Unexpected Features of the Intramolecular Spin Exchange in Imidazoline Nitroxide Biradicals Dissolved in Ionic Liquids

Three imidazoline-type nitroxide biradicals of the similar composition R ₅ ^NO –CH=N–N=CH–R ₅ ^N , B1, R ₅ ^NO –CH=N–N=C(CH₃)–R ₅ ^N , B2, and R ₅ ^N –C(CH₃)=N–N=C(CH₃)–R ₅ ^N , B3, with R ₅ ^N and R ₅ ^NO denoting, respectively, the nitroxide rings 1-oxyl-2,2,5,5-tetramethyl-3-imidazoline and 1-oxyl-2,2,5,5-tetramethyl-3-N–oxide imidazoline, have been studied by X-band electron paramagnetic resonance (EPR) spectroscopy. Variations of the intramolecular electron spin exchange in these biradicals dissolved in ethanol and the room temperature ionic liquid bmimBF₄ were characterized as a function of temperature by means of the analysis of the EPR lines shape. Thermodynamic parameters of the conformational rearrangements in ethanol were calculated. Analyzing the EPR spectra of these biradicals in bmimBF₄, it was revealed that the two-conformational model does not describe their conformational transitions. Moreover, the observed EPR spectra are not central symmetric especially at low temperatures that cannot be described and explained in the framework of the current theory of the intramolecular spin exchange. Probable reasons of this “strange” behavior are discussed.     

Vibronic-spin-orbit interactions in heterocyclic analogues of fluorene with the N and O heteroatoms

The transition dipole moments P _0n ^s for the transitions from the electronic triplet state ³ B ²(ππ*) to vibrational sublevels of the vibrational out-of-plane modes n of the carbazole and dibenzofuran molecules are calculated. The values of the radiative deactivation rate constant k _rad ^s of the triplet sublevels T ^s are determined along with the components k _SO ^s and k _VSO ^s of this constant, which depend on the intramolecular spin-orbit (SO) and vibronic-spin-orbit (VSO) interaction. It is ascertained that k _rad ^z > k _rad ^y . For different structural units of the molecules (the heteroatom and the carbon atoms of the dibenzene fragment), the effect of the SO coupling on the constant k _VSO～Σ_{s, n} (P _0n ^s )² is studied. A competition between the effects on k _VSO from the SO coupling in the carbon atoms and in the light N and O heteroatoms is revealed. This competition accounts for the weak influence of the heteroatom on this component of the rate constant k _rad in these molecules. It is ascertained that the intensity distribution among the vibronic lines in the phosphorescence spectra of carbazole and dibenzofuran I _0n ～Σs (P _0n ^s )² is different due to the substantially different influence of the N and O heteroatoms on the deactivation of the triplet sublevel T ^y .     

Magnetoresistance of granular YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>7 − δ</Subscript> HTSC in weak magnetic field: Angular dependence

The magnetoresistance of ceramic YBa₂Cu₃O_～6.5 HTSC samples is studied as a function of the mutual orientation of the current I and external magnetic field H _ext at T = 77.3 K in magnetic fields of up to ～500 Oe. It is found that, if the demagnetization factor D is taken into account, the effective critical field of complete penetration of Josephson vortices into weak links H _c2J ^eff does not depend on the mutual orientation of I and H _ext. The lower critical field H _c1A ^eff associated with the beginning of penetration of Abrikosov vortices into superconducting grains increases substantially with the angle between I and H _ext. The strongest variation with the mutual orientation of I and H _ext is exhibited by the critical field of the Bragg glass-vortex glass first-order phase transition H _BG-VG ^eff and by the magnetoresistance jump at this phase transition.     

