Absolute sign of the Mu* hyperfine parameters in diamond

Standard μSR experiments in diamond have shown that the relative sign of the hyperfine parameters of the anisotropic Mu^* state is negative (A _‖/A _⊥<0). We report an experimental determination of theabsolute sign of the Mu^* hyperfine parameters by studying the transferred muon polarization during the thermally-activated transition from the isotropic Mu state to Mu^*. The results demonstrate that the isotropic part of the Mu^* hyperfine interaction is negative. In a nitrogen-poor diamond, both the Mu disappearance rate and the enhancement of the Mu^* signals are well-described by a single Arrhenius law.     

EPR study of the Jahn-Teller effect of Cu2+ ions in ZnGa2O4

The Jahn-Teller effect in the ZnGa₂O₄ spinel single crystal has been investigated using electron paramagnetic resonance of Cu²⁺ ions in the temperature range 110–560 K. It has been shown that copper ions occupy octahedral sites 16d in the ZnGa₂O₄ crystal with cubic symmetry O _h ⁷ (Fd-3m). At T < 560 K, the octahedra undergo tetragonal distortions (predominantly tension) and rotation around the fourfold axes by the angle θ ≈ 2.6°. The parameters of the spin Hamiltonian, which characterize the prolate (g _‖ = 2.355, g _⊥ = 2.077, A _‖ = 116 Oe, A _tp = 12 Oe) and oblate (g _‖ = 2.018, g _⊥ = 2.246, A _‖ = 75 Oe, A _⊥ = 44 Oe) octahedra, have been determined. At temperatures above 560 K, the static Jahn-Teller effect transforms into the dynamic effect and the spectrum of the magnetic resonance becomes isotropic with g = 2.116 (the experimental frequency corresponds to the X band).     

Spin-orbit coupling,spin-lattice relaxation,and spin-memory studies ofF-center-molecular-ion pairs in alkali halides

Summary The spin-orbit parameter Δ, spin-lattice relaxation timeT ₁, and spin-mixing parameter ɛ ofF _H(OH⁻) andF _H(CN⁻) centers in several alkali halides have been studied with magnetic circular dichroism at ∼2 K. A close comparison of the experimental results before and after optically induced association of theF center with the molecular ion has been made. In crystals of NaCl structure the negative spin-orbit parameter Δ changes little betweenF andF _H centers in the same host. For CsCl and CsBr two values of Δ have been derived forF _H(CN⁻) centers with axis parallel or perpendicular to the magnetic field. In all studied systems, the spin-lattice relaxation timeT ₁ is already shorter before aggregation compared toF formation. The spin-mixing parameter ɛ decreases slightly forF _H(OH⁻) compared toF centers, while it increases drastically forF _H(CN⁻) defects and reaches its maximum possible value ɛ=0.5 in cesium halides. First attempts to interpret these magneto-optical results will be presented. In honour of Prof. Fausto Fumi on the occasion of his retirement from teaching.     

Self-consistent analysis of absorption and emission data forF A centres in alkali halides

Summary A theory which explains self-consistently the emission and the polarization rotation of transmitted light has been developed forF _A centres in crystals with cubic symmetry. Azimuthal dependences ofF _A luminescence in alkali halides are very informative for determining the electron-phonon interaction as well as the parameters related to the structural and optical quality for coulour centre lasers crystals. The theoretical results are applied to the interpretation of the luminescence properties ofF _A (Li) centres in KCl, RbCl and KF.     

Investigations of EPR parameters and impurity structure for Co<Superscript>2+</Superscript> in Ca(OH)<Subscript>2</Subscript> crystal

The electron paramagnetic resonance (EPR) parameters (g _‖ andg _⊥ factors and hyperfine structure constantsA _‖,A _⊥) for Co²⁺ in Ca(OH)₂ are studied from the second-order perturbation formulas on the basis of the cluster approach. In these formulas, the contributions to EPR parameters from the state interactions and covalency effects are considered and the parameters related to both effects are obtained from the optical spectra and impurity structure of the studied system. From the study, it is found that the β angle between the metal-ligand bond and the C₃ axis changes from 61° in a pure crystal to 53.68(26)° in the impurity center of a Co²⁺-doped Ca(OH)₂ crystal because of the impurity-induced local lattice relaxation. The reduction of the angle β in the impurity center is also supported by the result obtained by analyzing the EPR zero-field splitting for Mn²⁺ in the same Ca(OH)₂ crystal. The EPR parameters of Ca(OH)₂:Co²⁺ are also reasonably explained by considering the suitable local lattice relaxation.     

