On the Measurement of the Stiffness of Spin Waves in the Fe<Subscript>0.75</Subscript>Co<Subscript>0.25</Subscript>Si Helimagnet by the Small-Angle Neutron Scattering Method

The stiffness of spin waves in the Fe_0.75Co_0.25Si helimagnet with the Dzyaloshinskii–Moriya interaction in a state fully magnetized by an external field has been measured by the small-angle neutron scattering method. It has been shown that the dispersion of magnons in this state is anisotropic because the neutron scattering pattern consists of two circles for neutrons with obtaining and losing the magnon energy, respectively. The centers of the circles are shifted by the momentum transfer oriented along the applied magnetic field H and equal to the wave vector of the spiral ±k_s measured in inverse nanometers. The radius of the circles is directly related to the stiffness of spin waves and depends on the magnitude of the magnetic field. It has been shown that the stiffness of spin waves A for the helimagnet is equal to 46.0 meV Ų at T = 0 K and decreases weakly (by 20%) with increasing temperature up to the critical value T_c = 38 K.     

Discovery of a <Emphasis Type="Italic">P</Emphasis>-odd effect in triton emission from the reaction <Superscript>6</Superscript>Li(<Emphasis Type="Italic">n</Emphasis>, α)<Superscript>3</Superscript>H

The results of measuring the P-odd asymmetry (S_n · P_t) for triton emission from the reaction ⁶Li(n, α)³H are presented. Here, S_n is the neutron spin and P_t is the triton momentum. Three series of measurements were performed, one at the Petersburg Nuclear Physics Institute (Gatchina, Russia) in a vertical neutron beam from the PWR reactor and two in the PF1B beam from the reactor at the Institute Laue-Langevin (Grenoble, France). On the basis of all three experiments, the P-odd asymmetry coefficient was found to be α_PN = ?(8.6 ± 2.0) × 10^?8. The results of zero experiments and calculations give every reason to believe that the above P-odd asymmetry is due to the reaction being studied.     

Magnetic structure of Er<Subscript>5</Subscript>Ge<Subscript>3</Subscript> at 4.2 K

A symmetry analysis of the possible magnetic structures of Er₅Ge₃ in the ground state is performed using the results of measurements of elastic magnetic neutron scattering at 4.2 K. It is shown that the minimum discrepancy factor R _m ≈9.5% corresponds to a modulated collinear magnetic structure in which the magnetic moments of erbium atoms are oriented along the a ₃ axis of the unit cell of the crystal structure and induce an antiferromagnetic longitudinal spin wave (AFLSW). The magnetic structure is characterized by the wave vector k=2π(0, 0, μ /a ₃) (where μ≈0.293) and the modulation period λ≈3.413a ₃. The magnetic ordering temperature T _N ≈38 K is determined from the temperature dependence of the intensity of magnetic reflections. __________ Translated from Fizika Tverdogo Tela, Vol. 45, No. 9, 2003, pp. 1653–1659. Original Russian Text Copyright ? 2003 by Vokhmyanin, Dorofeev.     

Thermodynamics of the frustrated J<Subscript>1</Subscript>-J<Subscript>2</Subscript> Heisenberg ferromagnet on the body-centered cubic lattice with arbitrary spin

We use the spin-rotation-invariant Green’s function method as well as thehigh-temperature expansion to discuss the thermodynamic properties of the frustratedspin-S J ₁-J ₂ Heisenbergmagnet on the body-centered cubic lattice. We consider ferromagnetic nearest-neighborbonds J ₁<0 and antiferromagnetic next-nearest-neighbor bonds J ₂ ≥ 0 andarbitrary spin S. We find that the transition point\hbox{$J_2^c$}J2cbetween the ferromagnetic ground state and theantiferromagnetic one is nearly independent of the spin S, i.e., it is very closeto the classical transition point\hbox{$J_2^{c,{\rm clas}}= \frac{2}{3}|J_1|$}J2c,clas=23|J1|. At finite temperatures we focus on the parameterregime\hbox{$J_2<J_2^c$}J2<J2cwith a ferromagnetic ground-state. We calculate theCurie temperature T _C (S, J ₂)and derive an empirical formula describing the influence of the frustration parameterJ ₂ and spin S on T _C . We find that theCurie temperature monotonically decreases with increasing frustration J ₂, where veryclose to\hbox{$J_2^{c,{\rm clas}}$}J2c,clasthe T _C (J ₂)-curveexhibits a fast decay which is well described by a logarithmic term\hbox{$1/\textrm{log}(\frac{2}{3}|J_1|-J_{2})$}1/log(23|J1|?J2). To characterize the magnetic ordering below and aboveT _C , we calculate thespin-spin correlation functions ?S ₀ S _R ?, the spontaneous magnetization, the uniform static susceptibilityχ ₀ as well as the correlation lengthξ.Moreover, we discuss the specific heat C _V and the temperaturedependence of the excitation spectrum. As approaching the transition point\hbox{$J_2^c$}J2csome unusual features were found, such as negativespin-spin correlations at temperatures above T _C even though theground state is ferromagnetic or an increase of the spin stiffness with growingtemperature.     

