Thermal expansion anomalies in TbVO4 due to the cooperative Jahn-Teller effect

The thermal expansion anomalies in TbVO₄ due to the cooperative Jahn-Teller effect were studied experimentally and theoretically. Characteristic magnetoelastic anomalies were observed in the curves of Δa/a and Δc/c of the cell parameters at T<T _c. Calculations of the magnetoelastic contribution to Δa/a and Δc/c from fully symmetric and and low-symmetry ɛ^δ modes were performed using the general crystal-field formalism, and the values of the magnetoelastic coefficient B ^δ were obtained from spectroscopic and spontaneous-deformation data. It is shown that the thermal expansion of TbVO₄ in both the tetragonal and orthorhombic phases can be described well on the basis of a general model based on a single set of interaction parameters. Fiz. Tverd. Tela (St. Petersburg) 40, 1663–1666 (September 1998)     

Ellipsometric spectroscopy of the ZnO nonpolar(1\bar 100) surface

Ellipsometric spectroscopy has been performed on nonpolar ZnO surfaces in the spectral range 1.5 eV<ħω<4.0 eV. Absolute measurements with two different crystal orientations in air allow the determination of the optical constantsn _∥,k _∥ andn _⊥,k _⊥ for light polarized parallel and perpendicular to thec-axis. The ellipsometric angles Δ and ψ are changed remarkably on ultrahigh vacuum cleaved surfaces near the band gap energy of ∼3.4eV when oxygen or atomic hydrogen is adsorbed or when the crystal is annealed. This observation is interpreted in terms of a field effect on the optical constants in the space charge layer.     

Anomalies in the elastic properties of silicious iron single crystals at pressures of up to 9 GPa and the α−ɛ phase transformation

A Fe+5.07 at.%Si single crystal has been studied by ultrasonic-pulse technique. Its density and elastic constants were determined for p=0 and T=293 K. The dependence of the elastic properties of silicious iron on Si concentration was constructed. The compression, the effective elastic constants, and the Grüneisen parameters were measured at hydrostatic pressures of up to 9 GPa. It was found that for p=0, and . The elastic constants c ₄₄ and c′ increase linearly with pressure by 19.3 and 18.2% by p=9 GPa. The elastic anisotropy does not vary with pressure. For p>4 GPa, c ₁₁, c ₁₂, and K _S were observed to increase nonlinearly with decreasing pressure derivative. The Grüneisen parameter γ _LA decreases with pressure down to 0.70 at 9 GPa to become negative when extrapolated to the region of the α−ɛ phase transformation. The anomalies in c ₁₁ and the negative values of γ _LA for p>11 GPa indicate that the phase transformation in silicious iron at 13.5 GPa can take place by the crystallographic mechanism of the α−ɛ transformation in pure iron, i.e. by lattice compression in the [001] direction and shearing of the (110) planes along or . An assumption is put forward that pressure gives rise in silicious iron to sp-d hybridization, which results in increased screening of the ion-ion interaction and in anomalies in elastic properties. Similar phenomena are expected to occur in pure bcc Fe as well. Fiz. Tverd. Tela (St. Petersburg) 41, 516–522 (March 1999)     

Magnetic susceptibility of multilayered carbon nanotubes

A theoretical study of the magnetic susceptibility of multilayered carbon nanotubes in fields both parallel, H _∥, and perpendicular, H _⊥, to the tube axis has been carried out disregarding electron-electron interaction. The temperature dependences of the magnetic susceptibility obtained exhibit a nontrivial form for H _∥, which is related to the quasi-one-dimensionality of such a system as the nanotube. The dependences of the magnetic susceptibility on chemical potential χ(μ) have also been derived. At low temperatures, χ(μ) has sharp peaks in fields H _∥, which is connected with the presence of singularities in the density of states of nanotubes. The effect of interlayer coupling on magnetic susceptibility of small-radius tubes has been investigated numerically. Fiz. Tverd. Tela (St. Petersburg) 40, 1950–1954 (October 1998)     

Microwave photoresistance in a two-dimensional electron system with anisotropic mobility

The effect of microwave radiation on magnetotransport in single GaAs quantum wells with anisotropic mobility, whose maximum corresponds to the direction and minimum to the [110] direction, is investigated using the Van der Pauw method. In samples shaped as squares with sides oriented along the and [110] directions, giant oscillations of magnetoresistance arise under the effect of a microwave field for the both and [110] orientations of the measuring current I _ac. In the anisotropic two-dimensional system under study, the relative amplitude of microwave photoresistance oscillations in a magnetic field weakly depends on the orientation of I _ac. At a temperature of 4.2 K and a microwave frequency of 130 GHz, magnetic field intervals characterized by close-to-zero resistance manifest themselves only for the case of the [110] orientation of I _ac. The aforementioned experimental results are qualitatively explained by a quasi-one-dimensional potential modulation of the two-dimensional electron gas in the [110] direction. Original Russian Text ? A.A. Bykov, D.R. Islamov, A.V. Goran, A.K. Bakarov, 2007, published in Pis’ma v Zhurnal éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2007, Vol. 86, No. 12, pp. 891–895.     

