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.     

First-order phase transition from an antiferromagnetic ferroelectric to a cycloidal multiferroic with weak ferromagnetism during the joint action of applied magnetic and electric fields

The thermodynamics of the phase transition in a perovskite-like multiferroic, in which an antiferromagnetic ferroelectric transforms into a new magnetic state where a spiral spin structure and weak ferromagnetism can coexist in applied magnetic field H, is described. This state forms as a result of a first-order phase transition at a certain temperature (below Néel temperature T _N ), where a helicoidal magnetic structure appears due to the Dzyaloshinskii-Moriya effect. In this case, the axes of electric polarization and the helicoid of magnetic moments are mutually perpendicular and lie in the ab plane, which is normal to principal axis c. Additional electric polarization p, which decreases the total polarization of the ferroelectric P, appears in the ab plane. The effect of applied magnetic and electric fields on the properties of a multiferroic with a helicoidal magnetic structure is described. An alternating electric field is shown to cause a field-linear change in magnetic moment m, whose sign is opposite to the sign of the change of electric field E. The detected hysteretic phenomena that determine the temperature ranges of overheating and supercooling of each phase are explained. A comparison with the experimental data is performed.     

Theory of spatial dispersion of dielectric and magnetic constants in magnetic uniaxial gyrotropic crystals

The theory of spatial dispersion of dielectric and magnetic constants of magnetic uniaxial crystals based on generalized Maxwell’s equations D = ε?E = (ε + inγ E = ?ns ^× H and B = μ?H = (μ + inδ)H = ns ^× E with spatial dispersion parameters γ and δ is considered. Generalized Fresnel’s and polarization equations for the obtained vectors E, D, H, and B are analyzed for the wave normal direction s ⊥ C (where C is the optic axis of a crystal). The possibility of the existence of a third natural wave in a crystal is proved.     

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.     

Magnetic field effects on the phonon thermal electromotive force in n-Bi-Sb semiconducting alloys

The phonon thermal electromotive force component α₂₂ (?T ‖ C ₁) prevails in n-Bi_{1 ? x} Sb_x (0.07≤x≤0.16) semiconducting alloys at low temperatures. This component increases by almost an order of magnitude in a classically strong transverse magnetic field H with H ‖ C ₃, which results in an increase in thermoelectric efficiency. The transverse Nernst-Ettingshausen coefficient Q _{12, 3} (?T ‖ C ₁, H ‖ C ₃) changes sign from negative at T > 10 K to positive at T < 10 K. The observed characteristics of the phonon thermal electromotive force and the phonon transverse Nernst-Ettingshausen coefficient are explained in terms of the theory of electron-phonon drag for electrons with a strongly anisotropic spectrum.     

Spatial representation of groups of automorphisms of von Neumann algebras with properly infinite commutant

Theorem. Let a topological groupG be represented (a→φ _a ) by *-automorphisms of a von Neumann algebraR acting on a separable Hilbert spaceH. Suppose that

1. G is locally compact and separable,
2. R′ is properly infinite,
3. for anyT∈R,x,y∈H the function

$$a \to \left\langle {\phi _a (T)x,y} \right\rangle _H $$ is measurable onG. Then there exists a strongly continuous unitary representation ofG onH,a→U _a , such that forT∈R,a∈G, $$\phi _\alpha (T) = U_a TU_a *.$$ .     

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.     

Aging effect in CaLaBa{Cu1???xFex}3O7???�� with 0 �� x �� 0.07 studied by M?ssbauer spectroscopy

In this work, we study the long-term aging effect caused by Fe atoms in the superconductor CaLaBa{Cu_1???xFe_x}₃O_7????? with 0 ?? x ?? 0.07. XRD confirms that this system has a YBCO-like structure. The critical temperature (T_c) is strongly affected by aging and depends on the amount of Fe in the structure. Room temperature Mössbauer spectroscopy reveals the presence of the typical species A, B?CB ??, C and new species E ?? and F. Interestingly; A, which corresponds to the Fe^3?+? atom located in the Cu(1) of the chains with spin S _z = 3/2, shows a drastic reduction which means migration to the species B, B ?? and C. Species B and B ?? correspond to the Fe^3?+? in the Cu(2) site forming planar quasi-octahedral and planar square pyramidal, while the C specie is a square pyramidal with O(5) respectively (spin S_z = 3/2 in all these cases). Aging causes loss of superconductivity in the samples with 5 and 7% of iron content.     

