Spin Interaction Constants Research Articles

Spin Order Transfer from a Parahydrogen Molecule to a Cyanide Ion in the Iridium Complex under the SABRE Conditions

A possibility of generating a high degree of spin polarization of 13C and 15N nuclei in the cyanide ion, which forms the coordination bond with the metal ion, using parahydrogen is demonstrated for the first time for the new iridium carbene complex as an example. The spin–spin interaction constants in the synthesized complex and the structure of the hydride intermediate are determined by an analysis of the 13С NMR spectra detected using broadband and selective heteronuclear decoupling. The cyanide ion is shown to coordinate to the metal ion by the carbon atom in one of two equatorial positions, and two pyridine molecules are arranged in the axial and equatorial positions. The signal amplification factors for 13С and 15N nuclei of the cyanide anion (5665 and –49 555, respectively) are estimated by NMR spectroscopy of the polarized substrate using the SABRE method from an ultralow magnetic field of 0.5 μT. This amplification corresponds to 15.5% polarization of nitrogen nuclei achieved within several seconds at room temperature.

N-Vicinity Method for Ising Model with Long-Range Interaction

The previously developed n-vicinity method [3] allows us to calculate accurately critical values of inverse temperatures for Ising models with short-range interaction. We generalize the method to the case of long-range interactions in spin systems and obtain theoretical formulas for the inverse temperatures in terms of the spin interaction constants. The comparison of our theoretical estimates with computer simulations for the two- and three-dimensional Ising models shows that the larger the dimension of the problem the better their agreement.

Eigenvalues of Ising connection matrix with long-range interaction

We examine multidimensional Ising systems on hypercube lattices and calculate analytically the eigenvalues of their connection matrices. We express the eigenvalues in terms of spin–spin​ interaction constants and the eigenvalues of the one-dimensional Ising connection matrix (the latter are well known). To do this we present the eigenvectors as Kronecker products of the eigenvectors of the one-dimensional Ising connection matrix. For periodic boundary conditions, it is possible to obtain exact results for interactions with an arbitrary large number of neighboring spins. We present exact expressions for the eigenvalues for two- and three-dimensional Ising connection matrices accounting for the first five coordination spheres (that is interactions up to next-next-next-next nearest neighbors). In the case of free-boundary systems, we show that in the two and three dimensions the exact expressions could be obtained only if we account for interactions with spins of not more than first three coordination spheres.

Analysis of a coupled spin drift–diffusion Maxwell–Landau–Lifshitz system

The existence of global weak solutions to a coupled spin drift–diffusion and Maxwell–Landau–Lifshitz system is proved. The equations are considered in a two-dimensional magnetic layer structure and are supplemented with Dirichlet–Neumann boundary conditions. The spin drift–diffusion model for the charge density and spin density vector is the diffusion limit of a spinorial Boltzmann equation for a vanishing spin polarization constant. The Maxwell–Landau–Lifshitz system consists of the time-dependent Maxwell equations for the electric and magnetic fields and of the Landau–Lifshitz–Gilbert equation for the local magnetization, involving the interaction between magnetization and spin density vector. The existence proof is based on a regularization procedure, L2-type estimates, and Moser-type iterations which yield the boundedness of the charge and spin densities. Furthermore, the free energy is shown to be nonincreasing in time if the magnetization–spin interaction constant in the Landau–Lifshitz equation is sufficiently small.

Tuning of exciton states in a magnetic quantum ring

The exciton states in a CdTe quantum ring subjected to an external magnetic field containing a single magnetic impurity are investigated. We have used the multiband approximation which includes the heavy hole–light hole coupling effects. The electron–hole spin interactions and the s, p–d interactions between the electron, the hole and the magnetic impurity are also included. The exciton energy levels and optical transitions are evaluated using the exact diagonalization scheme. We show that due to the spin interactions it is possible to change the bright exciton state into the dark state and vice versa with the help of a magnetic field. We propose a new route to experimentally estimate the s, p–d spin interaction constants.

