Total Spin Quantum Number Research Articles

Independent magnon states on magnetic polytopes

For many spin systems with constant isotropic antiferromagnetic next-neighbour Heisenberg coupling the minimal energies E_{min}(S) form a rotational band, i.e. depend approximately quadratically on the total spin quantum number S, a property which is also known as Lande interval rule. However, we find that for certain coupling topologies, including recently synthesised icosidodecahedral structures this rule is violated for high total spins. Instead the minimal energies are a linear function of total spin. This anomaly results in a corresponding jump of the magnetisation curve which otherwise would be a regular staircase.

Magnetic-field-dependent heat capacity of the single-molecule magnet [Mn(12)O(12)(O(2)CEt)(16)(H(2)O)(3)

Accurate heat capacities of the single-molecule magnet [Mn(12)O(12)(O(2)CEt)(16)(H(2)O)(3)] were measured from 0.3 to 311 K by adiabatic calorimetry without an external magnetic field. Heat-capacity anomalies were separated by assuming several contributions including lattice vibration, magnetic anisotropy, and hyperfine splitting. Among them, a tiny thermal anomaly between 1 and 2 K is attributable to the presence of Jahn-Teller isomers. The heat capacities of the polycrystalline sample were also measured with applied magnetic fields from 0 to 9 T in the 2-20 K temperature region by the relaxation method. With an applied magnetic field of up to 2 T, a steplike heat-capacity anomaly was observed around the blocking temperature T(B) approximately 3.5 K. The magnitude of the anomaly reached a maximum at 0.7 T. With a further increase in the magnetic field, the step was decreasing, and finally it disappeared above 3 T. The step at T(B) under 0.7 T can be roughly accounted for by assuming that a conversion between the up-spin and down-spin states is allowed above T(B) by phonon-assisted quantum tunneling, while it is less effective below T(B). Excess heat capacity under a magnetic field revealed a large heat-capacity hump around 14 K and 2 T, which would be attributed to a thermal excitation from the S = 9 ground state to the spin manifold with different S values, where S is the total spin quantum number.

Selection rule of ESR for spin-gap systems

The direct ESR absorption between the singlet ground and triplet excited states of the spin-gap systems is investigated. Such an absorption, which is forbidden by the conservation of the total spin quantum number in the ordinary Heisenberg-Hamiltonian, is caused by the Dzyaloshinskii–Moriya interaction. We show the selection rule in the presence of the interaction, using the exact diagonalization of the finite cluster of the quasi-one-dimensional bond-alternating spin system. The selection rule is also modified into a suitable form for the investigation of the recent experimental result for CuGeO 3.

The gap symmetry in the Hubbard model

The gap symmetry for both the attractive (U<0) and repulsive (U> 0) Hubbard models has been studied. The gap symmetry in both singlet and triplet channels as well as in charge and spin channels is considered. It is shown that the gap for the attractive Hubbard model exists in the spin channel only, and has s-wave symmetry (ℓ = 0, where ℓ is the orbital momentum) for the spin-triplet state of p-wave symmetry (ℓ = 1) for the spin-singlet state with j = s + ℓ = 1, the total spin and orbital quantum number of a pair. The attractive Hubbard model describes superfluidity in the spin-channel and is an adequate model for liquid 3He as shown. However, for the repulsive Hubbard model the gap exists in the charge channel only and has s-wave (ℓ = 0) or d-wave (ℓ = 2) symmetry for the spin-angle state. The repulsive Hubbard model describes superconductivity in the charge channel. It is also shown that in the 2D case the strongly anisotropic s-wave gap has nodes in the direction of the nesting wave vector resembling the d x− y 2-wave symmetry.

An Electron Spin Resonance Selection Rule for Spin-Gapped Systems

The direct electron spin resonance (ESR) absorption between a singlet ground state and the triplet excited states of spin gap systems is investigated. Such an absorption, which is forbidden by the conservation of the total spin quantum number in isotropic Hamiltonians, is allowed by the Dzyaloshinskii-Moriya interaction. We show a selection rule in the presence of this interaction, using the exact numerical diagonalization of the finite cluster of the quasi-one-dimensional bond-alternating spin system. The selection rule is also modified into a suitable form in order to interpret recent experimental results on CuGeO$_3$ and NaV$_2$O$_5$.

