Some estimates for magnetic fluctuations in a turbulent medium

A new integral relationship between the fluctuations b(r, t) of a magnetic field and its mean B ₀(r, t) is derived for the steady-state magnetic field in a turbulent medium. This formula provides the estimate 〈b?curlb〉=?B ₀?curlB ₀. Simultaneously, the coefficient of amplification of the mean magnetic field α effect) is obtained: α=(η+β)B ₀? curlB ₀/B ₀ ² . The formula for α allows for a decrease in this coefficient owing to the back action of the magnetic field on the turbulent velocity field. It is shown that the Zel’dovich’s estimate 〈 b ²〉?β/η B ₀ ² for two-dimensional turbulence holds for magnetic fields at the instant the fluctuations 〈a ²〉 of the vector potential, rather than 〈b ²〉, reach a maximum. Here, η and β are the ohmic (molecular) and turbulent diffusion coefficients, respectively. This estimate is refined with allowance made for the fact that the condition for diffusion approximation itself relates the β, b, and B ₀ quantities to each other.     

Magnetostriction and thermal expansion of HoAl3(BO3)4

The magnetostriction and thermal expansion of rare-earth aluminoborate HoAl₃(BO₃)₄ have been studied theoretically. The calculated field and temperature dependences of the multipole moments of the Ho³⁺ ion in HoAl₃(BO₃)₄ made it possible to describe the known experimental data and to predict possible anomalies of thermal expansion. It has been shown that, for the direction of the field B ‖ c, the nonmonotonic character of magnetostriction along the axis a is determined by the multipole moments, the main of which is β _J 〈O ₄ ⁰ 〉. For B ‖ a and B ‖ b, the maximum moments are β _J 〈O ₄ ² 〉and α _J 〈O ₂ ² 〉; their variation with the field and temperature explain well the form of magnetostriction. It has been established that the greater value of magnetostriction Δa/a for B ‖ b than for B ‖ a and the greater value of magnetostriction for the field in the basal plane than for B ‖ c are caused by greater variations in the field of actual multipole moments.     

States on the current algebra

We introduce the field algebra Σ$\text{D}$(M;ⁿ?ⁿ$\text{g}$) associated with the current algebra $\text{D}$_r(M;$\text{g}$) for the Lie algebra $\text{g}$ over physical space M. The Heisenberg magnet model is generalized to this continuum. It is shown that the Hamiltonian can be given meaning as implementing a derivation of the field algebra in certain representations.We introduce new representations of the current algebra. For example, if G = SU(2), a representation in L²(R³)?³ is [σ(?)F]^j = ε^jkl?_kψ_l for (?_k) = ? in $\text{D}$_r(M;$\text{g}$)(ψ_l = F. This has cyclic subrepresentations with prime parts.     

Effect of an external electric field on liquid crystalline polymers

The effect of an external electric field on the order parameter and on the isotropic-anisotropic phase transition temperature for semi-flexible liquid crystalline polymers is studied by a mean-field approximation. For the polymers whose electric dipole moments are parallel to the chain backbone, the critical transition temperature T_c is extensively changed by gDT ∼ ∥E∥², where E is the external electric field.     

Bulk magnetization study of a DyNi5 single crystal

Magnetization and susceptibility measurements were performed on a single crystal of DyNi₅ along the three main symmetry axes of the ortho-hexagonal cell. Below its ordering temperature (T_c = 11.6 K), b and c are respectively the easy and hard magnetization axes. The strong anisotropy originates from the crystalline electric field acting on the 4f electrons of the Dy³⁺ ions. A small magnetization is induced on nickel atoms by the applied field and the exchange interactions with the dysprosium atoms. The crystal field parameters, the molecular field coefficients and the susceptibility of nickel atoms are determined from the experimental data.     

