Molecular magnetism of a linear Fe(III)-Mn(II)-Fe(III) complex. Influence of long-range exchange interaction

The magnetic properties of [L-Fe(III)-dmg₃Mn(II)-Fe(III)-L] (ClO₄)₂ have been characterized by magnetic susceptibility, EPR, and Mössbauer studies. L represents 1,4,7-trimethyl-, 1,4,7-triazacyclononane and dmg represents dimethylglyoxime. X-ray diffraction measurements yield that the arrangement of the three metal centers is strictly linear with atomic distancesd _Fe-Mn=0.35 nm andd _Fe-Fe=0.7 nm. Magnetic susceptibility measurements (3–295 K) were analyzed in the framework of the spin-Hamiltonian formalism considering Heisenberg exchange and Zeeman interaction:=J _Fe-Mn(S _Fe1+S _Fe2)S _Mn +J _Fe-Fe(S _Fe1 S _Fe2) +g_B S _total B. The spinsS _Fe1=S _Fe2 =S _Mn=5/2 of the complex are antiferromagnetically coupled, yielding a total spin ofS _total=5/2 with exchange coupling constantsF _Fe-Mn=13.4 cm^–1 andJ _Fe-Fe= 4.5 cm^–1. Magnetically split Mössbauer spectra were recorded at 1.5 K under various applied fields (20 mT, 170 mT, 4T). The spin-Hamiltonian analysis of these spectra yields isotropic magnetic hyperfine coupling withA _total/(g _{N N})=–18.5 T. The corresponding local componentA _Fe is related toA _total via spin-projection:A _total=(6/7)A_Fe. The resultingA _Fe/(g _NN)=–21.6 T is in agreement with standard values of ferric high-spin complexes. Spin-Hamiltonian parameters as obtained from Mössbauer studies and exchange coupling constants as derived from susceptibility measurements are corroborated by temperature-dependent EPR studies.     

SU(2)L×SU(2)R×U(1) gauge model

We determine here the most general electroweak interaction based on the groupSU(2)_L×SU(2)_R×U(1). When we rotate theZ ₁,Z ₂ basis to theZ,D basis such that the total interaction ofZ with the right-handed current is zero, we obtain an interaction that is free of triangle anomalies. This condition enables us to know the angle through whichZ ₁,Z ₂ basis is to be rotated. We show that the triangle anomaly free interaction obtained by others is contained here as a special case. We also determine the triangle anomaly free weak interaction whenever the neutral (Z,D) bosons are mass eigenstates and show that it reduces to the neutral sector of the standard model whenever g _R ² goes to infinity. The charged sector is also developed here. The most general elements of the masssquared matrix of theZ,D bosons are evaluated. The masses of the left- and right-handed charged bosons are also determined.     

Intervalley electron scattering by phonons in (AlAs)1(GaAs)3(001) superlattices

Intervalley electron scattering by phonons in (AlAs)₁(GaAs)₃(001) superlattices is studied using the pseudopotential method and a phenomenological model of the bonding forces. The deformation potentials between the conduction band extrema of the superlattice involving short-and long-wavelength phonons are calculated. It is shown that the mixing of states from the zinc-blende L valleys plays a greater role in intervalley scattering in a superlattice than the Γ-X mixing. In particular, due to L-L mixing, the Γ-X ₃ transitions, analogous to Γ-L transitions in zinc blende, have higher intensities than the analogues of Γ-X transitions (Γ₁-M ₅ and (Γ₁-Γ₃ transitions). The deformation potentials averaged over the scattering channels in the superlattice agree with the corresponding potentials in a solid solution, but all transitions in the superlattice have higher intensities for the lower states.     