Electron spin resonance and theoretical studies of the 14N⋅⋅⋅⋅14N and 15N⋅⋅⋅⋅15N spin-pair radicals in neon matrices: The effects of mixing among the 1Σg+, 3Σu+, 5Σg+, and 7Σu+ electronic states

The first experimental and theoretical study of the N⋅⋅⋅⋅N spin-pair radical is reported. Its high-resolution ESR (electron spin resonance) spectrum has been observed in neon matrices and interpreted on the basis of weakly interacting atoms using a model recently developed for the H⋅⋅⋅⋅H spin-pair. To fully interpret the N⋅⋅⋅⋅N radical results it was necessary to include electronic state mixing effects among all possible spin states, namely the 1Σg+, 3Σu+, 5Σg+, and 7Σu+ states. Several different trapping sites were observed which indicated the interaction of N atoms at distinctly different separation distances in the neon lattice. Calculated J values at the complete active space self-consistent field (CASSCF) level (TZP basis set) were compared with the experimental results for the various trapping site distances. The 15N⋅⋅⋅⋅15N radical in the dominant trapping site had magnetic parameters of g=2.0016(2), A(15N)=15.9(1) MHz, D=−178(1)MHz and J=468(2) MHz. Using the point dipole approximation this corresponds to a N⋅⋅⋅⋅N separation distance of 6.41 Å. A most unusual type of magnetic dipole transition was observed that involves a transition between electronic states of formally different S values where S is the total spin quantum number for a given electronic state.

Phase diagram of the 1D Kondo lattice model

We determine the bounday of the fully polarized ferromagnetic states in the one dimensional Kondo lattice model at partial conduction electron band filling by using a newly developed infinite size DMRG method which conserves the total spin quantum numbers. The obtained paramagnetic to ferromagnetic phase bounday is bellow J ≍ 3.5 for the whole range of band filling. By this we solve the controversy in the phase diagram over the extent of the ferromagnetic region close to half filling.

The First Four Moments of the Spectral Density Distribution of an N-Electron Hamiltonian Matrix Defined in an Antisymmetric and Spin-Adapted Model Space

Expressions for the first four moments of the spectral density distribution of a Hamiltonian matrix describing a system of N spin 1/2 particles are tabulated. The Hamiltonian matrix is defined in a model space of antisymmetrized products of spinorbitals combined to form eigenfunctions of the total spin operators. The moments are given as explicit functions of the interaction integrals and of three integers describing the space (the total number of particles, the total number of orbitals, the total spin quantum number).

N-Alkyl Group-Substituted Poly(m-aniline)s: Syntheses and Magnetic Properties

Preparation of n-alkyl group-substituted derivatives of poly(m-aniline) that we have proposed as a possible organic ferromagnetic polymer has been attempted. We started from the syntheses of the monomers, n-alkyl-substituted m-bromoanilines (R = methyl, ethyl, hexyl, dodecyl, and hexyloxy groups). The approximate solubilities of the methyl, ethyl, and hexyloxy group-substituted polymers in N-methyl-2-pyrrolidone (NMP) were nearly equal to that of poly(m-aniline). On the other hand, hexyl- and dodecyl-substituted polymers have high solubilities in the conventional organic solvents such as acetone, dichloromethane, and so forth. The ferromagnetic spin correlation was observed in the polymer oxidized by NOBF 4 in the temperature range above 50 K. The average total spin quantum number was determined to be 1.0 at 2 K. Moreover, in all polyradical samples, a weak antiferromagnetic interaction between spin clusters was observed at very low temperatures probably due to a conformational change in the present poly(m-aniline) derivatives.

Magnetic-susceptibility and magnetization measurements of polyacenic semiconductive materials.

Magnetic-susceptibility and magnetization measurements of several kinds of polyacenic semiconductive (PAS) materials prepared from the heat treatment (470--750 \ifmmode^\circ\else\textdegree\fi{}C) of phenol-formaldehyde resin were carried out using the Faraday-balance method. Magnetic parameters were determined from the analysis of the magnetic susceptibility measured in the temperature range 2--260 K. The temperature dependence of the magnetic susceptibility of each sample obeys a weak Curie-Weiss-type law. Analyses of the magnetization curves observed in the magnetic-field range 0--5 T have shown that the total spin quantum number S of the pristine PAS samples is in the range 1/2S1 and that of the ${\mathrm{I}}_{2}$-doped sample is S=1/2. Connection between the magnetic properties obtained here and electrical conductivity will be discussed in detail.

