Harmonically trapped ideal quantum gases

We solve the problem of a Bose or Fermi gas in d-dimensions trapped by δ ⩽ d mutually perpendicular harmonic oscillator potentials. From the grand potential we derive their thermodynamic functions (internal energy, specific heat, etc.) as well as a generalized density of states. The Bose gas exhibits Bose-Einstein condensation at a nonzero critical temperature T _c if and only if d + δ > 2, along with a jump in the specific heat at T _c if and only if d + δ > 4. Specific heats for both gas types precisely coincide as functions of temperature when d + δ = 2. The trapped system behaves like an ideal free quantum gas in d + δ dimensions. For δ = 0 we recover all known thermodynamic properties of ideal quantum gases in d dimensions, while in 3D for δ = 1, 2 and 3 one simulates behavior reminiscent of quantum wells, wires anddots, respectively. Good agreement is found between experimental critical temperatures for the trapped boson gases ₃₇ ⁸⁷Rb, ₃ ⁷Li, ₃₇ ⁸⁵Rb, ₂ ⁴He, ₁₉ ⁴¹K and the known theoretical expression which is a special case for d = δ = 3, but only moderate agreement for ₁₁ ²⁷Na and ₁ ¹H. Received 17 July 2002 / Received in final form 14 October 2002 Published online 21 January 2003 RID="a" ID="a"e-mail: mdgg@hp.fciencias.unam.mx     

Superconductivity of A15-and σ-phase of Nb-Ir

The superconducting properties of A15-, σ-, and tetragonal phases of the system Nb−Ir were investigated. The alloys were prepared by sintering and arc melting. They were subjected to optical and scanning electron microscopy. The lattice parameters were determined by x-ray diffraction technique. Superconducting transition temperatures,T _c , as well as upper critical fields,H _c2, were measured inductively and resistively. TheT _c -values of the σ-phase vary between 2.15 and 2.40 K whereas for the A15-phase they vary between 1.83 and 2.73 K. TheT _c -value of the tetragonal phase is 3.81 K. The upper critical fields of the tetragonal and the A 15-phase are nearly the same (≈13 kG) and lower compared with that of the σ-phase (≈18 kG). Several theoretically predicted values ofH _c2(0) are evaluated and compared with the experimental ones.     

Electron spin resonance in InGaAs/GaAs heterostructures with a manganese δ layer

The static and high-frequency dynamic magnetic properties and photoluminescence of two-dimensional semiconductor GaAs heterostructures containing an InGaAs quantum well and a thin manganese layer (δ layer) are studied. It is found that the Curie temperature is T _C ≈ 35 K and the magnetic anisotropy field of the ferromagnetic manganese δ layer is H _a ≈ 600 Oe. The spin resonance spectrum exhibits a line in weak fields (from −50 to 100 Oe), which is observed in the same temperature interval T < 40 K where the ferromagnetic ordering of the manganese δ layer occurs. This line is probably caused by the nonresonance contribution of the spin-dependent scattering of charge carriers to the negative magnetic resistance. The dependence of the degree of polarization of photoluminescence on the magnetic field also points to the ferromagnetic behavior of the manganese δ layer.     

Investigation of a magnetic phase transition in fcc iron-nickel alloys

A magnetic phase transition in carbon-doped (0.1 and 0.7 at. %) Fe₇₀Ni₃₀ Invar alloys was investigated by the method of depolarization of a transmitted neutron beam and by small-angle scattering of polarized neutrons. It is shown that for both alloys, two characteristic length scales of magnetic correlations coexist above T _c. Small-angle scattering by critical correlations with radius R _c is described well by the Ornstein-Zernike (OZ) expression. The longer-scale (second) correlations, whose size can be estimated from depolarization data, are not described by the OZ expression, and hypothetically can be modeled by a squared OZ expression, which in coordinate space corresponds to the relation 〈M(r)M(0)〉∝exp(−r/R _d), where R _d is the correlation length of the second scale. The temperature dependence of the correlation radius R _c was obtained: R _c ∝ ((T−T _c)/Tc)^−ν , where ν≈2/3 is the critical exponent for ferromagnets, over a wide temperature range up to T _c ^exp , at which the correlation radius becomes constant and equals its maximum value R _c(T _c)=R _c ^max . The maximum correlation radius established (R _c ^max =140 Å and 230 Å for the first and second alloys, respectively) characterizes the length-scale of the fluctuation for which the appearance of critical correlations first results in the formation of a ferromagnetic phase, and the phenomenon itself exhibits a “disruption” of the second-order phase transition at T=T _c ^exp , as a result of which a first-order transition arises. Temperature hysteresis was also detected in the measured polarization of the transmitted beam and intensity of small-angle neutron scattering in the alloy above T _c, confirming the character of this magnetic transition as a first-order transition close to a second-order transition. Zh. éksp. Teor. Fiz. 112, 2134–2155 (December 1997)     