Theoretical studies of ground and excited states in a series of Zn(II) complexes,derived from thiourea and thiosemicarbazide

Theoretical studies for a series of mono- and binuclear zinc (II) complexes Zn(CH₃COO)₂(H₂L)₂ [H₂L = N-2-propenyl-N ^′-2-pyridinylthiourea] (A), Zn₂(CH₃COO)₂(H₃L-a)₂ [H₃L-a = 2-[(2-hydroxy phenyl)methylene]hydrazine-N-phenylcarbothioamide] (B), and Zn(H₃L-b)₂ [H₃L-b = 2-[(2-hydroxy phenyl)methylene]hydrazine-N-(2-propenyl)carbothioamide] (C) have been performed on their structures and excited-state absorption spectra. The singlet ground-state geometries are fully optimised at three DFT levels, i.e., B3LYP, B3PW91, and M06. Different geometries, i.e., strongly distorted tetrahedral coordination environment in complex A, distorted square-pyramidal environment in complex B, and irregular octahedral mode in complex C are identified. Consequently, the spectroscopic properties are calculated by means of time-dependent density functional theory (TDDFT) with the Polarisable Continuum Model (PCM) based on the optimised gas-phase geometries. Three absorption peaks are identified for every complex, which are in good agreement with the experimental ones. For complex A, all three absorption peaks centered at 280.33 nm, 268.09 nm, and 250.87 nm, respectively, are ascribed to the (p,π) → π* transition with a mixed intraligand charge-transfer (ILCT)/ligand-ligand charge-transfer (LLCT) character. The composition of frontier orbitals involved in major absorption bands for the three complexes shows similarities, which results in the almost homologous transition attributions and characteristics. A remarkable bathochromic shift in the lowest-lying absorption band is observed for complexes B and C as compared with complex A, which is attributed to the decreased H (HOMO)-L (LUMO) energy gap (ΔE |HOMO-LUMO|) by the formation of conjugate metallocycles in complexes B and C.     

Phase diagram of antiferromagnetic cobalt fluoride

The H-T phase diagram of antiferromagnetic cobalt fluoride in an external magnetic field H perpendicular to the easy magnetization axis A is completed and used to construct a phase diagram in the variables H _z and H _y . In this diagram, the lines corresponding to second-order phase transitions (between an angular phase and a phase with antiferromagnetic vector I ⊥ A) begin and end in fields of a spin-flip transition (i.e., in an exchange field). A peculiarity of these lines of phase transitions is that each of them has two tricritical points at which this line of second-order phase transitions transforms into a line of first-order phase transitions. A critical angle between the direction of the external magnetic field and the basal plane within which the first-order phase transition takes place is determined.     

On the number of negative eigenvalues for a Schrödinger operator with magnetic field

We consider the Schrödinger operator with magnetic field $$H = \sum\limits_{j = 1}^n {\left( {\frac{1}{i}\frac{\partial }{{\partial x_j }} - a_j } \right)^2 + Vin\mathbb{R}^n .} $$ Under certain conditions on the magnetic fieldB=curla, we generalize the Fefferman—Phong estimates (Bull. A. M. S.9, 129–206 (1983)) on the number of negative eigenvalues for ?Δ+V to the operatorH. Upper and lower bounds are established. Our estimates incorporate the contribution from the magnetic field. The conditions onB in particular are satisfied if the magnetic potentialsa _j (x) are polynomials.     