Crystal structure of ice accretions

Summary The crystal size in accretions grown in an icing wind tunnel at ambient temperatures −18≥T _a ≥−27°C and different substrate temperatureT _s <0°C is studied. For constantT _s the mean area of crystal sections shows an approximately exponential dependence onT _a which may be written as , where ΔT≃−T _a represents the droplet supercooling. On the other hand, for fixedT _a , the crystal size is observed to decrease markedly withT _s . By considering previous results on the orientation of crystals forming the accretions, it is shown that the value of the mean angle formed by the crystalc-axis with the growth direction depends as well both onT _a andT _s . The exponential dependence of andT _a and the observed correspondence between the behaviour of and are correlated with a nucleation mechanism, accompanied by a process of orientation selection, which would be responsible of both the crystal size and the orientation. The application of the crystal structure analysis to the determination of the growth conditions of hailstones is discussed.

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Riassunto Si studia la dimensione di un cristallo in accrezioni cresciute in una galleria a vento congelante a temperature ambienti −18≥T _a ≥−27 °C e diversa temperatura di substratoT _s <0 °C. PerT _s costante, l’area media delle sezioni di cristallo mostra una dipendenza daT _a approssimativamente esponenziale che potrebbe essere scritta così: , dove ΔT≃−T _a rappresenta il superraffreddamento della gocciolina. D’altra parte, perT _a fisso, si osserva che la dimensione del cristallo decresce marcatamente conT _s . Considerando precedenti risultati sull’orientamento dei cristalli che formano le accrezioni, si mostra che anche il valore dell’angolo medio formato dall’assec del cristallo con la direzione di accrescimento dipende sia daT _a che daT _s . La dipendenza esponenziale di daT _a e la corrispondenza osservata tra il comportamento di e di sono collegate con il meccanismo di nucleazione, accompagnato da un processo di selezione dell’orientamento, che dovrebbe essere responsabile sia della dimensione che dell’orientamento del cristallo. Si discute l’applicazione dell’analisi della struttura del cristallo alla determinzione delle condizioni di accrescimento dei chicchi di grandine.

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To speed up publication, the authors of this paper has agreed to not receive the proofs for correction.

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Comisión Nacional de Energía Atómica and Consejo Nacional de Investigaciones Científicas y Técnicas.     

Properties of a pseudo-Hermitian Hamiltonian for harmonic oscillator decorated with Dirac delta interactions

We have investigated bound state solutions of the Schrodinger equation for one-dimensional harmonic oscillator potential together with even number of Dirac delta functions. These point interactions are located at symmetric points x = x _i and x = −x _i (i = 1, 2,..., N) and they have complex conjugate strengths and , respectively. We present explicit forms of eigenfunctions and an algebraic eigenvalue equation and numerical solutions for this -symmetric Hamiltonian. Presented at the 3rd International Workshop “Pseudo-Hermitian Hamiltonians in Quantum Physics”, Istanbul, Turkey, June 20–22, 2005.     

Excitonic light-absorption and amplification bands in the presence of laser radiation

We examine the absorption and amplification bands of a weak probe signal in the presence of Bose-Einstein condensation of excitons that emerges in nonequilibrium conditions in the field of coherent laser radiation with a wave vector k ₀. We assume that the detuning from resonance between the energy ħω _ex (k ₀)+L ₀ of the exciton level, which is shifted because of exciton-exciton interaction, and the laser photon energy ħω _L , is generally nonzero. The elementary excitation spectrum consisting of the quasiexcitonic and quasienergy branches determines the optical properties of the system. When there is real induced Bose-Einstein condensation, at the two branches touch, as they do in spontaneous Bose-Einstein condensation. In virtual induced Bose-Einstein condensation, when , instabilities emerge in the spectrum in certain regions of the k-space. These instabilities are caused by a real transformation of two laser photons into two extracondensate particles. Nonequilibrium extracondensate excitons strongly affect the absorption and amplification of the probe light signal. We show that light absorption is due to the quantum transition from the ground state of the crystal to the quasiexcitonic branch of the spectrum. On the other hand, amplification of the signal is caused by the transition from the quasienergy branch to the ground state of the crystal. The same transition can be explained by a real transformation of two laser photons into a vacuum photon of frequency ħcq and a crystal exciton with a wave vector 2k ₀−q. Finally, we show that the excitonic absorption and light-amplification bands are essentially anisotropic at and depend on the orientation of the vectors q and k ₀. Zh. éksp. Teor. Fiz. 112, 167–179 (July 1997)     