High-Resolution Infrared and Millimeter-Wave Study of the v(3) = 1 State of HSiF(3) and DSiF(3)

Millimeter-wave spectra of HSiF₃ and DSiF₃ in the v₃ = 1 excited state have been measured from 100 to 490 GHz. Infrared spectra have been recorded in the ν₃ regions, ν₀ 424.0301 and 420.9320 cm⁻¹ in HSiF₃ and DSiF₃, respectively, with a resolution of 2.4 × 10⁻³ cm⁻¹. Since in both species the parameters α^B₃ and α^C₃ have very similar values, no K structure could be resolved in the ^QP and ^QR clusters for low-to-medium K values. For high J the effect of the ground state D_JK term more and more dominates and spreads the J clusters into opposite directions such that medium-to-high K components, particularly those with K = 3p, are resolved. Rotational and infrared data have been fitted together using a model up to sextic centrifugal distortion constants. No perturbations were indicated. Hot bands (ν₃ + nν₆)–nν₆ with n = 1, 2, and 3 have been detected and analyzed.     

New approach in theory of Clebsch-Gordan coefficients foru(n) andU q(u(n))

A new method for calculation of Clebsch-Gordan coefficients (CGCs) of the Lie algebrau(n) and its quantum analogU _q(u(n)) is developed. The method is based on the projection operator method in combination with the Wigner-Racah calculus for the subalgebrau(n−1) (U _q(u(n−1))). The key formulas of the method are couplings of the tensor and projection operators and also a tensor form of the projection operator ofu(n) andU _q(u(n)). It is shown that theU _q(u(n)) CGCs can be presented in terms of theU _q(u)(n−1)) q−9j-symbols. Presented at the 9th International Colloquium: “Quantum Groups and Integrable Systems”, Prague, 22–24 June 2000. Supported by Russian Foundation for Fundamental Research, grant 99-01-01163. Supported in part by the U.S. National Science Foundation under Grant PHY-9970769 and Cooperative Agreement EPS-9720652 that includes matching from the Louisiana Board of Regents Support Fund.     

Raman studies and optical properties of some (PbO)x(Bi2O3)0.2(B2O3)0.8−x glasses

Five (PbO)_x(Bi₂O₃)_0.2(B₂O₃)_0.8−x glasses, where x = 0, 0.2, 0.3, 0.4 and 0.6, were prepared. The dilatometric glass transition temperature (T_g) was found in the region 470 (x = 0)≥ T_g ( °C) ≥ 347 (x = 0.6), and the density (ρ) varied within 4.57 (x = 0) ≤ ρ (g/cm³) ≤ 8.31 (x = 0.6). Raman spectra indicated the conversion of BO₃ to BO₄ entities for low x values but for x > 0.3, namely, for x → 0.6, back‐conversion occurred, most probably. From the measurements of the optical transmission on very thin bulk samples, the room temperature optical gap values (E_g) were determined to be in the range 4.03 (x = 0)≥ E_g (eV) ≥ 3.08 (x = 0.6). The temperature (T) dependence of the optical gap (E_g(T)) in the region 300 ≤ T(K) ≤ 600 was examined and approximated by a linear relationship of the form of E_g(T) = E_g(0)− γT, where γ × 10⁻⁴(eV/K) varied from 5.1 to 6.8. The non‐linear refractive index (n₂) was estimated from the optical gap values and it was found to correspond to the n₂ values calculated from the experimental third‐order non‐linear optical susceptibility taken from the literature. Copyright © 2008 John Wiley & Sons, Ltd.     

Realization ofU q (so(N)) within the differential algebra onR q N

We realize the Hopf algebraU _q–1 (so(N)) as an algebra of differential operators on the quantum Euclidean spaceR _q ^N . The generators are suitableq-deformed analogs of the angular momentum components on ordinaryR ^N . The algebra Fun(R _q ^N ) of functions onR _q ^N splits into a direct sum of irreducible vector representations ofU _q–1 (so(N)); the latter are explicitly constructed as highest weight representations.     