Magnetic Resonance Imaging of Diffusion in the Presence of Background Gradients and Imaging of Background Gradients

The measurement of the self-diffusion coefficient D by an NMR technique that uses an applied gradient G_A can be corrupted by systems that have a background magnetic field gradient G₀ and also by imaging gradients G₁, when used in an imaging mode. In a nonimaging mode, the corrupting cross term G_A · G₀can be eliminated in the diffusion measurement by use of an alternating-pulse-field-gradient (APFG) sequence that allows an accurate and uncorrupted measurement of D. A Carr-Purcell echo train enables the measurement of the expectation value, 〈DG²₀〉; assuming D and G₀ to be uncorrelated will allow 〈G²₀〉 to be determined. An image of D or of 〈DG²₀〉 may be obtained without the corrupting G_A · G₀ and G_A · G_I terms by appending a standard imaging sequence to an APFG sequence or a Carr-Purcell sequence, respectively; assuming D and G₀ to be uncorrelated will allow (〈G²₀〉 to be determined within each pixel. Measurements of D and 〈G²₀〉 and their images are made in apple flesh in which minute air bubbles are shown to produce the large 〈G²₀〉. Their values in an 81 g Golden Delicious apple at a measuring frequency of 100 MHz were D = 1.42 × 10⁻⁵ cm²/s and [formula] = 8.9 G/cm.     

Magnetic-field and temperature effects on the optical properties of dicyano-2,2′-bipyridyl-platinum(II) single crystals

Studies of the polarized emission of [Pt(CN)₂(bipy)] single crystals as function of temperature (1.9 K ⩽ T ⩽ 295 K) and homogeneous magnetic fields (0 ⩽ H ⩽ 6 T), and the temperature dependence of the polarized absorption spectrum are reported. Raising the temperature from 1.9 to 7 K or increasing the magnetic field from 0 to 1 T results in a blue shift of ≈175 cm^-1 in the E ⊥ a polarized emission (E: electric field vector, a: crystallographic a axis). Between 1.9 and 295 K at H = 0) and between 0 and 6 T (at T = 1.9 K), the emission lifetime decreases by factors of ≈10³ and ≈10², respectively. The results are explained within the C'_2v symmetry of the single complex assuming a coupling between neighboring central ions.     

Magnetic properties of the compounds N(CH3)4MnIIMIII(CN)6 ·8 H2O(MIII = Mn,Fe)

In the isostructural cyanobridged chain compounds N(CH₃)₄Mn^IIM^III(CN)₆ · 8H₂O high spin Mn(II) ions couple antiferromagnetically to low spin Mn(III) of Fe(III) ions. The Mn^II–Mn^III compound orders ferrimagnetically below T_N = 28.5 ± 1 K. The tetragonal a and b axes are easy ones for the magnetic moments. In the Mn^II–Fe^III compound antiferromagnetic order occurs below T_N = 9.3 K, with spins aligned along the tetragonal c axis. The compound undergoes a meta-magnetic transition from the antiferromagnetic to a ferrimagnetic phase. This occurs at 2 K for a field H_crit ≈ 1.2 T. The temperature dependence of H_crit, which vanishes at T_N, is followed. The tricritical temperature T¹ is ～ 5 K.     

Instability of electromagnetic waves in transversely magnetised semiconductor-plasmas

Using the hydrodynamic model of plasmas the general dispersion relation is derived in the collisiondominated regime when a d.c. magnetic field is applied (Y-axis) transversly to the propagation vector k (Z-axis), and the d.c. electric field is inclined to the Z-axis in the X-Z plane. The dispersion relation is solved for intrinsic and extrinsic semiconductors to explore the possibility of wave instability. The threshold conditions of wave oscillations are obtained. In n-InSb the frequency of the oscillation attains a maximum value when the electron cyclotron frequency is equal to the electron collision frequency. In intrinsic InSb instability is possible only in the long wavelength region for E₀ ? 10 kVm^?1 when B₀> 0.2 T, while for lower values of B₀, E₀ should be greater 20kVm^?1. The energy dependent collision frequency has a significant effect on the threshold frequency of oscillation.     

