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.     

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.     

Magnetic properties of HoFe3(BO3)4

The magnetic properties of an antiferromagnet with trigonal symmetry, namely, HoFe₃(BO₃)₄, have been investigated theoretically. The calculations have been performed in the molecular field approximation and in the framework of the crystal field model for the rare-earth subsystem. Extensive experimental data on the magnetic properties of HoFe₃(BO₃)₄ have been interpreted and good agreement between theory and experiment has been achieved using the obtained theoretical dependences. The spontaneous spin-reorientation transition and the spin-reorientation transition induced by a magnetic field B ‖ a from the easy-axis to easy-plane state, as well as the spin-flop transition in a magnetic field B ‖ c, have been described. It has been shown that the spontaneous spin-reorientation transition is a magnetic analog of the Jahn-Teller effect. The temperature dependences of the initial magnetic susceptibility at temperatures ranging from 2 to 300 K, the nonlinear curves of magnetization for B ‖ c and B ⊥ c in a magnetic field up to 1.2 T (which indicate the occurrence of first-order phase transitions), and their evolution with variations in the temperature have been described, as well as the temperature and field dependences of the magnetization in a magnetic field up to 9 T. The parameters of the trigonal crystal field for the rare-earth ion Ho³⁺ and the parameters of the Fe-Fe and Ho-Fe exchange interactions have been determined in the course of interpretation of the experimental data.     

Two-dimensional representation of position, velocity and acceleration by PFG-NMR

A novel view on the presentation of pulsed field-gradient nuclear magnetic resonance experiments to encode position and translational displacements is given. A conventional diffusion or flow experiment employing two magnetic field gradients of effective areak ₁, andk ₂ separated by a time interval Δ can formally be expressed as a means to probek space in a two-dimensional way. While for most applications, a full coverage of the [k ₁,k ₂] space is not necessary, an experiment withk ₁ = ?k ₂ can be regarded as a sampling of the secondary diagonal in [k ₁,k ₂] space. Likewise, the main diagonal is represented by the conditionk ₁ =k ₂ and encodes position. Thus, the [r ₁,r ₂] space conjugate to [k ₁,k ₂], which is obtained by Fourier transformation, can be transferred into a position/displacement correlation plot simply by rotation of the coordinate system by an angle of 45°. While displacementR =r ₂ ?r ₁ corresponds to an average velocity? =R/Δ, an extension towards higher-order derivations such as acceleration is straightforward by modification of the pulse sequence. We discuss this new concept in a general way, treating both the magnetic field and the particle position by Taylor expansions with respect to space and time, respectively, and present examples for fluid flowing through capillary systems in the light of the suggested interpretation.     

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.     

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.     

A Schiff-Based Colorimetric Fluorescent Sensor with the Potential for Detection of Fluoride Ions

A simple Schiff-based colorimetric fluorescent receptor 1 was prepared. It exhibits a “turn-on-type” mode with high sensitivity in the presence of F^?. The change in color is very easily observed by the naked eye in the presence of F^?, whereas other anions do not induce such a change. Job plot indicated a 1:2 complexation stoichiometry between receptor 1 and F^?. The association constant for 1-F^? in CH₃CN was determined as 1.32*10⁵ M^?2 by a Hill plot.

Indole-based Fluorescent Sensors for Selective Detection of Hg2+

A series of indole-based fluorescent chemosensors 1–4 were prepared and investigated characteristick features with transition metal ions. Sensors 1 and 2 were selective for Hg²⁺ ion among a series of metal ions in H₂O–DMSO with association constants of 4.60×10⁴ and 5.90×10⁴?M^?1 and detection limits of 140 and 101.6 μM, respectively.