Theory of the Resonating Valence Bond in Quantum Spin System

The theory of the resonating valence bond (RVB) for the antiferromagnetic Heisenberg model of spin 1/2 proposed by Anderson is generalized by taking account of singlet bonds connecting distant spins, and is solved exactly for the finite lattice. It is shown that the RVB wave function is S tot (total spin quantum number)=0, and that replacing a part of singlet bonds by triplet bonds, eigenfunctions with S tot =1, 2, … can be constructed. These are the new representation of eigenfunctions of the Heisenberg Hamiltonian.

Zeeman, hyperfine, and magnetic dipolar effects on the EPR spectrum of a cubic copper tetramer

The Zeeman interaction for an isolated multiplet of a cubic Cu2+ tetramer, characterized by the total spin quantum number S, is shown to be essentially isotropic, with g=(g∥+2g⊥)/3, where g∥ and g⊥ are single Cu2+ ion components. Matrix elements are given for the off-diagonal part of the Zeeman interaction within the three S=1 multiplets. The hyperfine structure for each isotope in a [100] direction is shown to be a 13 line structure. The intracluster magnetic dipole–dipole (MDD) interaction has nonzero matrix elements within the three S=1 multiplets, which are degenerate for an isotropic exchange interaction with equal coupling constants. With the MDD interaction treated as a perturbation of the Zeeman interaction, it is found that the single line at g=2.10, expected on the basis of the Zeeman interaction alone, is split into four lines separated from the former line by ±h0 and ±2h0, where h0≂480 G. The MDD coupling constant, calculated assuming point dipoles, is an order of magnitude too small to explain the zero-field splitting of the S=2 multiplet measured by EPR in Cu4OCl6(TPPO)4.

Matrix elements of a spin-adapted reduced Hamiltonian.

A formalism based on the unitary- and symmetric-group approaches to configuration-interaction methods has been applied to an evaluation of matrix elements of a spin-adapted reduced Hamiltonian (SRH). It has been shown that there is a simple closed-form expression for the matrix elements of the SRH matrices. This formula has been expressed as a linear combination of two-electron integrals with coefficients given as explicit functions of the parameters defining the finite-dimensional Hilbert space (number of orbitals, number of electrons, and the total spin quantum number).

Dilation operator in gauge theories

The electromagnetic field is expanded in a series of O(4) eigenstates of total spin, and quantized by specifying commutators on surfaces of constant ${x}_{\ensuremath{\mu}}{x}^{\ensuremath{\mu}}={R}^{2}$ in four-dimensional Euclidean space. It is demonstrated that, under an arbitrary gauge transformation, some of the O(4) eigenstates are invariant; these gauge-invariant states are labeled by SU(2) \ensuremath{\bigotimes} SU(2) total (orbital plus internal) spin quantum numbers ($A$,$B$) and with $A\ensuremath{\ne}B$. Only these gauge-invariant states are nontrivial in the absence of sources, and are quantized. The leading-twist quantum states of the dilation field theory contain the minimum number of these dilation photons. The remaining spin degrees of freedom of the electromagnetic field are most simply written as a function of the form ${\ensuremath{\partial}}_{\ensuremath{\mu}}\ensuremath{\varphi}(x)+{x}_{\ensuremath{\mu}}\frac{\ensuremath{\psi}(x)}{{R}^{2}}$. $\ensuremath{\varphi}(x)$ is obviously devoid of physics while $\ensuremath{\psi}(x)$ is a classical field propagating between radial projections of two electrical currents ${x}_{\ensuremath{\mu}}{J}^{\ensuremath{\mu}}(x)$ and ${y}_{\ensuremath{\mu}}{J}^{\ensuremath{\mu}}(y)$ only if ${x}_{\ensuremath{\mu}}{x}^{\ensuremath{\mu}}={y}_{\ensuremath{\mu}}{y}^{\ensuremath{\mu}}$. The quantization procedure described herein may be applied to non-Abelian theories. The procedure does not lead to a gauge-invariant decomposition of a non-Abelian field, but the identification of leading-twist quantum states is preserved in the zero-coupling limit.