Observation of positive and negative magneto-LC effects in all-organic nitroxide radical liquid crystals by EPR spectroscopy

The generation of spin glass-like inhomogeneous magnetic interactions (the average spin–spin interaction constant: > 0 or < 0), which we refer to as positive or negative “magneto-LC effects”, respectively, was observed in the bulk liquid crystalline (LC) phases of chiral all-organic radical compounds 2 with a positive dielectric anisotropy (Δε > 0) under weak magnetic fields. The sign and magnitude of depended on the type of LC phase or superstructure; stronger positive interactions ( > 0) operated in the chiral smectic A (SmA*) phase of (2S,5S)-2b (89% ee) than in the chiral nematic (N*) phase of (2S,5S)-2a (96% ee), whereas weak negative interactions ( < 0) were observed in the achiral nematic (N) phase of (±)-2a. The origin of the positive magneto-LC effects operating in the SmA* and N* phases was interpreted in terms of the generation of ferromagnetic head-to-tail spin–spin dipole interactions, whereas antiferromagnetic interactions arising from the formation of the RS magnetic dipolar interaction were responsible for the negative magneto-LC effects in the N phase.

Magnetic properties of a necklace spin ladder

The bottom part of the spectrum of a diagonal necklace spin ladder (s=1∕2) (NL) with spatial and spin anisotropy of neighboring interactions is studied using perturbation theory and numerical calculations which are performed by the Davidson and DMRG methods. It is shown that a first-order phase transition exists at zero temperature with respect to the spin anisotropy parameter, accompanied by a macroscopic jump in the magnetization. It is also shown that a plateau can appear in the field dependence of the magnetization with the z projection of the total spin M=1∕3Mmax as a result of the gap character of the excitations, which increase M. The amplitude of the spin wave characterizing the ground state of the NL with different isotropic spin interaction constants inside and between the cells takes on its maximum value when all interactions are the same.

Research on the temperature stability of triangular ferromagnetic nanowire arrays using the damage spreading method

The temperature stability of the quantum magnetic disk constructed on a triangular manowire array is studied by the damage spreading method. Three aspects are considered in order to make the Ising model more realistic. Firstly, we include the long-range interaction between spins. Secondly, we take into account the disorder of the nanowire lengths. At last, we present an estimation of the spin interaction constant through the system coercive force by deriving the relation between the spin interaction constant and the coercive force. It is shown that the longer the spin interaction acts, the more stable the system becomes. On the other hand, the system has greater temperature instability when the disorder degree of the nanowire lengths is increased.

Microwave spectra of O2–HF and O2–DF: Hyperfine interactions and global fitting with infrared data

Spectra of the open shell complexes O(2)-HF and O(2)-DF were recorded using Fourier transform microwave spectroscopy. A complete analysis of the hyperfine structure and a global fit including microwave and infrared frequencies [W. M. Fawzy, C. M. Lovejoy, D. J. Nesbitt, and J. T. Hougen, J. Chem. Phys. 117, 693 (2002)] are reported. The Fermi contact interaction between the electron and nuclear spins, the electron spin-nuclear spin dipolar interaction, the nuclear spin-nuclear spin dipolar interaction, and the nuclear electric quadrupole interaction (for O(2)-DF) were considered in the analysis. The correspondence between the magnetic hyperfine constants and the two nuclei of the H(D)F is unambiguously established. In both O(2)-HF and O(2)-DF, the Fermi contact parameter is larger for the fluorine than for the hydrogen, while for the nuclear spin-electron spin dipolar hyperfine constants, the reverse is true. The effective angle between the HF bond and the a axis of the complex, determined from the nuclear spin-nuclear spin interaction constant, is 38(4) degrees. The same angle for the DF complex, derived from the deuterium nuclear quadrupole coupling constant, is 31(4) degrees.