Excess 1/f noise in systems with an exponentially wide spectrum of resistances and dual universality of the percolation-like noise exponent

The excess 1/f noise in a random lattice with bond resistances r∼exp(−λx), where x is a random variable and λ≪1, is studied theoretically. It is shown that if the correlation function {δr ²}∼r r ^θ+2, then the relative spectral density of the noise in the system is expressed as C _e∼λ^m exp(−λ(1−p _c)), where p _c is the percolation threshold and m=νd (ν is the critical exponent of the correlation length and d is the dimensionality of the problem). It is hypothesized that the exponent m possesses a dual universality: It is independent of 1) the geometry of the lattice and 2) the θ-mechanism responsible for the generation of the local noise. Numerical modeling in a three-dimensional lattice gives m=52.3 for θ=1 and θ=0, in agreement with the hypothesis. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 8, 614–618 (25 April 1996)     

Intrinsic Josephson effects in 60-K phase YBCO thin film mesas

We fabricatedc-axis oriented meas on YBa₂Cu₃O_7−δ thin films. Columnar structures with an area of 20×20 μm² and a depth of 0.1 μm were formed on oxygen deficient films with a critical temperature (T _c ) of 64 K or less. The devices showed hysteretic I–V curves without any branches. The dependence of the critical current density on the temperature nearT _c is explained by the Ambegaokar-Baratoff relation.     

A local moment approach to the gapped Anderson model

We develop a non-perturbative local moment approach (LMA) for the gapped Anderson impurity model (GAIM), in which a locally correlated orbital is coupled to a host with a gapped density of states. Two distinct phases arise, separated by a level-crossing quantum phase transition: a screened singlet phase, adiabatically connected to the non-interacting limit and as such a generalized Fermi liquid (GFL); and an incompletely screened, doubly degenerate local moment (LM) phase. On opening a gap (δ) in the host, the transition occurs at a critical gap δ_c, the GFL [LM] phase occurring for δ<δ_c [ δ>δ_c] . In agreement with numerical renormalization group (NRG) calculations, the critical δ_c = 0 at the particle-hole symmetric point of the model, where the LM phase arises immediately on opening the gap. In the generic case by contrast δ_c > 0, and the resultant LMA phase boundary is in good quantitative agreement with NRG results. Local single-particle dynamics are considered in some detail. The major difference between the two phases resides in bound states within the gap: the GFL phase is found to be characterised by one bound state only, while the LM phase contains two such states straddling the chemical potential. Particular emphasis is naturally given to the strongly correlated, Kondo regime of the model. Here, single-particle dynamics for both phases are found to exhibit universal scaling as a function of scaled frequency ω/ω_m ⁰ for fixed gaps δ/ω_m ⁰, where ω_m ⁰ is the characteristic Kondo scale for the gapless (metallic) AIM; at particle-hole symmetry in particular, the scaling spectra are obtained in closed form. For frequencies |ω|/ω_m ⁰ ≫δ/ω_m ⁰, the scaling spectra are found generally to reduce to those of the gapless, metallic Anderson model; such that for small gaps δ/ω_m ⁰≪ 1 in particular, the Kondo resonance that is the spectral hallmark of the usual metallic Anderson model persists more or less in its entirety in the GAIM.     