Saturation magnetization distribution in the vicinity of a grain boundary in a plate of a triaxial silicon-iron-type ferromagnet

The one-dimensional saturation magnetization distribution M _S(x) in the vicinity of grain boundaries (GBs) is studied in $(01\bar 1)$ plates of soft magnetic alloys of the Fe-3% Si type in the framework of the theory of micromagnetism. The mechanisms of the emergence of spatial inhomogeneities of the saturation magnetization near planar GBs are discussed. Calculations show that macroscopic regions Δx≈10 mm in extent arise near GBs because of the μ* effect. This result is supported by the experimental data.     

Decay of helicity in homogeneous turbulence

The self-similar relaxation of helicity in homogeneous turbulence has been considered taking into account integral invariants ∫ ₀ ^∞ r ^m 〈u(x)ω(x + r)〉 dr = I _m ^h (where ω = curlu and r = |r|). It has been shown that integral invariants with m = 3 for both helicity and energy are possible in addition to helical analogs of Loitsyanskii (m = 4) and Birkhoff-Saffman (m = 2) invariants associated with the conservation laws of momentum and angular momentum, respectively. Helicity always relaxes more rapidly than the energy. Its decay exponent is in the interval from ?3/2 to ?5/2 versus the interval from ?6/5 to ?10/7 for the energy.     

Magnetic Properties of Sm0.7Ho0.3Fe3(BO3)4

The magnetic properties of a ferroborate single crystal of substituted composition Sm_0.7H_0.3Fe₃(BO₃)₄ with competing Sm-Fe and Ho-Fe exchange interactions are studied. The measured properties and effects are interpreted in terms of a general theoretical approach based on the molecular field approximation and calculations using the crystal field model for a rare-earth ion. The experimental temperature dependences of the initial magnetic susceptibility in the temperature range 2?C300 K, the anomalies in the magnetization curves for B ?? c and B ?? c in fields lower than 1.2 T, and the field and temperature dependences of magnetization in fields lower than 9 T are described. The crystal field parameters and the parameters of the R-Fe and Fe-Fe exchange interactions are determined during the interpretation of the experimental data.     

The microwave absorption of high-T c superconducting thin film samples

The experimental and theoretical investigations of microwave losses (ML) in HTSC thin films are carried out. It is shown theoretically that ML in the maximum of the magnetic componentB ₁ are essentially larger than those in the maximum of the electric componentE ₁. This is because eddy currents make much more substantial contribution to ML as compared to conventional conductivity currents. The consequence of this is the angular dependence of ML with respect to theB ₁ field direction which was experimentally observed. The angular dependences of ML with respect to theB ₀ field direction for both low and highB ₀ values were also investigated. The majority of experimental data can be well explained within the mixed model which predicts the existence of a critical state in inter- and intragranular Josephson medium.     

Specific features of the thermal electromotive force in Bi quantum wires in transverse magnetic and electric fields

The thermal electromotive force (emf) in Bi quantum wires has been calculated in the model of potential in the form of a paraboloid of revolution in a uniform magnetic field H, which is normal to the axis of the studied nanostructure, and in a direct-current (dc) electric field E ‖ H. It has been shown that, with an increase in E, the thermal emf α _xx is described by a nonmonotonic function at different values of H. A physical interpretation of this behavior of α _xx as a function of E is proposed with account for the interaction between carriers and the rough surface of the nanowire.     

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.     

Synthesis and Spectroscopy of Novel Branched Fluorescent Dyes Containing Benzophenone Parts and the Possibility as Fluorescence Probes

This paper describes a new fluorescent family of branched dyes containing benzophenone unit including 4-N, N-diphenylamino-4??-phenacyl-stilbene (C1), 4,4??-di(4-benzoylphenylethylene)yl-triphenylamine (C2) and 4,4??,4??-tri(4-benzoylphenylethylene)yl-triphenylamine (C3). Benzophenone part is coupled with core through C?CC double bond. The chemical structures of the derivatives are characterized with ¹H and ¹³C nuclear magnetic resonance and elemental analysis. Strong ?ШC?? stacking interactions are discovered with the analysis of the X-ray crystallographic data of C1. The absorption maxima and emission maxima of the derivatives exhibit gradual bathochromic shift from C1 to C3. The optical density of C1, C2 and C3 are shown to be related to the number of branches. The changes of dipole moments between the excited and ground states for C1, C2 and C3 were estimated to be 4.356, 8.091 and 8.479 Derby, respectively by Lippert equation, confirming that the internal charge transfer (ICT) dominates the process of excited singlet state. The possibility as fluorescence probes of the derivatives on the estimation of what region of micelles interacting with samples was evaluated.     