Fourier transform microwave spectroscopy of isotopically substituted diacetylenes: rs-structure, quadrupole coupling, and anisotropic nuclear spin–spin interaction

Monodeuterated diacetylene (HCCCCD) and its 13C-substituted species H 13CCCCD, HC 13CCCD, HCC 13CCD, and HCCC 13CD were investigated by Fourier transform microwave spectroscopy. The D nuclear quadrupole splittings were almost completely resolved. For H 13CCCCD hyperfine splittings caused by the anisotropic nuclear spin–spin interaction between the H and 13C nuclei were also observed. The analysis yielded rotational constants, centrifugal distortion constants, and the constants for the nuclear quadrupole coupling and anisotropic nuclear spin–spin interaction. The substitution structure of HCCCCD was calculated as follows: r s(C–H) = 1.056054(39) Å, r s(C C) = 1.208631(4) Å, r s(C–C) = 1.374117(6) Å, r s(C C) = 1.208116(4) Å, and r s(C–D) = 1.056231(17) Å, in the order of the arrangement of the bonds. A rough estimate of the equilibrium structure is also presented. The eQq constant for the deuterium nucleus is 0.2061(4) MHz. The anisotropic 13C–H spin–spin interaction constant was experimentally determined for the first time as b = −29.2(15) kHz, which is defined as the coefficient of (3 I 2 z I 3 z − I 2 · I 3), where I 2 and I 3 denote the H and 13C nuclear spins, respectively, and I 2 z and I 3 z their components along the molecular axis. The observed b constant is not accounted for by the direct magnetic dipole–dipole interaction only, suggesting a significant contribution from indirect anisotropic interaction.

Theoretical Study on Electronic and Spin Structures of [Fe2S2]2+,+ Cluster: Reference Interaction Site Model Self-Consistent Field (RISM-SCF) and Multireference Second-Order Møller−Plesset Perturbation Theory (MRMP) Approach

Electronic structures of [Fe(2)S(2)(SCH(3))(4)](2-,3-) in DMSO solution are calculated using reference interaction site model complete active space self-consistent field (RISM-CASSCF)/multireference second-order Møller-Plesset perturbation theory (MRMP) method. For the reduced state, we obtain both the low-spin Fe(3+)Fe(2+) localized and high-spin Fe(2.5+)Fe(2.5+) delocalized forms, which are very close in energy. The spin interaction constants obtained from the energies of states with various spin multiplicities are in good agreement with the available experimental estimates both for the oxidized and for the reduced states. The dynamic electron correlation effect is found to be important in estimating the spin interaction between the Fe ions. The redox potentials are calculated to be 2.87 and 2.78 eV for the localized and delocalized reduced states, respectively, which are close to the experimental values. We devise a simple model for calculating the free energy curves of the reduction process based on the RISM-SCF theory. The activation barrier height is calculated to be 7.4 kcal/mol at the equilibrium geometry of oxidized state, indicating that the reduction reaction will occur efficiently in DMSO solvent. The effect of solvent fluctuation on the free energy profiles is discussed on the basis of the present calculations.

Time-resolved infrared diode laser spectroscopy of the ν3 band of the jet-cooled Fe(CO)2 radical produced by ultraviolet photolysis of Fe(CO)5

The infrared spectrum of the iron dicarbonyl radical Fe(CO)2 produced in a supersonic jet expansion by the excimer laser photolysis of iron pentacarbonyl Fe(CO)5 was observed by time-resolved infrared diode laser spectroscopy. About 170 transitions, each split into one or two fine structure components, were assigned to the ν3 (CO antisymmetric stretch) band of Fe(CO)2. The assignment was greatly facilitated by spectral simplification caused by rotational as well as vibrational cooling in the supersonic jet. It was observed that lines are missing at alternate J quantum numbers in each spin component, which confirmed that Fe(CO)2 is a linear molecule with D∞h symmetry and that the electronic ground state is of 3Σg− symmetry. The rotational and centrifugal distortion constants in the ground state were determined to be B0=1414.675(46) MHz and D0=0.3077(74) kHz, respectively. The spin–spin interaction constants obtained, λ0=655.3(42) GHz, is comparable with that of the FeCO radical, λ0=684.470(51) GHz. The ν3 band origin was determined to be 1928.184335 (82) cm−1. The figures in parentheses are uncertainties (1σ) in units of the last digit.

