Proximity effect in the finite and incommensurate ferromagnet/superconductor systems

The original theory of a proximity effect is proposed for the bi- and tri-layered system ferromagnetic metal/superconductor (F/S) in dirty limit. The F₁/S/F₂ trilayer is examined more closely. The distinctions in materials, in thicknesses of F layers (d_f1 and d_f2), in parameters interfaces, and in local environments of layers are considered among the causes of incommensurability of trilayer. The peculiar T_c(d_f1, d_f2) interference pattern is predicted for the F₁/S/F₂ systems. The reentrant superconductivity and possibility of the better observability of the spin-valve regime are discussed.     

On the criterion of the crystal-liquid phase transition

A localization criterion is proposed for the crystal-liquid phase transition (PT). According to this criterion, the PT begins when the E _d/k _b T ratio reaches a boundary value E _d(s)/k _b T _m such that a solid phase is present above it and a liquid phase is present below it in a phase diagram. Here, E _d is the energy of atom delocalization, k _b is the Boltzmann constant, T is the temperature, and E _d(s) is the delocalization energy for a solid phase at melting point T _m. This criterion is shown to generalize the Lindemann criterion of melting to the case of crystallization and the Löven criterion of crystallization to the case of melting. This localization criterion is found to be applicable for both normally melting substances and substances that melt with a decrease in the specific volume upon the transition into a liquid phase. The relation of the localization criterion to the vacancy and diffusional criteria of the crystal-liquid PT has been studied. The inequality T _N < T _m, where T _N is the temperature of the onset of crystallization, is explained using the localization criterion. The calculated values of the T _N /T _m ratio coincide well with the experimental estimates. The maximum value of T _N /T _m is likely to be most probable in crystals with a bcc structure and a small value of the Grüneisen parameter. The T _N /T _m ratio is analyzed at the points in the PT where no change in the specific volume occurs and an entropy jump is nonzero.     

Transport studies of YBa2Cu3Oy/YxPr1−xBa2Cu3Oy and YBa2Cu3Oy/R0.7M0–3MnO3 superlattices,in which R=La or Nd,and M=Ca or Sr

We report the transport studies of YBa₂Cu₃O_y/Y_xPr_1−xBa₂Cu₃O_y and YBa₂Cu₃Oy/R_1−xM_xMnO₃ superlattices in magnetic fields in which R=La or Nd, and M=Ca or Sr. The X-ray diffraction of samples shows superlattice structure. The resistive transition in a magnetic field shows thermal activated behavior. The flux pinning is reduced when the coupling strength between YBCO layers is decreased. The angular dependence of the critical current of YBa₂Cu₃O_y/PrBa₂Cu₃O_y superlattices reveals the dimensionality of superlattices. The magnetoresistance ratio (MR), |Δρ(H=7 T)−Δρ(H=0)|/Δρ(H=7 T), of YBa₂Cu₃O_y/R_1−xM_xMnO₃ superlattices is affected by the layer coupling of R_1−xM_xMnO₃ layers. The enhancement of the MR ratio in the tri-layer YBa₂Cu₃O_y/La_0.7M_0.3MnO₃/YBa₂Cu₃O_y film in the low temperature regime is significant and has a value of 33650% at T=75 K. We attribute this enhancement of the MR to the ordering of magnetic moment in ferromagnetic layers in magnetic fields. The results are discussed in terms of existing theories.     

Breakdown of renormalizability in the Kondo problem in the high-temperature expansion of the free energy

It is shown that there are two energy scales in the Kondo problem: T _k and T ₀, one of which (T _k) is exponentially small in the coupling constant g. The second scale T ₀is proportional to the squared coupling constant. Perturbation theory is valid only in the region T? T ₀. The point T ₀ is apparently the crossover from weak to strong coupling. The first indications of the breakdown of the hypothesis of only one energy scale in the Kondo problem appear in fourth order of perturbation theory.     

Polarization properties of Li2−x Na x Ge4O9 (0.2 ≤ x ≤ 0.3) crystals

The polarization switching in sinusoidal fields and the pyroelectric properties of Li_2?x Na _x Ge₄O₉ (0.2 ≤ x ≤ 0.3) crystals are measured in the temperature range T _c ?T ≤ 40 K. The behavior of the P?E hysteresis loops with variations in temperature is investigated for crystals with phase transition temperatures T _c < 300 K and T _c > 300 K. It is shown that, for crystals with phase transition temperatures T _c < 300 K, the temperature dependence of the hysteresis loop exhibits a behavior typical of crystals with second-order phase transitions. The crystals with phase transition temperatures T _c > 300 K are characterized by double hysteresis loops in the temperature range T _c ?T ₁ ≈ 30 K. The correlation between the polarization properties and possible structural transformations of the Li_2?x Na _x Ge₄O₉ crystals due to the change in the concentration ratio of Na and Li ions is discussed.     

Two independent magnetic sublattices of Er in the Er5 − x LaxGe3 system

Magnetic measurements of Er_{5 ? x} La_xGe₃ with 1 ? x ? 5 have been done between 4·2 and room temperature. The compounds crystallize in the hexagonal (D8₈) structure (Mn₅Si₃ type) with space group P6₃/mcm. Two independent, ferromagnetic and antiferromagnetic, sublattices of Er exist. The magnetic interaction between the Er atoms in the 6(g) sites is ferromagnetic, while that between the Er atoms in the 4(d) sites is antiferromagnetic. The antiferromagnetic exchange interaction is weak in this system. The first and second La atom substitutes into the 6(g) site, while the third La in Er₂La₃Ge₃ is located in the 4(d) position. The fourth La is probably substituted in such a manner that all the Er atoms are left in the 6(g) sites.     