On a nonstandard two-parametric quantum algebra and its connections withU p,q (gl(2)) andU p,q(gl(1/1))

A quantum algebraU _{p, q} (,H,X _±) associated with a nonstandardR-matrix with two deformation parameters (p, q) is studied and, in particular, its universal -matrix is derived using Reshetikhin's method. Explicit construction of the (p, q)-dependent nonstandardR-matrix is obtained through a coloured generalized boson realization of the universal -matrix of the standardU _{p, q}(gl(2)) corresponding to a nongeneric case. General finite dimensional coloured representation of the universal -matrix ofU _{p, q}(gl(2)) is also derived. This representation, in nongeneric cases, becomes a source for various (p, q)-dependent nonstandardR-matrices. Superization ofU _{p, q}(,H,X _±) leads to the super-Hopf algebraU _{p, q}(gl(1/1)). A contraction procedure then yields a (p, q)-deformed super-Heisenberg algebraU _{p, q}(sh(1)) and its universal -matrix.     

(La0.7Sr0.3MnO3 )m(BiFeO3)n 超晶格结构的导电机理

利用射频磁控溅射的方法在SrTiO₃(001) 基片上制备了(La_0.7Sr_0.3MnO₃)_m(BiFeO₃)_n超晶格结构.对所制备的超晶格结构进行了50—150℃温度范围内的电流-电压测试分析.结果表明,随着BiFeO₃薄膜的厚度减小,温度的升高,(La_0.7Sr_0.3MnO₃)_m(BiFeO₃)_n超晶格结构的电流变大.进一步根据介质导电模型对(La_0.7Sr_0.3MnO₃)_m(BiFeO₃)_n超晶格结构的导电特性做了分析.在温度较低或者电场较弱时,所制备的(La_0.7Sr_0.3MnO₃)_m(BiFeO₃)_n超晶格结构表现为欧姆导电,而在高温,高电场的情况下,其导电行为由空间电荷限制电流机理主导. 关键词： 超晶格薄膜 多铁 空间电荷限制电流     

Chiral SU(4) × SU(4) breaking: masses and decay constants of charmed hadrons

The (4, 4*) ⊕ (4*, 4) model of broken chiral SU (4) × SU (4) symmetry has been used to calculate the third-order coupling constants involving charmed and ordinary pseudoscalar mesons. These coupling constants are exploited to derive some interesting new relations among the masses and decay constants of these charmed particles. Using the known masses and decay constants as inputs, we exploit these relations to predict:F _D = −1·41F _π ,F _F = −1·13F _π ,F _D/F_F = 1·25,m(D _s) = 1·43 GeV,m(F _s) = 1·39 GeV andm(K _s) = 1·02 GeV.     

Optical Properties of the (CuInSe2) x ·(2ZnSe)1−x and (CuInTe2) x (·2ZnTe)1−x Solid Solutions

Crystals of the compounds CuInSe₂, CuInTe₂, ZnSe, and ZnTe, and the solid solutions (CuInSe₂) _x ·(2ZnSe)_1–x and (CuInTe₂) _x ·(2ZnTe)_1–x were grown by the Bridgman and chemical transport reactions methods. Their transmission and reflection spectra in the region of the main absorption line edge were studied. The forbidden band gap of the indicated materials was determined and its concentration dependences were built for the solid solutions. It is established that the forbidden band gap changes linearly with the x composition and is satisfactorily described by the square-law dependence.     

Effective Action in Multidimensional (Super)Gravities and Spontaneous Compactification (Quantum Aspects of Kaluza-Klein Theories)

The review of modern status of problem of quantum effects in Kaluza-Klein theories is given. The effective action (EA) in multidimensional (super)gravities (SG's) on the compactified background is investigated. The standard gauge dependent EA in d=5 Einstein gravity and d=5 R²-gravity on the background R₄ × S₁, where R₄ is 4-dimensional space, S₁ is one-dimensional sphere is calculated. Gauge and parametrization independent Vilcovisky-De Witt EA in d=5 Einstein gravity and d=5 R²-gravity on the background R₄×S₁ at zero and non-zero temperature is obtained. We have found that there are no physically acceptable self-consistent solutions of the form R₄×S₁ at the one-loop level in d=5 Einstein gravity. We calculated also EA for arbitrary multidimensional SG on the background R₄×T_d-n where T_d is d-dimensional torus as expansion on the curvature and its derivatives. The mechanizm of induced of four-dimensional gravity with zero Λ-term is proposed. The Vilcovisky-De Witt EA in d=5 SG's on the background R₄×S₁ at non-zero temperature is obtained. The three gauge parameter dependent off-shell EA in N=2, d=5 gauged SG on R₄⁰×S₁ where R₄⁰ is flat four-dimensional space is calculated. The expression for vacuum energy for bosonic string with torus compactification is presented. Vacuum energy for superstrings with supersymmetry broken as the result of choice of boundary conditions on background R₄×T₆ is calculated.     