Modeling a dimer state in CuGeO3 in the two-dimensional anisotropic Heisenberg model with alternated exchange interaction

The two-dimensional Heisenberg spin-1/2 model with alternated exchange interaction along the c axis and an anisotropic distribution of the exchange interaction in the lattice, J _b/J _c=0.1, is examined. A quantum Monte Carlo method is used to calculate the phase diagrams of the antiferromagnet, the dimer state in a plane, the value of the alternation δ of the exchange interaction, and the anisotropy Δ=1−J ^xy/J ^z of the exchange interaction, Δ∼δ ^0.58(6). The following characteristics are calculated for Δ=0.25: the dependence of the temperature of the dimer-state-paramagnet transition on the alternation of the exchange interaction, T _c(δ)=0.55(4)(δ−0.082(6))^0.50(3), the singlet-triplet energy gap, and the dependence of the magnetization on the external field for some values of δ. The value of the exchange interaction, J _c=127 K, the alternation of the exchange interaction, δ=0.11J _c, and the correlation radius along the c axis, ξ _c≈28c, are determined. Finally, it is found that the temperature dependence of the susceptibility and the specific heat are in good agreement with the experimental data. Zh. éksp. Teor. Fiz. 112, 2184–2197 (December 1997)     

Compositional modulation of CuZn,CuAl and CuNi alloys

A differential reflectometer that is capable of measuring small differences in optical reflectivity or transmissivity of two specimens and therefore enhances the structure in the spectral reflectivity of materials was used to study various α-Cu-Zn, α-Cu-Al, and Cu-Ni alloys with the aim of investigating the changes in band structure as a function of composition. In Cu-Zn and Cu-Al alloys three main absorption peaks were identified that were associated with the Δ₅ → Δ₁, X₅ → X_4' and L_2' → L₁sitions. It was found that the Δ₅→ Δ₁transition increases slightly in energy with increasing Zn or Al concentration. These transitional energies are identical for both alloys in the entire α-phase region. The X₅ → X_4' and L_2' → L₁ transitions decrease in energy with increasing solute concentration. The shift in energy is significantly larger for the Cu-Al system. In Cu-Ni alloys no shift of the absorption edge around 2.2 eV was found, which is consistent with the predictions of the virtual-bound-state model.     

Elastic fields and physical properties of surface quantum dots

Elastic fields in a system consisting of a surface coherent axisymmetric quantum dot-island on a massive substrate have been theoretically studied using the finite element method. An analysis of the influence of the quantum dot shape (form factor) and relative size (aspect ratio) δ on the accompanying elastic fields has revealed two critical quantum dot dimensions, δ _c1 and δ _c2. For δ > δ _c1, the fields are independent of the quantum dot shape and aspect ratio. At δ ≥ δ _c2, the quantum dot top remains almost undistorted. Variation of the stress tensor component σ _zz (z is the quantum dot axis of symmetry) reveals a region of tensile stresses, which is located in the substrate under the quantum dot at a particular distance from the interface. Using an approximate analytical formula for the radial component of displacements, model electron microscopy images have been calculated for quantum dot islands with δ > δ _c1 in the InSb/InAs system. The possibility of stress relaxation occurring in the system via the formation of a prismatic interstitial dislocation loop has been considered.     

μ+SR studies on superconducting YBa2(Cu1−xFex)3Oy system

Spin-glass like magnetic ordering of iron moments was observed in both orthorhombic and tetragonal YBa₂(Cu_1−xFe_x)₃O_y (x=0.08) by μ⁺SR measurements. In a “Tetra” sample, all the muons sense the superconducting transition at 60 K and magnetic ordering at around 15 K, while in an “Ortho” sample they reveal that two magnetically different parts exist in the sample: about 40% of the sample is superconducting withT _c ≈90K and the remaining part is magnetic withT _M≈33K. These phenomena can be explained in terms of clustering of the Fe atoms in the “Ortho” sample.     