Magnetic properties of the Nd0.95Dy0.05Fe3(BO3)4 ferroborate with small substitution in the rare-earth element subsystem

The magnetic properties of a substituted Nd_0.95Dy_0.05Fe₃(BO₃)₄ ferroborate single crystal with competing Nd-Fe and Dy-Fe exchange interactions are studied experimentally and theoretically. A spontaneous spin-reorientation transition is detected near T = 4.3 K, and anomalies are observed in the low-temperature magnetization curves along trigonal axis c and in basal plane ab. The measured properties and the detected effects are interpreted in terms of a general theoretical approach, which is based on the molecular field approximation and crystal field calculations for a rare-earth ion. The experimental temperature dependences of the initial magnetic susceptibility in the range 2–300 K, the anomalies in the magnetization curves for B ‖ c and B ⊥ c in fields up to 1.5 T, and the field and temperature dependences of magnetization in fields up to 9 T are described. The effect of small substitution in the rare-earth subsystem on the magnetic properties is analyzed. The crystal field parameters and the parameters of the R-Fe and Fe-Fe exchange interactions are determined from the experimental data.     

Phosphorus(V)corrole- Porphyrin Based Hetero Trimers: Synthesis,Spectroscopy and Photochemistry

‘Axial-bonding’-type hetero trimers have been constructed by employing a simple ‘inorganic’ reaction such as axial bond formation of main group element containing phosphorus corrole. The approach is simple and modular in nature. The architecture of these hetero trimers such that, while a phosphorus(V)corrole forms the basal scaffolding unit, either two free-base porphyrins [(H ₂ ) ₂ –PCor] or Zn^II porphyrins [(Zn) ₂ –PCor] occupy the two axial sites via an aryloxy bridge. Both hetero trimeric species have been completely characterized by mass (FAB), UV/Vis, proton nuclear magnetic resonance spectroscopies and also by the differential pulse voltammetric method. Comparison of their spectroscopic and electrochemical data of these trimers with those of the corresponding reference compounds reveal that there is no apparent ring-to-ring interactions in these ‘vertically’ linked hetero trimers. Reduced fluorescence quantum yields were observed for [(H ₂ ) ₂ –PCor] and [(Zn) ₂ –PCor] when compared to corresponding monomeric chromophores. Finally, a comparison is made between the presently reported phosphorus(V)corrole based hetero arrays and the previously reported analogous arrays based on Ge(IV)corrole with regard to their spectroscopic properties and photochemical activities.     

Instantons, Poisson Structures and Generalized Kähler Geometry

Using the idea of a generalized Kähler structure, we construct bihermitian metrics on CP² and CP¹×CP¹, and show that any such structure on a compact 4-manifold M defines one on the moduli space of anti-self-dual connections on a fixed principal bundle over M. We highlight the role of holomorphic Poisson structures in all these constructions.     

Perpendicularev mass fromW decay

We point out properties of the “perpendicularev mass”, defined in terms of transverse momentap _t byM _T ² (ev)=2|p _eT | |p _vT |?2p _eT ·p _vT , that make it particularly well suited toW mass and width determinations. We give an analytic expression for its distribution inW production and subsequentW→ev decay a \(\bar pp\) colliders, accurate to order 〈p _WT ² /M _W ² 〉≈1%. A maximum likelihood fit of this formula to the five UA1 events givesM _W=80.3 _?3 ⁺⁶ GeV.