Electron paramagnetic resonance of NH 3 + radical in potassium sulphate

Room temperature EPR spectra of (NH₄)₂SO₄ doped K₂SO₄ monocrystals irradiated with x-rays show the presence of NH₃ ⁺ radicals. The EPR parameters areg ‖=2.0037 andg ⊥ = 2.0068;¹⁴NA _XX=13.75;A _YY=24.5;A _ZZ=25.5 gauss;¹HA _XX=A _YY=22 andA _ZZ=25 gauss. From the¹⁴N and¹H coupling constants it has been inferred that at room temperature the planar NH₃ ⁺ radical undergoes rotation about theC ₃ axis which corroborates with the equivalence of the protons, but the radical itself is in an asymmetric crystal field environment. The 77K spectra indicate a considerable reduction in the motion of the radical with the free motion almost completely stopped. Part of Ph.D. work of the second author     

EPR studies of Cu2+ and V4+ ions in phosphate glasses

Two lead-phosphate glass systems doped with both copper and vanadium ions in different ratios were studied by EPR (electron paramagnetic resonance) method. EPR spectra and parameters (g_‖ = 2.44, g_⊥ = 2.08 andA _‖ = 117.6 · 10⁻⁴ cm⁻¹) obtained for x(CuO · V₂O₅)(l−x)[2P₂O₅ · PbO] glasses withx ≤ 10 mol% suggest a tetrahedral (Td) coordination of Cu²⁺ ions and not a tetragonally elongated octahedron as has been assumed in previous works. The ground state of the paramagnetic electron is thed _xy copper orbital with a 4p_z contribution of 6%. For 20 ≤x ≤ 40 mol% a broad line (ΔB = 307 G) characteristic for clustered ions appears atg = 2.18. The V⁴⁺ ions are evidenced only in the spectra of x(CuO · 2V₂O₅)(1 −x)[2P₂O₅ · PbO] glasses and the resonance parameters suggest a pentacoordinated C_4v local symmetry for these ions. The hyperfine structures characteristic for Cu²⁺ and V⁴⁺ ions disappear for 10 ≤x ≤ 40 mol% due to the mixed exchange Cu²⁺−V⁴⁺ pair formation in these glasses.     

The estimates of periodic potentials in terms of effective masses

LetG _n=(A _n ⁻ , A _n ⁺ ),n≧1, denote the gaps,M _n ^± be the effective masses and Σn=[A _n−1 ⁺ ,A _n ^- ],A ₀ ⁺ =0, be the spectral bands of the Hill operatorT=−d ²/dx ²+V(x) inL ² (R), whereV is a 1-periodic real potential fromL ²(0,1). Let the length gapL _n=|G_n|, h_n be the height of the corresponding slit on the quasimomentum domain and Δ_n=π²(2n−1)−∣Σ_n∣>0 be the band reduction. Let ,n≧1, denote the gap length for the operator . Introduce the sequencesL={L_n}, h={h_n}, l={l_n}, Δ={Δ_n},M ^±={M _n ^± } and the norms ,m≧0. The following results are obtained: i) The estimates of‖V‖, ‖L‖, ‖h‖ ₁, ‖l‖₁, ‖δ‖ in terms of ‖M^±‖₂, ii) identities for the Dirichlet integral of quasimomentum and integral of potentials and so on, iii) the generation of i), ii) for more general potentials. The research described in this publication was made possible in part by grant from the Russian Fund of Fundamental Research and INTAS.     

Lattice thermal expansion of silver indium disulphide

Lattice parameters of chalcopyrite type compound silver indium disulphide (AgInS₂) were determined as a function of temperature by the x-ray method in the temperature range 28 to 685°C. Using these data, the coefficients of thermal expansion,a _⊥ anda _‖, were evaluated by a graphical method. The temperature dependence ofa _⊥ anda _‖ is represented by a suitable equation. The anisotropic thermal expansion of AgInS₂ is explained in terms of the thermal expansion of the Ag-S and In-S bonds of the AgInS₂ lattice.     