Magnetooptical evidence of exchange interactions in zero-gap Hg1−xFexTe mixed crystals

Interband magnetoabsorption is carried out on zero gap Hg_1-xFe_xTe alloys of x ～ 0.015.Γ₆ → Γ₈ magnetooptical spectra for σ⁺, σ^-, γ 6 H polarization are quantitatively interpreted within the “quasi Ge” model modified by the inclusion of exchange contributions. The field dependence of the magnetization provides evidence of antiferromagnetic interactions between localized spins.     

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.     

Dependence of electron spin g-factor on magnetic field in quantum wells

The dependence of electron spin g-factor on magnetic field has been investigated in GaAs/AlGaAs quantum wells. We have estimated the electron g-factor from spin precession frequency in time-resolved photoluminescence measurements under a magnetic field in different configurations; the magnetic field perpendicular (g_⊥) and parallel (g_∥) to the quantum confinement direction. When the angle between the magnetic field and the confinement direction is 45°, we have found that g-factor varies depending on the direction of magnetic field and the circular polarization type of excitation light (σ⁺ or σ^?). These dependences of g-factor exhibit main features of Overhauser effect that nuclear spins react back on electron spin precession. The value of g_⊥ and g_∥ corrected for the nuclear effects agree well with the results of four-band k·p perturbation calculations.     

Commensurate and incommensurate states of a spin density wave in a quasi-two-dimensional system with an anisotropic energy spectrum in an external magnetic field of arbitrary direction relative to magnetization

A theory of thermodynamic properties of a spin density wave (SDW) in a quasi-two-dimensional system (with a preset impurity concentration x) is constructed. We choose an anisotropic dispersion relation for the electron energy and assume that external magnetic field H has an arbitrary direction relative to magnetic moment M _Q . The system of equations defining order parameters M _Q ^z , M _Q ^σ , M _z , and M ^σ is constructed and transformed with allowance for the Umklapp processes. Special cases when H ‖ M _Q and H ⊥ M _Q (H _Z H ^σ = 0) are considered in detail as well as cases of weak fields H of arbitrary direction. The condition for the transition of the system to the commensurate and incommensurate states of the SDW is analyzed. The concentration dependence of magnetic transition temperature T _M is calculated, and the components of the order parameter for the incommensurate phase are determined. The phase diagram (T,~x) is constructed. The effect of the magnetic field on magnetic transition temperature T _M is analyzed for H _Z H ^σ = 0, and longitudinal magnetic susceptibility χ‖ is calculated; this quantity demonstrates the temperature dependence corresponding to a system with a gap for x < x _c and to a gapless state for x > x _c . In the immediate vicinity of the critical impurity concentration (x ～ x _c ), the temperature dependence of the magnetic susceptibility acquires a local maximum. The effect of anisotropy of the electron energy spectrum on the investigated physical quantities is also analyzed.     

Analysis of the spin splitting of maxima of quantum oscillations of the resistivity of n-Bi-Sb semiconductor alloys in a magnetic field parallel to the bisector axis