Rapid solidification and dendrite growth of ternary Fe-Sn-Ge and Cu-Pb-Ge monotectic alloys

The phase separation and dendrite growth characteristics of ternary Fe-43.9%Sn- 10%Ge and Cu-35.5%Pb-5%Ge monotectic alloys were studied systematically by the glass fluxing method under substantial undercooling conditions. The maximum undercoolings obtained in this work are 245 and 257 K, respectively, for these two alloys. All of the solidified samples exhibit serious macrosegregation, indicating that the homogenous alloy melt is separated into two liquid phases prior to rapid solidification. The solidification structures consist of four phases including α-Fe, (Sn), FeSn and FeSn2 in Fe-43.9%Sn-10%Ge ternary alloy, whereas only (Cu) and (Pb) solid solution phases in Cu-35.5%Pb-5%Ge alloy under different undercoolings. In the process of rapid monotectic solidification, α-Fe and (Cu) phases grow in a dendritic mode, and the transition "dendrite→monotectic cell" happens when alloy undercoolings become sufficiently large. The dendrite growth velocities of α-Fe and (Cu) phases are found to increase with undercooling according to an exponential relation.     

Specific features of the electronic structure of cerium and its 4d and 5d partners in CeM2 Laves phases (M=Fe, Co, Ni, Ru, Rh, Os, Pt, Mg, Al)

The x-ray line shift method has been used to study the electronic state of Ce (the 4f population) and of its 4d and 5d partners in the CeM₂ Laves phases (M=Fe, Co, Ni, Ru, Rh, Os, Pt, Mg, Al). It is shown that the valence of Ce in CeM₂ decreases monotonically from the limiting value m≈3.35 to m≈3 with decreasing intracrystalline compression of Ce atoms. The population of the outer 4d and 5d orbitals of Ru, Rh, and Os in the Laves phases has been found to be larger than that in metals. Fiz. Tverd. Tela (St. Petersburg) 40, 1397–1400 (August 1998)     

Magnetism of LiMn<Subscript>2</Subscript>O<Subscript>4</Subscript> manganite in structurally ordered and disordered states

The specific features of the crystal structure and the magnetic state of stoichiometric lithium manganite in the structurally ordered Li[Mn₂]O₄ and disordered Li_{1 − δ}Mn_δ[Mn_{2 − δ}Li_δ]O₄ (δ = 1/6) states have been investigated using neutron diffraction, X-ray diffraction, and magnetic methods. The structurally disordered state of the manganite was achieved under irradiation by fast neutrons (E _eff ≥ 1 MeV) with a fluence of 2 × 10²⁰ cm⁻² at a temperature of 340 K. It has been demonstrated that, in the initial sample, the charge ordering of manganese ions of different valences arises at room temperature, which is accompanied by orthorhombic distortions of the cubic spinel structure, and the long-range antiferromagnetic order with the wave vector k = 2π/c(0, 0, 0.44) is observed at low temperatures. It has been established that the structural disordering leads to radical changes in the structural and magnetic states of the LiMn₂O₄ manganite. The charge ordering is destroyed, and the structure retains the cubic symmetry even at a temperature of 5 K. The antiferromagnetic type of ordering transforms into ferrimagnetic ordering with local spin deviations in the octahedral sublattice due to the appearance of intersublattice exchange interactions.     

Directed spiral site percolation on the square lattice

A new site percolation model, directed spiral percolation (DSP), under both directional and rotational (spiral) constraints is studied numerically on the square lattice. The critical percolation threshold p _c ≈ 0.655 is found between the directed and spiral percolation thresholds. Infinite percolation clusters are fractals of dimension d _f ≈ 1.733. The clusters generated are anisotropic. Due to the rotational constraint, the cluster growth is deviated from that expected due to the directional constraint. Connectivity lengths, one along the elongation of the cluster and the other perpendicular to it, diverge as p → p _c with different critical exponents. The clusters are less anisotropic than the directed percolation clusters. Different moments of the cluster size distribution P _s(p) show power law behaviour with | p - p _c| in the critical regime with appropriate critical exponents. The values of the critical exponents are estimated and found to be very different from those obtained in other percolation models. The proposed DSP model thus belongs to a new universality class. A scaling theory has been developed for the cluster related quantities. The critical exponents satisfy the scaling relations including the hyperscaling which is violated in directed percolation. A reasonable data collapse is observed in favour of the assumed scaling function form of P _s(p). The results obtained are in good agreement with other model calculations. Received 10 November 2002 / Received in final form 20 February 2003 Published online 23 May 2003 RID="a" ID="a"e-mail: santra@iitg.ernet.in     

Impurity effects on the critical behaviour of the electrical resistance of binary liquid mixtures

The electrical resistance of the binary liquid system cyclohexane + acetic anhydride is measured, in the critical region, both in the pure mixture and when the mixture is doped with small amounts (≈ 100 ppm) of H₂O/D₂O impurities.T _c was approached to aboutt=3×10⁻⁶ wheret=(T −T _c )/T _c . The critical exponentb ≈ 0.35 in the fit of the resistance data to the equationdR/dT ∼t ^−b does not seem to be affected appreciably by the impurities. There is a sign reversal ofdR/dt in the non-critical region. Binary liquid systems seem to violate the universality of the critical resistivity.     