Phase transitions in random uniaxial systems with dipolar interactions

The critical behaviour of random uniaxial ferromagnetic (ferroelectric) systems with both short range and long range dipolar interactions is investigated, using the field theoretic renormalization method of Brézin et al. for the free energy above and below the transition pointT _c. The randomness is due to externally introduced fluctuations in the short range interactions (quenched case) or (and) magneto-elastic coupling to the lattice (annealed case). Strong deviations in the critical behaviour with respect to the pure systems are found. In the quenched case e.g. the specific heatC and the coefficientf ₂ (ofM ³ in the equation of state, whereM is the magnetization) change fromC |ln|t^1/3,f ₂ |ln|t^–1 in the pure system toC is the reduced temperature andA _±,C _± are constants) in the random situation. This change should e.g. be experimentally observable by deuterization of the ferroelectric tri-glycine sulfate where the logarithmic behaviour off ₂ has already been detected in the pure case. For nonvanishing magnetoelastic coupling a complex critical behaviour is obtained and discussed. We find the interesting result that if both quenched randomness and a weak magnetoelastic coupling are present the quenched random critical behaviour dominates in the close vicinity ofT _c. Finally the influence of the magnetoelastic coupling on the longitudinal phonons in investigated and it is found that the relative changes in the corresponding elastic constant and structure factor are proportional to the specific heat and the wavevector dependent energy-energy correlation function respectively, suggesting new experiments.     

He diffraction study of the OH(1×1)−Ag(110) phase

Summary The OH(1×1)−Ag(110) phase obtained after H₂O dissociation on the O(2×1)−Ag(110) surface is investigated. Structural and electronic properties are studied by He diffractive scattering and angularly resolved ultraviolet photoemission spectroscopy (ARUPS). Diffractive data are interpreted in terms of the hard corrugated wall (HCW) potential leading to the determination of the corrugation function ζ(R). The shape of ζ(R) indicates that the phase under study is formed of OH rows along where hydroxil groups interact strongly. The interaction between rows instead is weak and essentially republsive. In honour of Prof. Fausto Fumi on the occasion of his retirement from teaching.     

Evaluation of certain statistical sums

Summary Certain statistical ensembles,e.g. open chemical systems with randomly varying number of particles, are characterized by partition functions of the type ,n being a natural number anda _j ’s generalized temperatures. The state of the system is well defined if one knows the dependence ofa _j ’s on ensemble averages 〈n ^j 〉. For making the equations 〈n ^j 〉=〈n ^j 〉 (a ₁, ...,a _s) at least more accessible for numerical calculations a transformation of the partition function to a series of Fourier integrals is proposed. In the special case of the integrals can be calculated analytically transforming the statistical sum into a series of error functions.     

Fourier transform of supermeasures

In the note, a Smolyanov-Shavgulidze model of infinite-dimensional superspace H _Λ = Λ₀ H ₀ ⊕ Λ₁ H ₁ corresponding to a Hilbert space H = H ₀ ⊕ H ₁ over a Hilbert superalgebra Λ = Λ₀ ⊕ Λ₁ is considered. Its relation to the Khrennikov superspace is discussed. Moreover, H _Λ is equipped with the structure of Hilbert superspace with an inner superproduct (·, ·)_Λ. The supermeasures are defined as Λ^ℂ (∧H ₁)-valued measures on H ₀ (Λ^ℂ stands for the complexification of Λ). The definition of the Fourier supertransform is similar to the ordinary one, (y) = μ(dz). It turns out that the values of the Fourier supertransform of a supermeasure on the subspace = H ₀ ⊕ Λ₁ H ₁ can be obtained by applying a certain operator to the values of the classical Fourier transform. The main result is the theorem claiming that the Fourier supertransform of supermeasures is isometric on superspaces with zero even part (H ₀ = {0}). As a corollary, we note that the operator of Fourier supertransform is injective. We also give necessary and sufficient conditions for the countable additivity of cylindrical supermeasures in terms of continuity of their Fourier supertransforms (an analog of the Minlos-Sazonov theorem).     