Covalent binding parameters and the ground state wavefunctions of vanadyl ion complexes

The Steven’s method of molecular orbitals for octahedral complexes containing transition metal ions has been used for estimating the binding parameters and interpreting theg factors of VO ₂ ⁺ ion in single crystals. The expressions forg factors have been given in terms ofK _‖ andK _⊥ taking into account the tetragonal crystalline field and covalent binding effects. Computations show thatK _⊥ should be less than 0.066 in order to fit the experimentalg values. The ground state wave function (GSWF) of VO ₂ ⁺ ion doped in different single crystals has been estimated using crystal field theory. The GSWF is found to be ind _xy state with slight admixture of the excited states ,d _xz andd _yz. The hyperfine interaction parameterP and Fermi contact termX have also been estimated.     

Diffusion and transport phenomena in a collisional magnetoplasma having both streaming and temperature anisotropy: Collisional kinetics

Boltzmann-transport equation is analytically solved for two-component magnetoplasma using Chapman-Enskog analysis to include collisional diffusion transport having anisotropies in both streaming velocity and temperature components. The modified collisional integrals are analytically solved with flux integrals and perturbed kinetic equation to arrive at drift diffusion velocity and resulting transport coefficients which are markedly affected by both streaming and temperature anisotropy. The early isotropic results are recovered in the limit V ₀ = 0 and T _‖ = T _⊥ which reduce to eqs (11.30) and (11.31) of [1] and eqs (2.7) and (2.13) of [2]. The electrical resistivity (η_⊥) diminishes sharply in fusion temperature limit kT _⊥ = 1 keV. The shape of the curves for both electrical resistivity and thermal conductivity is rectangular hyperbolic. However, for low thermal ratio (T _‖/T _⊥ < 1), the curves are raised up and for high thermal ratio (T _‖/T _⊥ > 1), they are lowered down the isotropic case (T _‖/T _⊥ > 1), showing comparatively diminished magnitudes of the quantities.      

Studies of local phase transition behavior for Co2+ in CsCaCl3 crystals from EPR data

In this paper, we establish the calculation formulas ofg factorsg _∥,g _⊥ and the hyperfine structure constantsA _∥,A _⊥ for 3d⁷ ions in tetragonal octahedral field from a cluster approach. In these formulas, besides the configuration interaction, the covalency effect due to the admixture between d electrons of 3d⁷ ion and the p electrons of ligands is considered. The parameters used in these formulas (except the core polarization constantsk in the calculation ofA _i) can be obtained from optical spectra of the studied crystal. From these formulas, the local release (or elongation) factork, which is introduced to characterize the release effect of impurity-ligand bond along C₄ axis at the cubic to tetragonal phase transition, is estimated for CsCaCl₃:Co²⁺ crystal by calculating the electronic paramagnetic resonance (EPR) parametersg _i andA _i . These EPR parameters are therefore explained reasonably and the results are discussed.     

Nonlinear dynamics of vortices pinned to unidirectional twins

The nonlinear resistive properties of superconductors in the mixed state in the presence of a system of unidirectional planar defects (twins) have been investigated theoretically within the framework of the two-dimensional stochastic model of anisotropic pinning based on the Fokker-Planck equations with a concrete form of the pinning potential. These equations allow one to obtain an exact analytical solution of the problem. Formulas are obtained for experimentally observable even and odd (relative to reversal of the direction of the external magnetic field) nonlinear longitudinal and transverse magnetoresistivities ρ _‖,⊥ ^± ( j,t,α,ε) as functions of the transport current density j, temperature t, the angle α between the directions of the current and the twins, and the relative volume fraction ε occupied by the twins. In light of the great variety of types of nonlinear resistive dependences contained in these expressions for ρ _‖,⊥ ^± the most characteristic of them are presented in the form of graphs with commentary. The desired nonlinear dependences ρ _‖,⊥ ^± are linear combinations of the even and odd parts of the function v(j,t, α,ε), which has the sense of the probability of overcoming the potential barrier of the twins; this makes it possible to give a simple physical treatment of the nonlinear regimes. New scaling relations for the Hall conductivity are obtained and investigated which differ from the previously known relations for isotropic pinning. The interaction of vortex motion directed along the twins and the Hall effect is considered for Hall constants which are arbitrary in magnitude and sign, and it is shown that in the case of small Hall viscosity vortex motion directed along the twins has an effect on the odd magnetoresistivities ρ _‖ ⁻ and ρ _⊥ ⁻ , whereas the reverse effect can be neglected. It is shown that pinning anisotropy is sufficient to manifest the new nonlinear (in the current) magnetoresistivities ρ _⊥ ⁺ and ρ _‖ ⁻ . Zh. éksp. Teor. Fiz. 116, 2103–2129 (December 1999)     