Spin coupling between magnetic impurities in metals.

The spin scattering of conduction electrons by the local moments of transition-metal ions dissolved in metals, e.g., manganese in copper or silver, comes from the s-d mixing interaction. The characteristic energy and angular dependence of this scattering has a marked influence on the spin coupling between two local moments. We have derived expressions for this coupling due to s-d mixing. However, rather than evaluate the coupling itself, its envelope is much more relevant when one is interested in the range of the coupling. We have determined the envelope function by using only single-ion parameters. We find that in the range Rl15a, the decay of the spin coupling is much slower than that of the Rudermen-Kittel-Kasuya-Yosida interaction, i.e., 1/${R}^{3}$. This difference comes from the energy and angular dependence of the scattering which have been taken into account in the calculation. The calculations are made both with and without mean-free-path effects. We find that the preasymptotic corrections are far more important than mean-free-path effects for dilute systems. We have also calculated spin-interaction constants. Our results are very close to the values obtained from the low-field magnetization measurements.

Infrared diode laser kinetic spectroscopy of the CCO radical in the X̃ 3Σ− state generated by the excimer laser photolysis of carbon suboxide

The ν1 band of the CCO radical in the X̃ 3Σ− ground electronic state has been observed in the gas phase by diode laser kinetic spectroscopy. The CCO radical was generated by the 193 or 248 nm excimer laser photolysis of carbon suboxide. By fixing ground state parameters to the microwave values, the band origin and the vibrational changes of the rotational (αB=B0−B1) and spin–spin interaction (αλ=λ1−λ0) constants have been determined to be 1970.864 34(95), 0.003 075 4(85), and 0.008 3(12) in cm−1 with 2.5 standard errors in parentheses.

Test of exchange models in BCC 3He by neutron scattering

A quasi-elastic neutron scattering study of bcc 3 He in the paramagnetic phase at T ≈ 10 mK is proposed. The measurement of the wavevector dependent static susceptibility could give the effective two spin interaction constants J n ( n = 1, 2, 3,…) between nth neighbours and provide a new test of the three + four particle exchange model which provides characteristic relations between the effective J n .

Fine structure of 3s,3d: 3Σ, 3Π, 3Δ complex of H2 by Doppler-free, laser spectroscopy

We have used the method of Doppler-free laser spectroscopy to resolve, for the first time, the fine structure of the H2, 3s,3d complex: h (3s)3Σg+, g (3d)3Σg+, i (3d)3Πg, and j (3d)3Δg. A collimated beam of H2 molecules in the metastable c 3Πu state was crossed with a tunable, dye laser beam. The absorbed light quenched the metastable molecules and changed the detected molecular beam intensity. The 3s,3d fine structure intervals have been measured to an accuracy of a few MHz (∼0.0001 cm−1) for all of the rotational levels in the v=0, 1 levels, which are connected by allowed transitions to the N=2 rotational level of the c (2p)3Πu state of parahydrogen. The fine structure constants of the N=1 rotational level of the i (3d)3Πg− state, extrapolated to the equilibrium internuclear separation are Aπ+γ=−145±4MHz and Bπ0−√6Bπ2=958±13MHz and MHz. These results are discussed in terms of the transition from united to separated atom values. The remaining states are coupled to each other by configuration interaction and rotational interactions. By parametrizing such interactions, we find that an account of the fine structure of these states can be given by considering only interactions within the triplet 3s, 3d complex. With only one exception, interactions with states outside this complex do not have to be taken into account. This analysis gives values for 15 spin interaction constants.

The ESR spectrum and linewidth measurements of atomic iodinea)

The experimental spectrum from ground-state 2P3/2 atomic iodine is compared with a theoretical calculation using a best-fit g value equal to 1.333980±0.000006 and previously determined nuclear and electronic spin interaction constants. A rate coefficient for iodine-atom wall recombination (γ?10−3) is reported. Broadening coefficients and hyperfine interaction relaxation cross sections for the iodine-atom ground state with He, O2, and HI are determined from the line broadening of the MJ=3/2→1/2 and MJ=1/2→−1/2 transitions of I and compared with theory.