Formation of the incommensurate ordered phase in TaC<Subscript>y</Subscript> carbide

Structural neutron diffraction studies indicate that only one ordered phase arises after the disorder-order transition in nonstoichiometric cubic tantalum carbide TaC_y. This phase arises in the composition range y = 0.79–0.89 due to long-term annealing with a decrease in temperature from 1600 to 300 K. It is incommensurate in the [1–11]_B1 direction, but it is close to commensurate M₆C₅ structures (C2/m and P3₁ space groups) in mutual arrangement of atoms and vacancies in nonmetallic (1–11)_B1 planes. The disorder-order transition channel that is associated with the formation of the incommensurate superstructure in TaC_y carbide includes two arms k ₅ ⁽⁶⁾ ≈ 0.473b₂ and k ₅ ⁽⁵⁾ = ?k ₅ ⁽⁶⁾ of the {k₅} star and arms of the {k₄} and {k₃} stars. The translation period of the incommensurate phase in the [1–11]_B1 direction is 8.9–9.1 nm, which is larger than that in the commensurate phase M₆C₅ by a factor of about 18.     

Tailored Nitroxide Radicals and Biradical Containing <Superscript>13</Superscript>C Enriched Acetylene Groups: ENDOR and DFT Investigation

A specially synthesized nitroxide biradical R₅-C≡¹³C-(p-C₆H₄)₂-¹³C≡C-R₅ (B4) and two radicals, R₅-C≡¹³CH (RCC) and R₅-C≡¹³C-C₆H₅ (RCCPh), where R₅ is 1-oxyl-2,2,5,5-tetramethyl-pyrroline group, have been studied by X- and W-band electron paramagnetic resonance (EPR) spectroscopy, and by W-band electron-nuclear double resonance (ENDOR). Spin density distribution and hyperfine splitting (hfs) constants on ¹³C atoms were experimentally determined and also calculated using ORCA 3.0.3 program package. The biradical and radicals geometries were optimized on UKS/B3LYP/cc-pVDZ level. Hfs constants were calculated using density functional theory (DFT) with PBE0 functional and N07D, and were compared with the experimental value of the hfs constant on ¹³C atoms, measured from ENDOR spectra. It is concluded that at small values of the exchange integral as J ≤ a/2 ≈ 7–8 G, the current quantum chemical approaches do not allow determining precise values of the hfs constants on the ¹³C atoms in the bridge connecting two paramagnetic nitroxide rings of the biradical.     

High-frequency EPR of Cr<Superscript>2+</Superscript> ions in CdGa<Subscript>2</Subscript>S<Subscript>4</Subscript>

High-frequency broad-band (65–240 GHz) EPR is used to study impurity centers of bivalent chromium in a CdGa₂S₄ crystal. It is found that the EPR spectra correspond to tetragonal symmetry. The spin Hamiltonian H = βB · g · S + B ₂ ⁰ O ₂ ⁰ + B ₄ ⁰ O ₄ ⁰ + B ₄ ⁴ O ₄ ⁴ with the parameters B ₂ ⁰ =23659±2 MHz, B ₄ ⁰ =1.9±1 MHz, |B ₄ ⁴ |=54.2±2 MHz, g_‖=1.93±0.02, and g_⊥=1.99±0.02 is used to describe the observed spectra. It is concluded that chromium ions occupy one of the tetrahedrally coordinated cation positions.     

Heavy-quark production in p $$\bar p$$ collisions and unintegrated gluon distributions

The inclusive production of heavy (c and b) quarks in high-energy p\(\bar p\) collisions are considered within the semihard approach in QCD. The dependence of the cross section for heavy-quark production, σ(p_T>p _T ^min ), on unintegrated gluon distributions is studied. The results of this consideration are compared with experimental data obtained by the D0 and CDF Collaborations at Tevatron.     

Ordering of the lowest tungsten carbide W<Subscript>2</Subscript>C

Atomic-vacancy ordering of the lowest tungsten carbide W₂C with the basis hexagonal structure of the L’3 type is analyzed by neutron and x-ray diffraction studies. It is found that the trigonal phase ?-W₂C (space group \(P\bar 3\) 1m) is the only ordered phase in the temperature range from ～2700 to 1370 K. The disorder-order phase transition channel associated with the formation of the trigonal ?-W₂C phase is found to include three superstructure vectors k ₁₅ ⁽¹⁾ , k ₁₅ ⁽²⁾ , and k ₁₇ ⁽¹⁾ of two stars {k ₁₅} and {k ₁₇}. The distribution function of the carbon atoms in the trigonal ?-W₂C superstructure is calculated.     