Coexistence of one-electron- and monoprotonated two-electron-reduced species of the K5[PMo2VW9O40] · 24H2O heteropolyoxometalate identified by EPR

The simulation of the room-temperature experimental electron paramagnetic resonance spectrum of K₅[PMo₂VW₉O₄₀] · 24 H₂O heteropolyoxometalate indicates the presence of equal amounts of a one-electron-reduced species (g _∥ = 1.922,g _⊥ = 1.972,A _∥ = 181 G,A _⊥ = 63 G) and a monoprotonated two-electron-reduced species with mixed-valence V^IV, Mo^V and Mo^VI ions (g _iso = 1.972, ΔB _iso(p-p) = 450 G). Two unprotonated one-electron-reduced isomers are identified in dimethylsulfoxide-H₂O solution of the sample atT = 100 K (g _∥¹ = 1.929,g _⊥¹ = 1.990,A _∥¹ = 179 G,A _⊥¹ = 65 G andg _∥² = 1.918,g _⊥² = 2.000,A _∥² = 187 G,A _⊥² = 80 G, respectively). The values of the in-plane π(V−O) bond π₂² coefficient for the one-electron-reduced species (0.87 at room temperature and 0.83 and 0.74 for the species in frozen solution) suggests the delocalization of the vanadium unpaired electron towards the molybdenum ions via O_b atoms.     

Transmission spectra of thin CdS and CdSe crystals near higher-order isotropic points

Summary For photon energies below the absorption edge in CdS, CdSe and other II–VI crystals the polariton dispersion curves forE⊥c andE‖c (c-axis in a wurtzite crystal) corss at some points called isotropic points (IP). The occurrence of isotropic points provides the possibility of mode coupling between ordinary and extraordinary waves. Since the consequences of mode coupling on the optical properties for photon energies near the lowest IP lying much below the first excitonic state were widely discussed in recent years, more attention is now paid to isotropic points lying near the band gap and related to then=2,3, … excitonic states (?higher isotropic points?). Making use of Stahl's real density matrix approach we derive the polariton dispersion relationsk _⊥ (ω), andk _‖ (ω), for CdS and CdSe bulk crystals and determine the positions of IP's due to the crossing of theB-polariton with higherA-excitonic resonances. By the method of multiple internal reflection we calculate the transmission spectra for various crystal thicknesses (between 3 μm and 0.5 mm) and coupling mechanisms. The calculated transmission shows sharply peaked structures centred at the isotropic points.     

Superhyperfine structure of the EPR spectra of Ce<Superscript>3+</Superscript> ions in Li<Emphasis Type="Italic">R</Emphasis>F<Subscript>4</Subscript> (<Emphasis Type="Italic">R</Emphasis> = Y,Lu, Tm) double fluorides

The EPR spectra of Ce³⁺ impurity ions in LiYF₄, LiLuF₄, and LiTmF₄ double-fluoride single crystals have been investigated at a frequency of ∼9.3 GHz in the temperature range 5–25 K. The effective g factors of the ground Kramers doublet of the cerium ions in three crystals are close to each other (g _‖ = 2.737, g _⊥ = 1.475 for LiYF₄:Ce³⁺). A superhyperfine structure of the EPR spectrum of Ce³⁺ ions in the LiTmF₄ Van Vleck paramagnet has been observed in the external magnetic field B oriented along the crystallographic axis c (B ‖ c). The superhyperfine structure of the EPR soectra of the Ce³⁺ ions in the LiYF₄ and LiLuF₄ diamagnetic matrices is resolved for B ⊥ c. Possible factors responsible for this pronounced difference in the properties of the systems studied have been discussed.     