Morphology and electrical properties of pulsed-laser deposited Bi2Sr2CaCu2O8+δ films on vicinal substrates

Thin films of Bi₂Sr₂CaCu₂O_8+δ have been grown on vicinal (001) SrTiO₃ substrates by pulsed-laser deposition. Transmission electron microscopy (TEM) and X-ray diffraction reveal well ordered films with the c axis of the film parallel with the c axis of the substrate for miscut angles up to θ_S≈15°. TEM also reveals the step-like film morphology due to step-flow growth. The in-plane and out-of-plane resistivities are independent of film thickness within the range 20–300 nm and agree quite well with Bi₂Sr₂CaCu₂O_8+δ single-crystal data. Received:15 May 2000 / Accepted:17 May 2000 / Published online: 9 August 2000     

Paramagnetic susceptibility of Bi-Mn alloys in the liquid state

The magnetic susceptibility of Bi_{100 − x} Mn _x (x = 5, 7.5, 10, 12.5, 15, 17.5, 20, 25) alloys is experimentally studied by the Faraday method in the temperature range T = 300−1200°C and the magnetic-field range B = 0.6−1.3 T. To calculate the electronic characteristics of the Bi-Mn alloys, the experimental results are approximated by the generalized Curie-Weiss law. The calculated parameters of the electronic structure of the alloys demonstrate that manganese is present in the melt in an ionic state with an effective magnetic moment μ_eff ≈ 5μ_B, all Bi-Mn alloys have negative paramagnetic temperatures (which indicate the antiferromagnetic character of the exchange between transition 3d element atoms), and the density of states near the Fermi level n(E _F) is low. Therefore, the Fermi level is outside the d band of manganese and its position is controlled by the sp band of bismuth.     

Critical behavior of electrical resistivity in amorphous Fe-Zr alloys

Electrical resistivity (ρ) of the amorphous (a-)Fe_100−c Zr _c (c=8.5, 9.5 and 10) alloys has been measured in the temperature range 77 to 300 K, which embraces the second-order magnetic phase transition at the Curie temperature point T _c. Analysis of the resistivity data particularly in the critical region reveals that these systems have a much wider range of critical region compared to other crystalline ferromagnetic materials. The value of T _c and specific heat critical exponent, α has the same values as those determined from our earlier magnetic measurements. The value of α for all the present investigated alloys are in close agreement with the values predicted for three-dimensional (3D) Heisenberg ferromagnet systems, which gives contradiction to the earlier results on similar alloys. It is observed from the analysis that the presence of quenched disorder does not have any influence on critical behavior.     

Field theoretic calculation of energy cascade rates in non-helical magnetohydrodynamic turbulence

Energy cascade rates and Kolmogorov’s constant for non-helical steady magnetohydrodynamic turbulence have been calculated by solving the flux equations to the first order in perturbation. For zero cross helicity and space dimensiond = 3, magnetic energy cascades from large length-scales to small length-scales (forward cascade). In addition, there are energy fluxes from large-scale magnetic field to small-scale velocity field, large-scale velocity field to small-scale magnetic field, and large-scale velocity field to large-scale magnetic field. Kolmogorov’s constant for magnetohydrodynamics is approximately equal to that for fluid turbulence (≈ 1.6) for Alfvén ratio 05 ≤r _A ≤ ∞. For higher space-dimensions, the energy fluxes are qualitatively similar, and Kolmogorov’s constant varies asd ^1/3. For the normalized cross helicity σ_c →1, the cascade rates are proportional to (1 − σ_c)/(1 + σ_c , and the Kolmogorov’s constants vary significantly with σ_cc.