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.     

Small-angle scattering during formation of periodic structures in light-sensitive films subjected to laser radiation

Patterns of small-angle scattering that appear in thin AgCl films containing granular silver upon the formation of spontaneous periodic structures by p-polarized and circularly polarized laser beams (He-Ne laser, P=8 mW, λ = 632.8 nm) are studied. It is found that, at angles of incidence exceeding 4° regardless of the type of polarization, the diffraction of the waveguide modes excited by the dominant C gratings from neighboring microgratings with the vectors K ≠ K c dominantly contributes to the small-angle scattering. In the case of circularly polarized light, the pattern of small-angle scattering becomes more complicated as a result of the formation of S _? gratings and related secondary regular gratings.     

Spin observables in <Emphasis Type="Italic">np</Emphasis> elastic scattering in the energy range 200–600 MeV. Complete experiment

A survey of available experimental data on the measurement of spin observables in neutron-proton (np) elastic scattering in the neutron energy range 200–600 MeV is presented. Sixteen spin observables (the polarization of recoil particles P _0n00, the analyzing power A _00n0, the spin correlation parameters A _00nn , A _00ss , A _00sk , and A _00kk , the spin transfer parameters K _0nn0, K _0ss0, and K _0sk0, the depolarization parameters D _0n0n , D _0s0s , and D _0s0k , and the three-spin parameters N _0nkk , N _0skn , N _0ssn , and N _0sns for energies of 200–590 MeV and scattering angles in the center of mass system of 60°–164°) were studied in experiments using polarized neutron beams and polarized proton targets at the Paul Scherrer Institute. The results of these investigations present a complete set of precision data on np elastic scattering which, along with the complete set of data for proton-proton (pp) elastic scattering obtained earlier, provides a basis for unambiguous determination of the amplitudes of the scattering matrix for nucleon-nucleon (NN) elastic scattering for the channel with the isotopic spin I = 0 and makes it possible to describe NN interaction in a model-independent way.     

Some exact solutions of the local induction equation for the motion of a vortex in a Bose–Einstein condensate with a Gaussian density profile

The dynamics of a vortex filament in a Bose–Einstein condensate whose equilibrium density in the reference frame rotating at the angular velocity Ω is Gaussian with the quadratic form r·D?r has been considered. It has been shown that the equation of motion of the filament in the local-induction approximation permits a class of exact solutions in the form R(β, t) = βM(t) + N(t) of a straight vortex, where β is the longitudinal parameter and is the time. The vortex slips over the surface of an ellipsoid, which follows from the conservation laws N · D?N=C ₁ and M · D?N=C ₀=0. The equation of the evolution of the tangential vector M(t) appears to be closed and has integrals of motion M ·D?M=C ₂ and (|M| ? M· G?Ω) = C, with the matrix G? = 2(I?TrD? ? D?)^?1. Crossing of the respective isosurfaces specifies trajectories in the phase space.     

Liquid-crystalline dendrimer Cu(II) complexes and Cu(0) nanoclusters based on the Cu(II) complexes: An electron paramagnetic resonance investigation