Spin-orbit interactions in heterocyclic analogues of fluorene

For carbazole, dibenzofuran, and dibenzothiophene—heterocyclic analogues of fluorene containing N-H, O, and S groups, respectively—the transition dipole moments P ₀₀ ⁱ for the transitions ³ B ₂→S ₀ and ³ A ₁→S ₀ from the sublevels i=z, y, x of the triplet electronic ππ* states, which are caused by intramolecular spin-orbit (SO) interactions, are calculated. The effect that the SO coupling between the S ₀ state and highest triplet states has on the calculation results is considered. The effects exerted on the value of P ₀₀ ⁱ by such specific features of the molecular structure as the position of a heteroatom on the symmetry axis, its valence, and different constants of SO coupling in heteroatoms are discussed. The reason for the weak influence of the quantity ?_HA on the rate constant of radiative deactivation of the lowest T state is ascertained.     

Hysteresis of the magnetoresistance of granular HTSC YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>7 − δ</Subscript> in weak fields

Hysteresis of the magnetoresistance of ceramic YBa₂Cu₃O_～6.95 HTSC samples is studied at T = 77.3 K in an external magnetic field H _ext changing in 0 → H _max → 0 cycles, where H _max is the maximum magnitude of H _ext. Information is obtained about the dependences of the critical fields of Josephson weak links H _c2J , the lower critical fields of superconducting grains H _c1A , and the critical fields H _BG-VG of the Bragg glass-vortex glass phase transition in the vortex matter on transport current I, magnetic field, and the mutual orientation of I and H _ext. It is found that the magnetoresistance δρ⁺/ρ_{273 K} measured with increasing H _ext is significantly higher than Δρ^?/ρ_{273 K} and that H _c2J ⁺ < H _c2J ^? , H _c1A ⁺ < H _c1A ^? , and H _BG-VG ⁺ < H _BG-VG ^? .     

Integral characteristics of vibronic-spin-orbit interactions in a phosphorus-containing analogue of the fluorene molecule

The strengths (P ₀₀ ^s )² and F _VSO ² of the transitions from the triplet sublevels s = z, y, and x of the electronic state ³A″ of the phenyldibenzophosphole (DB(P-Ph)) molecule are calculated taking into account the intramolecular spin-orbit (SO) and joint vibronic-spin-orbit (VSO) interactions. The contributions to the vibronic transition strengths from the SO interactions in different structural elements of the molecule (the C atoms of the dibenzene framework, the P atom, and the Ph substituent) are determined. The effect of the nonplanar nuclear configuration of the DB(P-Ph) molecule on the values of F _VSO ^s is investigated. The radiative deactivation rate constants of the k _rad ^s triplet sublevels T ^s are estimated. It is found that the vibrations of the A′(B₁) symmetry in the fine-structure phosphorescence spectrum of DB(P-Ph) occur due to both the SO coupling exclusively in the P atom and the T ^x → S₀ transition (the x axis is perpendicular to the planar dibenzene framework of the molecule) with a high (preferential) population of this triplet sublevel.     

Electroproduction of <Emphasis Type="Italic">J/ψ</Emphasis> mesons within the semihard QCD approach and the color-singlet model

The deep-inelastic production of J/ψ mesons in electron-proton interactions at the HERA collider is considered within the semihard (k_T-factorization) QCD approach and within the color-singlet model. The dependence of the Q², p _T ² , z, y* and W distributions of J/ψ mesons on various sets of unintegrated gluon distributions and the dependence of the spin parameter α on p _T ² and Q² are investigated. The results of the calculations are compared with the latest experimental data obtained by the H1 and ZEUS Collaborations at the HERA collider. It is shown that experimental investigations of the polarization properties of J/ψ mesons over the kinematical region Q²<1 GeV² may provide an additional test of the statement that the dynamics of gluon distributions is governed by the Balitsky-Fadin-Kuraev-Lipatov equations.     