Levi-Civita Connections on the Quantum Groups SLq(N), Oq(N) and Spq(N)

For bicovariant differential calculi on quantum groups various notions on connections and metrics (bicovariant connections, invariant metrics, the compatibility of a connection with a metric, Levi-Civita connections) are introduced and studied. It is proved that for the bicovariant differential calculi on SL _q (N), O _q (N) and Sp _q (N) from the classification in [18] there exist unique Levi-Civita connections. Received: Received: 28 February 1996 / Accepted: 1 October 1996     

EPR investigation of the spin-spin interactions in a Cu(II)-Gd(III)-Fe(III) heterospin system

The spin-spin interactions in a system that contains three different spin carriers, [{LCu}Gd(H₂O)₃×{Fe(CN)₆}] _n ·4nH₂O (1) [L²⁻, N,N-propylenedi(3-methoxysalicylideneiminato)], were investigated by electron paramagnetic resonance spectroscopy. Additional information was obtained by analyzing the discrete heterobinuclear system [LCu(OH₂)Gd(O₂NO)₃] (2), which contains the Cu(II)-Gd(III) pair also existing in the structure of 1, and the compounds [{LCu}Gd(H₂O)₃{Co(CN)₆}] _n ·3.5nH₂O and [{LCu}La(H₂O)₃×{Fe(CN)₆}] _n ·4nH₂O, which are isostructural with 1 and in which the paramagnetic low-spin Fe(III) and Gd(III) ions were replaced by diamagnetic low-spin Co(III) and La(III), respectively. The investigations were carried out in the temperature range of 293–4 K in both X- and Q-bands and also using a dual-mode X-band. The experimental spectra of the Cu(II)-Gd(III) pairs in 2 were interpreted as the sum of spectra of the ground spin state with total S = 4 and the excited state with S = 3 appearing due to the ferromagnetic exchange interaction between Cu(II) and Gd(III) ions. By fitting the experimental and simulated spectra, the zero-field splitting parameters of the Gd(III) ion are estimated and it is shown that no influence of the anisotropic interaction is detected. The magnetic properties of 1 are discussed from the perspective of the interaction of the Cu(II)-Gd(III) binuclear fragments with the Fe(III) ions.     

Relations between SU(2)- and SU(3)-LECs in chiral perturbation theory

Chiral perturbation theory in the two-flavour sector allows one to analyse Green functions in QCD in the limit where the strange quark mass is considered to be large in comparison to the external momenta and to the light quark masses m _u and m _d . In this framework, the low-energy constants of SU(2) _R × SU(2) _L depend on the value of the heavy quark masses. For the coupling constants which occur at order p ² and p ⁴ in the chiral expansion, we worked out in [1] the dependence on the strange quark mass at two-loop accuracy, and provided in [2] analogous relations for some of the couplings c _i which are relevant at order p ₆. This talk comments on the methods used, and illustrates implications of the results obtained.     