In samples of semiconductor alloys n-Bi_0.93Sb_0.07 with different electron concentrations (n ₁ = 8 × 10¹⁵ cm^?3, n ₂ = 1.2 × 10¹⁷ cm^?3, and n ₃ = 1.9 × 10¹⁸ cm^?3), dependences of the electrical resistivity on magnetic fields up to 45 T parallel to the current and the bisector axis (H ‖ C ₁ ‖ j) have been measured at temperatures of 1.5, 4.5, and 10 K. The obtained dependences ρ₂₂(H) demonstrate quantum oscillations of the resistivity (Shubnikov-de Haas effect), and, in high magnetic fields, there is a resistivity maximum far away from other maxima. On assumption that this maximum is related to the spin-split Landau level N = 0^? for electrons of the main ellipsoid, the spin-splitting parameters are calculated for electrons of the main ellipsoid: γ₁ = 0.87, γ₂ = 0.8, and γ₃ = 0.73. Using these values, the oscillation maxima can be reliably related to the numbers of split Landau levels for electrons of the main and secondary ellipsoids. The dependences of the resistivity ρ₁₁ and the Hall coefficient R _31.2 on magnetic field have been measured in a transverse magnetic field at H ‖ C ₁ and j ‖ C ₂ on the sample with the electron concentration n ₄ = 1.4 × 10¹⁷ cm^?3. Using similar analysis, the spin-splitting parameter is found to be γ₄ = 0.85, which is close to the value of γ₂ = 0.8 obtained for the sample with close electron concentration (n ₂ = 1.2 × 10¹⁷ cm^?3) during the measurements in a longitudinal magnetic field. The quantum oscillation maxima of Hall coefficient R _31.2 are shifted to the range of high magnetic fields as compared to the quantum oscillation maxima of resistivity ρ₁₁.     

Ab initio SCF-Cl studies on the large amplitude bending motion of the water molecule: Rigid,semirigid, and nonrigid bender models for the Hamiltonian

Self-Consistent Field (SCF) and Configuration Interaction (CI) studies are performed on the bending mode of the water molecule using a double zeta plus polarization basis set. The ab initio points are fitted to a three-parameter double minimum potential consisting of a quadratic plus Lorentzian terms. The vibration-rotation energies are then evaluated using the large amplitude Hamiltonian developed by P. R. Bunker and co-workers at various levels of approximations. It is found that the calculated frequencies improve significantly as one proceeds from approximate H_b⁰⁰(ρ) to rigid bender H_b⁰(ρ) [P. R. Bunker and J. M. R. Stone, J. Mol. Spectrosc.41, 310–332 (1972)] to semirigid bender H_b⁰(r, ρ) [P. R. Bunker and P. M. Landsberg, J. Mol. Spectrosc.67, 374–385 (1977)] Hamiltonian. With H_b⁰(r, ρ), the ab initio calculated bending frequency ν₂ differs from the observed value (1595 cm^?1) by 30 cm^?1 and the barrier height is 12 229 cm^?1. It is also shown that ν₂ and its first four overtones are better calculated by 45–98 cm^?1 when the ab initio potential is used directly instead of the three-parameter analytic potential fitted to ab initio data. Finally, rotation bending energy levels are calculated for v₂ ≤ 3 and J ≤ 10 on the basis of a nonrigid bender Hamiltonian of A. R. Hoy and P. R. Bunker [J. Mol. Spectrosc.74, 1–8 (1979)], using the ab initio quadratic force field of P. Hennig, W. P. Kraemer, G. H. F. Diercksen, and G. Strey, [Theor. Chim. Acta47, 233–248 (1978)]. These results show that the accuracy of calculated force constants and frequencies is critically dependent not only on the size of the basis set but also on the number and spacing of the ab initio points used to derive the force field.     

Electric field properties at cationic sites in normal, incommensurate and commensurate K2ZnCl4 crystals

The local electric properties at K and Zn sites in the normal, incommensurate and commensurate phases of K₂ZnCl₄, as derived from a numerical computation of the lattice contributions to the electric potential V(r), electric field intensityE(r) and electric field gradient tensorV _αβ(r) are reported. The numerical data obtained at each cationic position were correlated with the experimental³⁹K NMR, Cu²⁺ and Mn²⁺ EPR and⁵⁷Fe Mössbauer results in pure and doped K₂ZnCl₄. A proportionality between crystal field and zero-field splitting was taken into account for Mn²⁺, whereas for K⁺, Cu²⁺ and Fe³⁺ ions the electric field gradient is directly related to the crystal field parameter. By this comparison, on computations done in the ionic fractional charge and relaxed lattice approximations, the insertion of probe-species of iron, copper and manganese ions on off-center Zn sites is proposed. The³⁹K electric field gradient tensor calculations in the incommensurate phase fit well with the NMR data reported recently.     