New nanostructured materials, namely, the liquid-crystalline copper(II) complexes that contain poly(propylene imine) dendrimer ligands of the first (ligand 1) and second (ligand 2) generations and which have a columnar mesophase and different copper contents (x = Cu/L), are investigated by EPR spectroscopy. The influence of water molecules and nitrate counterions on the magnetic properties of complex 2 (x = 7.3) is studied. It is demonstrated that water molecules can extract some of the copper ions from dendrimer complexes and form hexaaqua copper complexes with free ions. The dimer spectra of fully hydrated complex 2 (x = 7.3) are observed at temperatures T < 10 K. For this complex, the structure is identified and the distance between the copper ions is determined. It is shown that the nitrate counterion plays the role of a bridge between the hexaaqua copper(II) complex and the dendrimer copper(II) complex. The temperature-induced valence tautomerism attended by electron transport is revealed for the first time in blue dendrimer complexes 1 (x = 1.9) with a dimer structure. The activation energy for electron transport is estimated to be 0.35 meV. The coordination of the copper ion site (NO₄) and the structural arrangement of green complexes 1 (x = 1.9) in the columnar mesophase are determined. Complexes of this type form linear chains in which nitrate counterions serve as bridges between copper centers. It is revealed that green complexes 1 (x = 1.9) dissolved in isotropic inert solvents can be oriented in the magnetic field (B ₀ = 8000 G). The degree of orientation of these complexes is rather high (S _z = 0.76) and close to that of systems with a complete ordering (S _z = 1) in the magnetic field. Copper(0) nanoclusters prepared by reduction of complex 2 (x = 7.3) in two reducing agents (NaBH₄, N₂H₄ · H₂O) are examined. A model is proposed for a possible location of Cu(0) nanoclusters in a dendrimer matrix.     

Excitonic representation: Collective excitation spectra in the quantized Hall regime and spin biexciton

The excitonic representation method for describing collective excitations in the quantized Hall regime makes it possible to simplify analysis of the spectra and to obtain new results in the strong magnetic field limit, when E _C ??ω_c (ω_c is the cyclotron frequency and E_C is the characteristic Coulomb energy). For an integer odd filling factor ν greater than unity (i.e., for ν = 3, 5, 7,...), the spectra of one-cyclotron magneto-plasma excitations are calculated. For unit filling factor, the existence of a spin biexciton (bound state of two spin waves) corresponding to excitation with a spin change (δ_S = δ_Sz = ?2) is proved. The exact equation determining the ground state of the biexciton is derived in the thermodynamic limit N_Φ → ∞ (_N? is the system degeneracy). The exchange energy of this state is lower than for a single spin wave (with δ_S = δ_Sz = ?1) for the same value of the 2D wavevector q. In the limit q → ∞ corresponding to the decay of a biexciton into a pair of quasiparticles one of which is a trion with a spin of ?3/2, the energy is found to be lower than the energy (e²/εl _B )√π/2 required for exciting an electron-hole pair in the strictly 2D case (l_B is the magnetic length and ε is the dielectric constant), although this energy is higher than another “classical” result (e²/εl _B )√π/2, corresponding to the excitation of a skyrmion-antiskyrmion pair (|δS|=|δS _z |?1). The solution of the exact equation gives the trion binding energy and the activation gap for quasiparticles whose excitation corresponds to a change in the total spin by δS = δ S_z =?3. The energy of a spin biexciton is calculated for values of the wavevector such that ql _B ?1.     

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.     

Bad communities with high modularity

In this paper we discuss some problematic aspects of Newman and Girvan’s modularity function Q _N . Given a graph G, the modularity of G can be written as Q _N = Q _f ? Q ₀, where Q _f is the intracluster edge fraction of G and Q ₀ is the expected intracluster edge fraction of the null model, i.e., a randomly connected graph with same expected degree distribution as G. It follows that the maximization of Q _N must accomodate two factors pulling in opposite directions:Q _f favors a small number of clusters and Q ₀ favors many balanced (i.e., with approximately equal degrees) clusters. In certain cases the Q ₀ term can cause overestimation of the true cluster number; this is the opposite of the well-known underestimation effect caused by the “resolution limit” of modularity. We illustrate the overestimation effect by constructing families of graphs with a “natural” community structure which, however, does not maximize modularity. In fact, we show there exist graphs G with a “natural clustering” V of G and another, balanced clustering U of G such that (i) the pair (G, U) has higher modularity than (G, V) and (ii) V and U are arbitrarily different.     

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.     

Field Confinement Energy at a Nonlinear Interface between Nonlinear Defocusing Media

The dependences of the resistance of the layered quasi-one-dimensional semiconductor TiS₃ on the direction and magnitude of the magnetic field B have been measured. The anisotropy and angular dependences of the magnetoresistance indicate the two-dimensional character of the conductivity at T < 100 K. Below T₀ ≈ 50 K, the magnetoresistance for the directions of the field in the plane of the layers (ab plane) increases sharply, whereas the transverse magnetoresistance (B ∥ c) becomes negative. The results confirm the possibility of an electron phase transition to a collective state at T₀. The negative magnetoresistance (at B ∥ c) below T₀ is explained by the magnetic-field-induced suppression of two-dimensional weak localization. The positive magnetoresistance (at B ∥ ab) is explained by the effect of the magnetic field on the spectrum of electronic states.     