EPR and optical-absorption studies of Cu2+-doped Zn(NH2(CH2)3NHOH)2Ni(CN)4 single crystals

Electron paramagnetic resonance of Cu²⁺-doped catena-trans-bis(N-(2-hydroxyethyl)-ethylenediamine) zinc(II)-tetra-μ-cyanonicelate(II) [Zn(NH₂(CH₂)₃NHOH)₂Ni(CN)₄] single crystals and powder are examined at room temperature. The spectra show the substitution of the Zn²⁺ ion with the Cu²⁺ ion. The crystal field around the Cu²⁺ ion is nearly axial. There is a single paramagnetic site withg _xx=2.073,g _yy=2.060,g _zz=2.248,A _xx=40.5 G,A _yy=50.8 G,A _zz=172.0 G. The ground-state wave function is an admixture of d _x ²−y ² and d _z ² states. The optical-absorption studies show two bands at 320 nm (31250 cm⁻¹) and 614 nm (16286 cm⁻¹) which confirm the axial symmetry. The crystal field parameters and the wave function are determined.     

Finite-dimensional representations of U q (osp(1/2n)) and its connection with quantum so(2n+1)

It is shown that the quantum supergroup U _q (osp(1/2_n)) is essentially isomorphic to the quantum group U _-q (so(2n+1)) restricted to tensorial representations. This renders it straightforward to classify all the finite-dimensional irreducible representations of U _q (osp(1/2n)) at generic q. In particular, it is proved that at generic q, every-dimensional irrep of this quantum supergroup is a deformation of an osp(1/2n) irrep, and all the finite-dimensional representations are completely reducible.     

Spectroscopic parameters and molecular constants of HI(X~1Σ~+),DI(X~1Σ~+) and TI(X~1Σ~+) isotope molecules

The potential energy curve (PEC) of HI(X¹Σ⁺) molecule is studied using the complete active space self-consistent field method followed by the highly accurate valence internally contracted multireference configuration interaction approach at the correlation-consistent basis sets, aug-cc-pV6Z for H and aug-cc-pV5Z-pp for I atom. Using the PEC of HI(X¹Σ⁺), the spectroscopic parameters of three isotopes, HI(X¹Σ⁺), DI(X¹Σ⁺) and TI(X¹Σ⁺), are determined in the present work. For the HI(X¹Σ⁺), the values of D₀, D_e, R_e, ω_e, ω_eχ_e, α_e and B_e are 3.1551 eV, 3.2958 eV, 0.16183 nm, 2290.60 cm^-1, 40.0703 cm^-1, 0.1699 cm^-1 and 6.4373 cm^-1, respectively; for the DI (X¹Σ⁺), the values of D₀, D_e, R_e, ω_e, ω_eχ_e, α_e and B_e are 3.1965 eV, 3.2967 eV, 0.16183 nm, 1626.8 cm^-1, 20.8581 cm^-1, 0.0611 cm^-1 and 3.2468 cm^-1, respectively; for the TI (X¹Σ⁺), the values of D₀, D_e, R_e, ω_e, ω_eχ_e, α_e and B_e are of 3.2144 eV, 3.2967 eV, 0.16183 nm, 1334.43 cm^-1, 14.0765 cm^-1, 0.0338 cm^-1 and 2.1850 cm^-1, respectively. These results accord well with the available experimental results. With the PEC of HI(X¹Σ⁺) molecule obtained at present, a total of 19 vibrational states are predicted for the HI, 26 for the DI, and 32 for the TI, when the rotational quantum number J is equal to zero (J = 0). For each vibrational state, vibrational level G(?), inertial rotation constant B_? and centrifugal distortion constant D_? are determined when J = 0 for the first time, which are in excellent agreement with the experimental results.     

Effective action in multidimensional (Super)gravities

In the present paper we have obtained unique effective action ford=5 gravity on the backgroundM ₄×s ₁, whereM ₄ is the Minkowski space,S ₁ is a one-sphere. The effective action is calculated forN=1d=11 supergravity on the backgroundR _n xT _11–n whereR _n is then-dimensional curved space, T_d is thed-dimensional torus. A mechanism of inducing the Einstein gravity with zero--term is proposed.We thank A. O. Barvinsky, E. S. Fradkin, I. V. Tyutin and A. A. Tseytlin for helpful discussions. We are grateful to L. G. Fonova for technical assistance.