Hyperfine Structure of Thallium Chloride

The radio-frequency spectra of TlCl at very weak electric and magnetic fields have been measured with a molecular beam electric resonance spectrometer. From these spectra the hyperfine interaction constants for the four isotopic species of the molecule were calculated. The constants for 205Tl35Cl in the J = 2, υ = 0 state are: eqQ = − 15793.32(50) kHz, cCl = 1.38(10) kHz, cTl = 76.35(10) kHz, c3 = − 0.13(10) kHz, c4 = − 1.54(10) kHz. A test was made for the polarization of the chlorine nucleus in the electric field of the molecule by comparing the ratio of the quadrupole interaction constants for 205Tl35Cl and 205Tl37Cl to the ratio of the quadrupole interaction constants for the free chlorine atoms. The agreement of the two ratios is within their uncertainties, thus providing no evidence for a polarization effect. In addition, the dependence of the spin–rotation and spin–spin interaction constants on isotope was found to show good agreement with theory.

Radio-Frequency Spectra of KF and KCl by the Molecular-Beam Electric-Resonance Method

The molecular-beam electric-resonance method has been used to obtain quadrupole-coupling constants eq(v)Q, spin—rotation constants c, and tensorial and scalar spin—spin interaction constants dT and dS for 39K19F, 39K35Cl, and 39K37Cl in several vibrational states. For 39K35Cl and 39K37Cl also the electric dipole moments have been determined. For the first five measured vibrational levels of 39K19F and 39K35Cl, the values of the quadrupole coupling constants and dipole moments can be written as a polynomial of second degree in (v+½).

Rotational Analysis of Some Bands of the Triplet←Singlet Transition in Formaldehyde

Using the absorption frequencies measured by Robinson and DiGiorgio, a rotational analysis of the 0+←0 and 1+←0 bands of the 3A2←1A1 transition in H2CO has been performed. Each band contains a number of overlapping subbands which are themselves made up of several branches consisting of individual rotational lines. Despite the overlapping, it was found possible to give assignments to a large number of lines. All branches are q-type branches; that is, only ΔK = 0 transitions are observed. The positions of the triplet-state rotational levels relative to the lowest rotational level of the ground vibronic state were obtained with the aid of the very accurate ground-state rotational levels determined interferometrically by Parkin and Poole. These triplet-state levels were found to fit accurately the Hamiltonian proposed by Van Vleck for an asymmetric-rotor molecule in a triplet electronic state provided that further terms were added to take account of rotational distortion. Values of the rotational constants, rotational distortion constants, and spin-interaction constants of the 3A2(0+) and 3A2(1+) states have been determined. The rotational constants for the 3A2(1+) state are as follows: A = 8.6275 (±0.0008) cm−1; B = 1.1491 (±0.0001) cm−1; and C = 1.0343 (±0.0001) cm−1. The results for the 3A2(0+) state are very similar. From these constants it is possible to show that the equilibrium nuclear geometry of formaldehyde in this state is highly nonplanar, the geometrical parameters having the following values: r(C–H) = 1.10 Å; r(C–O) = 1.28 Å; ∠HCH = 118°; out-of-plane angle = 36°. The spin-interaction constants, which determine the extent of the triplet splitting of the rotational levels, take account not only of spin—molecular rotation, spin—orbit, spin—other-orbit, and spin—spin interactions, but also of the effect of rotational asymmetry upon these interactions. The observed relative intensities of the rotational lines agree very well with those predicted by the recent theory of Hougen. In particular, the almost complete absence in the spectrum of transitions to the F2 component of the triplet state is understandable in the light of this theory. As a consequence of the fact that only ΔK = 0 transitions are observed (the theoretically possible ΔK = ±2 transitions were not detected), it is possible to deduce with the aid of Hougen's theory that it is a 1A1 state that, by spin—orbit coupling with the 3A2 state, permits the formally forbidden triplet←singlet bands to occur. This result is in complete agreement with the theoretical deductions of Sidman made some years ago.