Magnetic Measurements on Stable Fe(0) Microclusters. Part I

AbstractFe(0) microclusters have been isolated in a zeolite matrix. The magnetization isotherm at 4.2 K has been analyzed in terms of a sum of Brillouin functions corresponding to a distribution of cluster sizes. Each function represented a fraction of individual clusters with total cluster spin quantum number (N · S). The (N · S)‐value of clusters with an average of 7 atoms per cluster was found to be 4.

Spin quantum number in the ground state of the Mattis-Heisenberg model

Total spin quantum number is rigorously calculated for a quantum version of the Mattis model of random spin systems. Crossover between three universality classes of the Ising model, theXY model, and the Heisenberg model is explicitly worked out in the presence of randomness. The randomness of the type of the Mattis model is shown to have no thermodynamic effects even in quantum systems.

Electron scattering from hydrogen: Collisions in which the total spin quantum numbers change

In several recent experiments in which spin-polarized electrons were scattered from hydrogen atoms the investigators isolated the spin-exchange effects which arise in the theory from the antisymmetrization of the wave functions of the electrons. Noting the recent advances in techniques of producing and detecting polarized electrons, this paper considers the possibility of finding the terms in the effective transition operator that are spin dependent. The spin-dependent parts of the first Born term in the transverse photon and the instantaneous photon are calculated. The $1s\ensuremath{-}1s$, $1s\ensuremath{-}2s$, and $1s\ensuremath{-}2p$ scattering amplitudes are discussed specifically. A brief comparison is made of the magnitude of these effects and the accuracy of the present experiments.

EPR of Crystals of Na4[(Fe EDTA)2O]12H2O

Crystals of Na 4 [(Fe EDTA) 2 O]12H 2 O were investigated by means of electron paramagnetic resonance (EPR) spectroscopy. The spectra were obtained at various temperatures and crystals orientations. These spectra are very complex and have many absorption bands. The antiferromagnetic coupling between the iron atoms in the bridge Fe-O-Fe gives rise to states with total spin quantum number S=0, 1, 2, 3, 4, and 5. Analyses of the EPR spectra as a function of temperature permitted the identification of the EPR absorption lines. They were found to be due to the state with S=2. It was also possible to evaluate the exchange parameter as J≃202±10 cm -1 . From the study of the angular dependence of the absorption lines it was found that the magnetic axes X , Y , Z and the trial crystal axes a , b , c are related with a precision of 5°, by

The spin optimized separated pair method

The separated pair method, for systems containing even and odd numbers of electrons, is generalized by allowing for contributions from all available spin coupled states of the same total spin quantum numbers S and M. The total wavefunction is expressed as a linear combination of products of a given spin eigenfunction, which is constructed out of singlet and triplet coupled pairs, and a suitable spatial function built out of symmetric (for singlet) and antisymmetric (for triplet) spatial pair functions. The electron and spin density functions are then presented in a ‘ sum of pair ’ densities form, so enabling the effects of spin optimization on the chemical bonding to be interpreted in a simple and obvious way. Finally, a discussion is given of the practical application of the spin optimized separated pair method.

Transformation Properties of Antisymmetric Spin Eigenfunctions under Linear Mixing of the Orbitals

After recalling the duality between the general linear group GL(m), represented by its N-fold inner product, and the permutation group SN, we have given a survey of its quantum chemical consequences. It causes the one-to-one correspondence between the total spin quantum number and the permutation symmetry of N-electron spin functions, and, via the Pauli principle which imposes permutation symmetry on the spatial part also, it leads to specific properties of antisymmetric spin eigenfunctions under orbital transformations. Such functions can be classified according to the irreducible representations of GL(m). For special orbital transformations, often occurring in quantum chemistry, which mix only orbitals in different subsets among each other, we have derived how the transformation of the N-electron wavefunctions simplifies, by a reduction of the representations of GL(m). The theory is illustrated by an example and some applications are discussed.