The effect of the nonplanarity of heterocyclic analogues of fluorene with the phosphorus atom on spin-orbit interactions

The transition dipole moments P ₀₀ ^S for the transitions from the sublevels s=z,y, and x of the triplet electronic states ³ A″, which are caused by intramolecular spin-orbit (SO) interactions, are calculated. The calculation is carried out for molecules of heterocyclic analogues of fluorene containing phosphorus and nitrogen (namely, the groups P-H, P-C₆H₅, and N-H). The influence that the planar and nonplanar models of the molecules, as well as the substituents ?C₆H₅ and ?H at the heteroatom (HA), exert on the values of (P ₀₀ ^S )² and on the directions of the corresponding vectors is considered. The values of the component \(k_{SO^ \sim } \sum _s (P_{00}^s )^2 \) of the radiative deactivation rate constant of the T ₁ state are calculated. It is ascertained that, in the series of molecules with HA = N, O, P, and S, both the calculated values of k _SO and those experimentally determined from an analysis of the intensity distribution in fine-structure phosphorescence spectra vary little, whereas the constant of the SO coupling in the heteroatom ?_HA increases substantially along this series. The reason for the weak influence of ?_HA on values of k _SO—common for both planar and nonplanar molecules—is found.     

Stability of Coulomb systems

The stability of m ₁ ⁺ m ₂ ⁺ m ₃ ^? m ₄ ^? Coulomb systems formed by particles of unit charge against dissociation is considered as a function of the particle mass. It is shown that, from the stability of the m ₁ ⁺ m ₂ ⁺ m ₃ ^? three-particle system, it follows that the m ₁ ⁺ m ₂ ⁺ m ₃ ^? m ₄ ^? four-particle system containing an additional particle of mass satisfying the condition m ₄ ^? ? m ₃ ^? is stable. The results of calculations of the stability domain for m ₁ ⁺ m ₂ ⁺ m ₃ ^? systems asymmetric in particle masses are reported. The stability of 39 asymmetric exotic four-particle molecules and mesic molecules against dissociation is established.     

Excitons in monoclinic zinc diphosphide: The <Emphasis Type="Italic">A</Emphasis>-exciton series and Fano effect

The A-exciton series in the absorption spectra of β-ZnP₂ monoclinic zinc diphosphide samples is investigated at different directions of the wave vector and different polarization states of radiation. It is shown that the oscillator strengths determined for the observed transitions are adequately described by the relationship F _n ∝n^?3 characteristic of S-type exciton states. The assumption is made that the A-exciton series is associated with the partially allowed dipole transitions to nS states of the orthoexciton with Γ ₂ ^? (x) symmetry at m _s =0. These states are mixed, to a first approximation, with nS states of the Γ ₂ ^? (z) singlet exciton due to the spin-orbit 2 interaction and are split off by the long-range (nonanalytical) part of the exchange interaction. The Fano antiresonances arise in the absorption spectra at resonances of the A-exciton series when the radiation vector E (or the induction vector D) has a component along the crystallographic axis c. These antiresonances are induced by the configurational interaction of discrete exciton states of the A series with the continuum of the exciton-phonon spectrum due to indirect transitions to the 1S band of the singlet exciton with phonon emission.     

Long-range spin correlations in a honeycomb spin model with a magnetic field

We consider the spin-1/2 model on the honeycomb lattice [A. Kitaev, Ann. Phys. 321, 2 (2006)] in the presence of a weak magnetic field h _α ? J. Such a perturbation treated in the lowest nonvanishing order over h _α leads [K.S. Tikhonov, M.V. Feigel’man, and A.Yu. Kitaev, Phys. Rev. Lett. 106, 067203 (2011)] to a powerlaw decay of irreducible spin correlations 《s ^z (t, r)s ^z (0, 0)》 ∝ h _z ² f(t, r), where f(t, r) ∝ [max(t, Jr)]^–4. We have studied the effects of the next order of perturbation in h _z and found an additional term of the order h _z ⁴ in the correlation function 《s ^z (t, r)s ^z (0, 0)》 which scales as h _z ⁴ cosγ/r ³ at Jt? r, where γ is the polar angle in the 2D plane. We demonstrate that such a contribution can be understood as a result of a perturbation of the effective Majorana Hamiltonian by the weak imaginary vector potential A _x ∝ i h _z ² .     