High pressure tuning of optical transitions in Mg[Pt(CN)4]·7H2O

Mg[Pt(CN)₄]·7H₂O belongs to the class of tetracyanoplatinates(II) which crystallize in columnar structures. In different M_x[Pt(CN)₄]·yH₂O (MCP) single crystals the in-chain Pt-Pt-distance R varies between 3.67 Å (NaCP) and 3.15 Å (MgCP). Two optical transitions can be observed in polarized emission with the electric field vector E either parallel or perpendicular to the columnar (c)-axis. Polarized emission spectra of MgCP are recorded under hydrostatic pressure up to p ≈ 18 kbar (at 295 K). The transition energy v?₆ can be tuned from 17,600 cm^-1 to about 12,000 cm^-1 (2.18-1.48 eV). The pressure induced red shift for the two transitions is: E 6 c: dv?₆/dp = -320±20 cm^-1/kbar, E ⊥ c: dv?_⊥/dp = -270±20 cm^-1/kbar. These values are discussed in the context of the known functional relationship (for ambient conditions) between v? and R.     

Effect of an external magnetic field and a trapped magnetic flux on the current-voltage characteristics of a granular high-temperature superconductor YBa2Cu3O7−δ

A comparative study of the current-voltage characteristics of the high-temperature ceramic superconductor YBa₂Cu₃O_～6.95 at T = 77.3 K is performed over wide ranges of external magnetic fields H _ext and “treatment” fields H _treat. It is found that the field dependences of the parameters a and j _c involved in the exponential equation E = a(j ? j _c)^v describing the current-voltage characteristics depend substantially on the method used for applying the magnetic field, whereas the exponent v ～ 2 depends on neither the method of application nor on the magnetic field strength. The field dependence of the trapped magnetic field H _trap is determined.     

New N2+Electronic States in the Region of 23–28 eV

Threshold photoelectron spectra of N₂⁺were measured between 23.4 and 27.6 eV with high resolution and high intensity by using the penetrating field technique and synchrotron radiation. Five vibrational progressions were observed. The first of these progressions was theC²Σ_u⁺state. The second progression was identified as the transition to the second state of²Π_gsymmetry found by P. Baltzer, M. Larsson, L. Karlsson, B. Wannberg, and M. Carlsson (1992.Phys. Rev. A46,5545). The third progression, which was discovered by F. Merkt and P. M. Guyon (1993.J. Chem. Phys.99,3400), can be designated as the²Σ_u⁻state by comparison with previous theoretical study (E. W. Thulstrup and A. Andersen, 1975.J. Phys. B8,965). The fourth and fifth progressions were designated as the²Δ_uand 2²Π_ustates by similar comparison with previous theories.     

Nuclear magnetic resonance in noncollinear antiferromagnet Mn3Al2Ge3O12

The ⁵⁵Mn nuclear magnetic resonance spectrum of noncollinear 12-sublattice antiferromagnet Mn₃Al₂Ge₃O₁₂ has been studied in the frequency range of 200–640 MHz in the external magnetic field H ‖ [001] at T = 1.2 K. Three absorption lines have been observed in fields less than the field of the reorientation transition H _c at the polarization h ‖ H of the rf field. Two lines have been observed at H > H _c and h ⊥ H. The spectral parameters indicate that the magnetic structure of manganese garnet differs slightly from the exchange triangular 120-degree structure. The anisotropy of the spin reduction and (or) weak antiferromagnetism that are allowed by the crystal symmetry lead to the difference of ≈3% in the magnetization of sublattices in the field H < H _c. When the spin plane rotates from the orientation perpendicular to the C ₃ axis to the orientation perpendicular to the C ₄ axis, all magnetic moments of the electronic subsystem decrease by ≈2% from the average value in the zero field.