the low-lying excitations of the mean-field theory are described by the Fermi-liquid picture with a quasiparticle weight and charge which is justified by a $1/{N}_{\ensuremath{\psi}}$ expansion, expected to be exact in the limit of infinite degeneracy (or very high fermionic spin) ${N}_{\ensuremath{\psi}}\ensuremath{\rightarrow}\ensuremath{\infty}$. Our emphasis is placed on the novel conditions for chemical equilibrium and how many-body chemical reactions renormalize the bosonic chemical potential, modifying condensation and superfluid-insulator transitions.

Transverse and Longitudinal Excitation Modes in Interacting Multispin Systems

Magnetic excitation in coupled multispin system is studied theoretically focusing on Cu 2 Fe 2 Ge 4 O 13 and Cu 2 CdB 2 O 6 as typical examples of such system. These compounds consist of spin dimer and spin monomer parts and show an antiferromagnetic phase transition at low temperatures due to the spin monomer part. A multispin containing a spin dimer and spin monomers is treated as a basis unit. The multispin forms a spin multiplet and its energy levels are separated into high and low regions reflecting the characteristic energies of the dimer and monomer parts. We regard the system as interacting multispins and apply an extended Holstein–Primakoff theory by introducing bosons for each energy level of a spin multiplet. In the low-energy region, the obtained magnon dispersion and dynamical spin correlation function agree quantitatively with experimental results of inelastic neutron scattering performed in Cu 2 Fe 2 Ge 4 O 13 . Analyzing dynamical spin correlation functions, we find several high-energy modes with longitudinal spin fluctuations peculiar to the coupled spin dimer and spin monomer system. One-magnon Raman scattering is studied to probe such longitudinal modes. Magnetic excitation in Cu 2 CdB 2 O 6 is also studied in the same way.

Inelastic neutron scattering and frequency-domain magnetic resonance studies ofS=4andS=12Mn6single-molecule magnets

We investigate the magnetic properties of three ${\text{Mn}}_{6}$ single-molecule magnets by means of inelastic neutron scattering and frequency domain magnetic resonance spectroscopy. The experimental data reveal that small structural distortions of the molecular geometry produce a significant effect on the energy-level diagram and therefore on the magnetic properties of the molecule. We show that the giant spin model completely fails to describe the spin-level structure of the ground spin multiplets. We analyze theoretically the spin Hamiltonian for the low-spin ${\text{Mn}}_{6}$ molecule $(S=4)$ and we show that the excited $S$ multiplets play a key role in determining the effective energy barrier for the magnetization reversal, in analogy to what was previously found for the two high spin ${\text{Mn}}_{6}$ $(S=12)$ molecules [S. Carretta et al., Phys. Rev. Lett. 100, 157203 (2008)].

Theory of Tunneling Spectroscopy in aMn12Single-Electron Transistor by Density-Functional Theory Methods

We consider tunneling transport through a Mn12 molecular magnet using spin density functional theory. A tractable methodology for constructing many-body wave functions from Kohn-Sham orbitals allows for the determination of spin-dependent matrix elements for use in transport calculations. The tunneling conductance at finite bias is characterized by peaks representing transitions between spin multiplets, separated by an energy on the order of the magnetic anisotropy. The energy splitting of the spin multiplets and the spatial part of their many-body wave functions, describing the orbital degrees of freedom of the excess charge, strongly affect the electronic transport, and can lead to negative differential conductance.

Current exchanges for reducible higher spin multiplets and gauge fixing

We compute the current exchanges between triplets of higher spin fields which describe reducible representations of the Poincare group. Through this computation we can extract the propagator of the reducible higher spin fields which compose the triplet. We show how to decompose the triplet fields into irreducible HS fields which obey Fronsdal equations, and how to compute the current-current interaction for the cubic couplings which appear in ArXiv:0708.1399 [hep-th] using the decomposition into irreducible modes. We compare this result with the same computation using a gauge fixed (Feynman) version of the triplet Lagrangian which allows us to write very simple HS propagators for the triplet fields.

U(n) Operator manifolds for electron propagator applications

U(n) operator manifolds necessary for the derivation of correlated propagator decouplings within a unitary group formulation of electron propagator theory are discussed. An explicit representation of 2h – p type operators is constructed and examined. Several types of linear dependencies are identified and eliminated. Finally, it is demonstrated how the correct spin multiplets arising from ionization of doubly occupied orbitals in reference states of arbitrary spin multiplicity are generated.

A pattern calculus for the unitary group approach to the electronic correlation problem

A pattern-type calculus is formulated enabling a very simple generation of the N-electron spin-symmetry adapted orthonormal basis for an arbitrary spin multiplet as well as an efficient calculation of the matrix representatives of the elementary raising (lowering) generators in such bases. A simple example illustrating this technique is also presented.