Rotation of the plane of polarization and linear birefringence of sound in hematite below the morin point

The linear antiferromagnetic birefringence of sound in hematite (α-Fe₂O₃) residing in the collinear easy-axis phase (L ‖ C ₃) below the Morin point is experimentally studied. The plane of polarization of a linearly polarized transverse acoustic wave propagating along the trigonal axis C ₃ of a hematite crystal placed in a magnetic field H applied in the basal plane (H ⊥ C ₃, 3.5 ≤ H ≤ 15 kOe) is found to rotate after a temperature-driven orientational phase transition to the easy-axis state. The angle of rotation exhibits a 180° angular dependence on the direction of the magnetic field in the basal plane and varies from zero to ～π/2. Numerical estimates suggest that the conditions necessary for rotation of the plane of polarization through appreciable angles (～π/2) can be satisfied in the easy-axis phase at orientational phase transition temperatures close to the Morin point, which actually takes place in the fields employed. The results obtained are described sufficiently well by the theory of linear antiferromagnetic birefringence of sound (E.A. Turov) and confirm its main conclusions.     

Radiation of electromagnetic waves by a dipole in an external uniform electrostatic field

Exact solution for the electromagnetic field densities E and H of a dipole of uniformly accelerated point-charges with identical masses is discussed. It is shown that, for any fixed time t and a large distance R between the center of the dipole and the fieldpoint, |E| ~ R ^?4, |H| ~ R ^?5, while for large c|t| ~ R, |E| ~ |H| ~1/R as in spherical electromagnetic waves. Nevertheless, any irreversible radiation of electromagnetic waves is absent since the wave zone does not exist.     

Anisotropic resonant magnetoplasticity of NaCl crystals in the Earth’s magnetic field

Resonant relaxation of the dislocation structure under the action of crossed magnetic fields, i.e., constant magnetic field of the Earth (B _Earth) and alternating radio-frequency field ( $\tilde B$ ), has been experimentally studied in a series of dielectric (NaCl) crystals with various compositions of impurities under variations in the frequency, direction of the pumping field $\tilde B$ , and orientation of the samples in the Earth’s magnetic field. The frequency dependence of the dislocation path length l(ν) exhibits peaks with various heights (l _max) and resonant frequencies (ν_res). The maximum resonant effect has been observed for dislocations with the direction L orthogonal to the plane of crossed magnetic fields in a configuration of mutually perpendicular vectors {L, $\tilde B$ , B _Earth} belonging, together with sample edges {a, b, c}, to the 〈100〉 system. Variation of the concentration C of calcium impurity in crystals of the NaCl_Ca series only influenced the resonant peak height as $l_{\max } \propto 1/\sqrt C $ . Rotation of the magnetic field $\tilde B$ in the (b, c) plane from direction $\tilde B$ ⊥ B _Earth to $\tilde B$ ∥ B _Earth also did not influence the frequency of the resonance but changed its amplitude. Depending on the crystal type, this influence changed from rather insignificant (in crystals of the NaCl_LOMO series) to complete suppression of the effect for $\tilde B$ ∥ B _Earth (in the NaCl_Nik series). The resonant frequency ν_res is sensitive to orientation of the sample with respect to B _Earth. Upon rotation of the crystal by the angle θ = ∠(c, B _Earth) about the a ⊥ B _Earth edge, the initial peak for dislocations L ‖ a at the crystal orientation θ = 0 and the frequency ν _res ⁰ is replaced by a pair of peaks at frequencies ν_{1, 2} ≈ ν _res ⁰ cosθ_{1, 2}, where θ₁ = 90° ? θ and θ₂ = θ. Previously, these peaks were observed separately in NaCl_Nik crystals for $\tilde B$ ∥ c and $\tilde B$ ∥ b. In the present study, these peaks have been observed simultaneously for both orientations of $\tilde B$ in NaCl_LOMO and NaCl_Ca crystals, where the resonance is not completely suppressed for $\tilde B$ ∥ B _Earth.     