Specific features of the states of cobalt fluoride in the vicinity of the critical field

The state of cobalt fluoride in the vicinity of the critical value H _c of a longitudinal magnetic field H, in which the magnetic subsystem of a CoF₂ crystal with a strong Dzyaloshinskii interaction is transformed from the antiferromagnetic phase into the canted phase, has been investigated taking into account the increasing number of experimental studies related to the use of cobalt fluoride. It has been found that, despite the unusually high magnetic anisotropy of the crystal, the state of the magnetic subsystem at H = H _c is extremely sensitive to a small deviation of the vector H from the C ₄ axis. Another feature is that the high sensitivity disappears with an increase or decrease in the magnetic field by only a few thousandths of H _c . The results of the investigations performed in this work are applicable to magnetically ordered crystals FeF₃ and Cu₂OSeO₃, which, as well as the CoF₂ crystals, are characterized by a strong Dzyaloshinskii interaction and a significant magnetic anisotropy. The revealed anomaly in the reduction of the effective magnetic anisotropy is of interest in connection with numerous attempts to decrease the magnetic anisotropy in crystals with giant magnetostriction, which are necessary for the use as sensors and vibrators.     

Dynamic phenomena connected with magnetic and antiferroelectric interactions in trirutiles

Dynamic effects caused by the magnetoelectric and antiferroelectric interactions in tetragonal antiferromagnets are studied. The analysis is based on the example of trirutiles that are a series of antiferromagnets with different exchange structures and orientation states. We are mainly dealing with the excitation by an alternating electric field E(t) of spin waves typical of these magnets (antiferroelectric resonance) and the nuclear magnetoelectric resonance connected with these interactions. In the first case, special emphasis is placed on specific magnons (antimagnons), where only the antiferromagnetism vectors L take part in oscillations, whereas the total ferromagnetism vector M remains unchanged. The nuclear magnetoelectric resonance can be generated by oscillations of both L and M caused by field E(t). In this way, the field contributes to the hyperfine field, which acts on the nuclear spins. It is shown that the magnetic and antiferroelectric interactions in the dynamics can manifest themselves both at high (usually, exchange) frequencies ωw_E (antiferroelectric resonance) and at rather low nuclear frequencies of ω_n?ω_E. Particular cases of magnetic structures (phases) are considered where field E(t) can excite not only antimagnons, but also quasiantiferromagnons that have lower eigenfrequencies than those of quasimagnons (relativistic and semirelativistic).     

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.     

Long-wavelength magnetic excitations in the Fe<Subscript>65</Subscript>Ni<Subscript>35</Subscript> alloy

A theoretical analysis of small-angle neutron scattering is performed for the Fe₆₅Ni₃₅ alloy at a temperature T=0.9T _C =450 K. The results obtained indicate the existence of long-wavelength magnetic excitations that do not correspond to spin waves of the Holstein-Primakoff type. The possible nature of these excitations is discussed.     

Magnetic nesting and coexistence of ferromagnetism and superconductivity

If the condition ε_σ(p)=ε_?σ(?p+nI/v_F) for magnetic nesting is fulfilled for the electron dispersion law with spin σ along a certain preferential direction n, ferromagnetism and the inhomogeneous superconducting state can coexist up to a very high magnetization I. This fact was used to explain the coexistence of ferromagnetism and superconductivity for layered cuprates of the RuSr₂GdCu₂O₈ type, which possess a finite, though rather high, critical magnetization, because the conditions for magnetic nesting are fulfilled only approximately.     

Magneto-optical signature of broken mirror symmetry of two-dimensional conductors

An unusual aspect of macroscopic electrodynamics of two-dimensional mirror-odd conducting structures bound up with the band spin–orbit coupling H _so = α(p × c) · σ of current carriers (where c is one of two none-quivalent normals to a given structure) is pointed out. Namely, it is shown that due to the spin–orbit coupling the presence of the in-plane magnetic field H ₀ gives rise to a dependence of the reflection/transmission amplitudes on the structure orientation c, the wave vector of the incident radiation q, and H ₀ of the form q · (c × H ₀). This q- and H ₀-odd dependence can be the foundation of the optical way to determine the value of the spin–orbit coupling α.