Magnetostriction relative to pretransition in Ni50.5Mn24.5Ga25 single crystal

The strain behaviors as well as the structural and magnetic changes relative to the pretransition in the Ni_50.5Mn_24.5Ga₂₅ single crystals have been characterized by various methods, such as pretransition strain, magnetostriction, magnetization measurements, and TEM observations. A large magnetostriction up to 505 ppm measured in the [001] direction of the sample is obtained at the pretransition temperature with only a low magnetic field of about 1 kOe applied along the [010] direction. We found that not only the pretransition strain pronounces a more large change, but also the magnetostriction at a certain temperature exhibits a more large magnitude for field applied along the [010] direction than with field along the [001] direction. It is concluded that the magnetoelastic interaction is responsible for the premartensitic transition, and the magnetoelastic interaction in the [010] direction is stronger than that in the [001] direction.     

A sharp decrease of resistivity in La0.7Ca0.3Mn0.96Cu0.04O3: Evidence for Cu-assisted coherent tunneling of spin Polarons

Nearly a 50% decrease of the resistivity ρ(T, x) is observed upon just 4% Cu doping at the Mn site of La_2/3Ca_1/3Mn_1−x Cu_xO₃. When the observed phenomenon is attributed to a decrease of the spin-polaron energy E _σ(x) below T _C (x), all of the data are found to be well fitted by the nonthermal coherent tunneling expression , assuming that the magnetization in the ferromagnetic state is given by the expression . The best fits through all the data points suggest and E _σ(x)≃E _σ(0)(1−x)⁴ for the explicit x dependence of the Cu-induced modifications of the Mn-spin-dominated zero-temperature spontaneous magnetization, residual paramagnetic contribution, and spin-polaron tunneling energy, respectively, with E _σ(0)=0.12 eV. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 11, 812–815 (10 June 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Large number hypothesis and the matter-dominated universe

Dirac’s large number hypothesis (LNH), in the formG/G ₀=HH ₀ ⁻¹ , is applied to the matter-dominated cosmological era, using the framework of the scale covariant theory (Canuto et al., 1977). We obtain explicit expressions forR andβ _a as functions ofR _E , whereR andR _E are the scale factors of the cosmological Robertson-Walker metric, expressed in atomic and gravitational units, respectively, andβ _a is the ratio between the rates of gravitational and atomic clocks. The parameters in these expressions are , the deceleration parameter in gravitational units, and (t ₀)H ₀ ⁻¹ where (t ₀) is the present epoch value of the derivative ofβ _a with respect to atomic time. We find that a necessary condition for the LNH to be compatible with a Robertson-Walker model is that (t ₀)H ₀ ⁻¹ ≥ ₂ ¹ . The only experimental values for (t ₀) available at present are those based on the lengthening of the Moon’s period of revolution around the Earth, suggesting 0.86≥ (t ₀)H ₀ ⁻¹ ≥0.21; the more promising technique of radar ranging to the inner planets has not yet produced a value for (t ₀). Using the lunar data, it follows that 0≤ ≲0.42 corresponding to an open universe (k=−1). Closed models (k=1, >1/2) are not compatible with the LNH since the required values of (t ₀)H ₀ ⁻¹ are more than an order of magnitude above the observational upper limit. Presented at the Dirac Symposium, Loyola University, New Orleans, 1981.     

Neutral current cross-sections for neutrinos on protons

Defining the ratiosr _p =σ(vp →vx)/σ(vp →μ ⁻ x) and we obtain the bounds 0.28 ⩽r _p ⩽ 0.61 and using only the parton model and the data of CDHS group with iron target. We also give the complete set of parton-model relations which would allow the determination of all the neutral-current coupling constants from inclusive cross sections alone.     

Effect of a magnetic field on the yield point of NaCl crystals

A constant magnetic field is found to have a substantial effect on the macroplasticity of NaCl crystals when they are being actively strained at a constant rate during magnetic treatment. We have measured the dependence of the yield point σ _y on the magnetic induction B=0–0.48 T and the strain rate . It is shown that this magnetic effect has a threshold character and is observed only for B>B _c , where B _c grows with increasing as . The lower the strain rate , the larger the relative decrease in the yield point σ _y (B)/σ _y (0) at fixed field B>B _c . At small enough strain rates the threshold field B _c ceases to depend on and goes constant. A theoretical model is proposed which is in good agreement with the observed regularities. The model is based on the competition between thermally activated and magnetically stimulated depinning of dislocations from paramagnetic impurity centers. Zh. éksp. Teor. Fiz. 115, 951–958 (March 1999)