Nonmonotonic magnetic-field dependence of transport coefficients for n-Bi-Sb semiconducting alloys

The transport coefficients of tellurium-doped n-Bi_{1 ? x} Sb _x semiconducting alloys (0.07 ≤ x ≤ 0.15) are studied for single-crystal samples in the temperature range 1.5 ≤ T ≤ 40 K and in magnetic fields 0 ≤ H < 20 kOe. The theory developed in this study attributes the specific features in the behavior of the transport coefficients observed in a magnetic field to a strong anisotropy of the electron spectrum and anisotropy in the electron relaxation time. It is found that the dependences of the transport coefficients on the magnetic field for H ∥ C ₃ can be theoretically expressed through one anisotropy parameter δ, and those for H ∥ C ₂, by means of several anisotropy parameters, namely, γ, η, ζ, and m ₃/m ₁. It is established that the anisotropy parameter δ in the n-Bi-Sb semiconducting alloys can be estimated from measurements of the electrical resistivity ρ₂₂(∞)/ρ₂₂(0) ? δ and the Hall coefficient R _12.3(∞)/R _12.3(H → 0) ? δ in a magnetic field H ∥ C ₃. It is shown that the observed increase in the thermoelectric efficiency by a factor of 1.5–2.0 in the transverse magnetic fields H ∥ C ₃ and H ∥ C ₂ originates from the nonmonotonic dependence of the diffusion component of the thermopower Δα₂₂(H)(?T ∥ C ₁) on the magnetic field. The nonmonotonic dependence of the diffusion thermopower in n-Bi-Sb semiconducting alloys is associated with the strong anisotropy of the electron spectrum, the anisotropy in the electron relaxation time, and the many-valley pattern of the spectrum.     

Magnetic Bloch states and Hall conductivity of a two-dimensional electron gas in a periodic potential without inversion center

Quantum states of 2D electrons are studied in a periodic potential without inversion center in the presence of a magnetic field. It is shown that the energy spectrum in magnetic subbands is not symmetric about the center of magnetic Brillouin zone E(k)≠E(?k). Singularities (phase branching points) of the electron wave function, which determine the quantization law of Hall conductivity σ_xy, are studied in the k space. It is found that a sharp change takes place in the number of points in the magnetic Brillouin zone and in the corresponding values of topological invariants determining the Hall conductivity of filled subbands. It is noted that the longitudinal conductivity of a lattice without inversion center placed in a magnetic field is not invariant with respect to a change in sign of the electric field, and a photovoltaic effect must arise in an ac electromagnetic field.     

Mössbauer absorption by soft ferromagnets in radio-frequency magnetic field

The simultaneous influence of periodical magnetic field reversals at the nucleus between the values ±h ₀ and of magnetostrictive vibrations on the shape of the Mössbauer absorption spectrum is analyzed. The effect of a constant external magnetic field is taken into account by assuming unequal durations of the states ?h ₀ and +h ₀. It is shown that such asymmetric reversals of the magnetic field lead to splitting of the absorption lines into Zeeman patterns corresponding to the time-averaged magnetic field h ₀ R, where R is the asymmetry parameter of the reversals. The calculations agree well with experiment.     

Role of critical fluctuations in the formation of a skyrmion lattice in MnSi

The region in the H–T phase diagram near the critical temperature (T _c ) of the cubic helicoidal MnSi magnet is comprehensively studied by small-angle neutron diffraction. Magnetic field H is applied along the [111] axis. The experimental geometry is chosen to simultaneously observe the following three different magnetic states of the system: (a) critical fluctuations of a spin spiral with randomly orientated wavevector k _f , (b) conical structure with k _c ∥ H, and (c) hexagonal skyrmion lattice with k_sk ⊥ H. Both states (conical structure, and skyrmion lattice) are shown to exist above critical temperature T _c = 29 K against the background of the critical fluctuations of a spin spiral. The conical lattice is present up to the temperatures where fluctuation correlation length ξ becomes comparable with pitch of spiral d _s . The skyrmion lattice is localized near T _c and is related to the fluctuations of a spiral with correlation length ξ ≈ 2d _s , and the propagation vector is normal to the field (k_sk ⊥ H). These spiral fluctuations are assumed to be the defects that stabilize the skyrmion lattice and promote its formation.     

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.