Spin-dependent correction to the relativistic-electron mass in QED in the presence of an external electric field

A new expression is found for the spin-dependent contribution Δm _s to the self-energy of an electron moving with a transverse momentum p⊥ in an electric field. The structure of an asymptotic expansion of Δm _s (r, χ) as a function of two dynamical invariants r = γ _⊥⁻² and χ = γ _⊥|ɛ|/ɛ _c (γ _⊥² ≡ 1 + p _⊥²/m ² c ² and ɛ _c ≡ m ² c ³/|e|ℏ) is clarified with the aid of this expression. The expansion of Δm _s (r, χ) can be represented in the form of a Taylor series in r, the coefficients in this series, F ₀(χ), F ₁(χ), etc., being integrals of the Mellin type. The major coefficient F ₀(χ) is universal and, in the case of an appropriate interpretation of χ, describes well-known spin-dependent corrections to the mass in three different cases of a constant external field (for r → 0). The asymptotic properties of the function F ₁(χ) are studied in detail, but only order-of-magnitude estimates are obtained for F ₂(χ) and F ₃(χ). A comparison of these contributions revealed that, in the semiclassical region χ ≪ 1, r is indeed the parameter of the aforementioned expansion, while, for χ ≫ 1, the true parameter is rχ ² ≡ β ². In particular, the anomalous magnetic moment develops, owing to F ₁(χ), a term that grows logarithmically for χ ≫ 1, but which does not violate the hierarchy of terms in the Taylor series being considered, provided that β remains smaller than unity.     

Dielectric properties of 4′-n-alkyl-4-cyanobiphenyls in their nematic phases

The principal dielectric constants of the pentyl to octyl derivatives of 4′-n-alkyl-4-cyanobiphenyl have been measured as functions of temperature in their nematic and isotropic phases. All the compounds exhibit a strong positive dielectric anisotropy due to the presence of a large dipole moment along the major molecular axis. The principal dielectric constantsε _‖ andε _⊥ as well as the anisotropy Δε decrease with increasing alkyl chain length. The experimental value of (ε_‖+2ε_⊥) decreases with decreasing temperature, and is throughout less than the extrapolated isotropic value, in conformity with the model of antiferroelectric short range order proposed by Madhusudana and Chandrasekhar.     

Radical formation in lithium trifluoromethane-sulfonate for ESR dosimetry

Lithium trifluoromethane-sulfonate (Li-TFMS:CF₃SO₃Li) irradiated by γ-rays showed an electron spin resonance (ESR) powder spectrum having the rhombicg-factor ofg _xx = 2.0259 ± 0.0005,g _yy = 2.0112 ± 0.0005 andg _zz = 2.0025 ± 0.0005 and a triplet hyperfine coupling constant ofA _xx/gβ= 0.8 ± 0.15 mT.A _yy andA _zz are not obtained because of the broadened spectrum. The energy levels,g-factor,A _xx/gβ and optical absorption spectrum of several conceivable radicals such as C^⋅F₂SO₃Li, CF₃-S-O^⋅ and CF₃-S-O-O^⋅ have been calculated by softwares MOPAC-V2 and Gaussian-98 based on ROHF (Restricted Hatree-Fock for open shell molecule). The most probable radical was ascribed to CF₃-SO^⋅ from both calculated and experimental results. The response to γ-ray dose and the thermal stability have been studied in addition to the effect of UV illumination for possible use of the signal intensity in ESR dosimetry. The obtained number of free radicals per 100 eV (G-value) was 1.23 ± 0.40.     

ESR of V4+ in α-RbTiOPO4 single crystals

We have recorded and investigated the ESR spectrum of vanadium-doped α-RbTiOPO₄ single crystals in the temperature interval 77–300 K. Two types of structurally distinct centers, V1 and V2, with a 4:1 ratio of the peak intensities were observed. The angular dependences of the resonance magnetic fields are described by a spin Hamiltonian corresponding to axial symmetry with the parameters g _∥1=1.9305, g _⊥1=1.9565, A _∥1=−168.2×10⁻⁴cm⁻¹, and A _⊥1=−54.3×10⁻⁴cm⁻¹ for V1 centers and g _∥2=1.9340, g _⊥2=1.9523, A _∥2=−169.0×10⁻⁴cm⁻¹, and A _⊥2=−55.2×10⁻⁴cm⁻¹ for V2 centers. A model of a paramagnetic center is proposed: The vanadium ions replace titanium ions in two structurally distinct positions Ti1 and Ti2 (V1 and V2 centers, respectively). The possibility that a VO²⁺ ion forms when α-RbTiOPO₄ crystals and crystals of the KTP group (KTiOPO₄, NaTiOPO₄, α-and β-LiTiOPO₄), studied earlier, are doped with vanadium is discussed. Fiz. Tverd. Tela (St. Petersburg) 40, 534–536 (March 1998)