Dipole moment functions for electronic transitions from ion-pair states of the second tier of molecular iodine

The emission spectra caused by the transitions from the ion-pair states and f0 _g ⁺ and G1_g of the I₂ molecule are obtained by excitation of individual rovibronic levels of the molecule by the method of optical-optical double resonance. The emission spectra from the state F0 _u ⁺ populated due to collisions I₂(f) + I₂(X) are also measured. By modeling the experimental emission spectra, the dipole moment functions for the electronic transitions f _g ⁺ -B0 _u ⁺ , A0 _u ⁺ , and B″0 _u ⁺ ; G1_g-A0 _u ⁺ and B″0 _u ⁺ ; and F0 _u ⁺ -X0 _g ⁺ and a′0 _g ⁺ of the iodine molecule are reconstructed.     

Genesis of the anomalous Hall effect in CeAl<Subscript>2</Subscript>

The Hall coefficient R _H , resistivity ρ, and Seebeck coefficient S of the CeAl₂ compound with fast electron density fluctuations were studied in a wide temperature range (from 1.8 to 300 K). Detailed measurements of the angular dependences R _H (? T, H≤70 kOe) were performed to determine contributions to the anomalous Hall effect and study the behavior of the anomalous magnetic R _H ^am and main R _H ^a components of the Hall signal of this compound with strong electron correlation. The special features of the behavior of the anomalous magnetic component R _H ^am were used to analyze the complex magnetic phase diagram H-T determined by magnetic ordering in the presence of strong spin fluctuations. An analysis of changes in the main contribution R _H ^a (H, T) to the Hall effect made it possible to determine the complex activation behavior of this anomalous component in the CeAl₂ intermetallic compound. The results led us to conclude that taking into account spin-polaron effects was necessary and that the Kondo lattice and skew-scattering models were of very limited applicability as methods for describing the low-temperature transport of charge carriers in cerium-based intermetallic compounds. The effective masses and localization radii of manybody states in the CeAl₂ matrix were estimated to be (55–90)m₀ and 6–10 Å, respectively. The behaviors of the parameters R _H , S, and ρ were jointly analyzed. The results allowed us to consistently describe the transport coefficients of CeAl₂.     

Spin-frustrated antiferromagnets based on <Emphasis Type="Italic">BEDT-TTF</Emphasis> and manganese dicyanamide complexes

The magnetic properties of new radical cation salts (BEDT-TTF)₂[CuMn(dca)₄] (I) and (BEDT-TTF)₂[Mn(dca)₃] (II) [where BEDT-TTF = bis(ethylenedithio)tetrathiafulvalene and dca = N(CN₂)] are investigated using superconducting quantum interference device (SQUID) magnetometry and electron paramagnetic resonance (EPR) spectroscopy. It is established that, at temperatures below 25 K, both salts are characterized by antiferromagnetic deviations from the paramagnetic behavior. The Weiss constants for compounds I and II are determined to be ?5 and ?10 K, respectively. The corresponding correlations in the structure of compound I are short-range correlations and do not lead to a change in the effective spin equal to 5/2. It is found that the widths of the EPR lines attributed to the BEDT-TTF conducting sublattice correlate with the widths of the EPR lines associated with the magnetic sublattice of the Mn(dca) ₃ ^? counterion in the structure of salt II. This correlation suggests that the antiferromagnetic ordering in the magnetic sublattice of compound II affects the spin-lattice relaxation in the BEDT-TTF sublattice. The dependence of the magnetic moment on the magnetic field for compound II at a temperature of 2 K is typical of weakly frustrated uniaxial antiferromagnets and exhibits a kink in a magnetic field of 20 kOe, which corresponds to spin-flop transitions.