151Eu Mössbauer effect study of T′- and T*-phase superconductors

The (La,Eu(₂ CuO ₄ system shows superconductivity by dopingCe orSr. Carriers inT′-phase doped withCe are electrons and those inT ^*-phase doped withSr are holes. In this work,¹⁵¹ Eu Mössbauer analysis is applied for theT′-phase(La _1?x Eu _x)_2?y Ce _y CuO ₄ and theT ^*-phase(La _1?x Eu _x)_2?y Sr _y CuO ₄ in order to compare the electronic state and the lattice vibration ofEu in these superconductors. In addition, correlations betweenT _c and Mössbauer parameters are examined. The isomer shift of¹⁵¹ Eu is 0.784–0.840 mm/s in theT ^*-phase and 0.689–0.733 mm/s in theT′-phase, which shows that the lanthanide in these superconductors is tri-valent. The Debye temperature of¹⁵¹ Eu is 180–208 K in theT ^*-phase and 160–192 K in theT′-phase. The difference of isomer shift between these two phases is explained by theEu?O distance. For(La _1?x Eu _x)_2?y Ce _y CuO ₄, a light correlation betweenT _c and the Debye temperature is observed, which means the importance of the lattice vibration in high-Tc superconductivity.     

A model Hamiltonian for phonon energy transfer in gas—solid collisions

Using the formalism of second quantization in the occupation number representation, a model Hamiltonian of the form H = H_loc + H_nonloc + H_loc?nonloc is developed. H_loc describes the gas atom-phonon system when the gas atom is near the surface, and the phonon operators are only in this term. H_nonmloc describes the gas atom moving in a static potential with no bound states, and H_loc-nonloc couples these two parts of H. The method of solution is to diagonalize H_loc and then to embed it in the continuum of scattering states of H_nonloc. The model is designed so that this diagonalization can be performed essentially exactly for a large class of gas-metal systems. The procedure is illustrated with a simple example which nevertheless shows how multi-phonon processes can dominate in desorption.     

Development of mechanoluminescence technique for impact studies

A new technique called, mechanoluminescence technique, is developed for measuring the parameters of impact. This technique is based on the phenomenon of mechanoluminescence (ML), in which light emission takes place during any mechanical action on solids. When a small solid ball makes an impact on the mechanoluminescent thin film coated on a solid, then initially the elastico ML (EML) intensity increases with time, attains a maximum value I_m at a particular time t_m, and later on it decreases with time. The contact time T_c of ball, can be determined from the relation T_c=2t_c, where t_c is the time at which the EML emission due to compression of the sample becomes negligible. The area from where the EML emission occurs can be taken as the contact area A_c. The maximum compression h is given by h=A_c/(πr), where r is the radius of the impacting ball, and thus, h can be determined from the known values of A_c and r. The maximum force at contact is given by F_m=(2mU₀)/T_c, where m is the mass of the impacting ball and U₀ is the velocity of the ball at impact. The maximum impact stress σ_m can be obtained from the relation, σ_m=F_m/A_c=(2mU₀)/(T_cA_c). Thus, ML provides a real-time technique for determining the impact parameters such as T_c, A_c, h, F_m and σ_m. Using the ML technique, the impact parameters of the SrAl₂O₄:Eu film and ZnS:Mn coating are determined. The ML technique can be used to determine the impact parameters in the elastic region and plastic region as well as fracture. ML can also be used to determine the impact parameters for the collision between solid and liquid, if the mechanoluminescent material is coated on the surface of the solid. The measurement of fracto ML in microsecond and nanosecond range may provide a tool for studying the fragmentations in solids by the impact. Using the fast camera the contact area and the depth of compression can be determined for different intervals of time.     

Effect of polymers doping on flux pinning behavior of MgB2

The effects of polymers doping on irreversibility field (H_irr) and critical current density (J_c) of MgB₂ have been investigated in this work. It is found that both J_c, and H_irr, are improved by doping at relative lower temperature region. The J_c−B curves of all samples studied in this work are well fitted using J_c(B) formula in percolation model. The values of upper critical field anisotropy (γ) are obtained from the fitting result at various temperatures. It is observed that values of γ for polymers doping samples are reduced at these temperatures. This is considered to be responsible for the enhancement of values of J_c for doped samples. Moreover, the percolation threshold, p_c, is found to be enhanced with increasing temperature. It is believed that the grain boundary pinning is still dominating in MgB₂, while the deviation of experimental data from the theoretical values is due to the percolation of suppercurrent in polycrystalline MgB₂.     

On Two-Temperature Problem for Harmonic Crystals

We consider the dynamics of a harmonic crystal in d dimensions with n components, d,n≥1. The initial date is a random function with finite mean density of the energy which also satisfies a Rosenblatt- or Ibragimov–Linnik-type mixing condition. The random function is translation-invariant in x ₁,...,x _d?1 and converges to different translation-invariant processes as x _d →±∞, with the distributions μ _±. We study the distribution μ _t of the solution at time $t \in \mathbb{B}$ . The main result is the convergence of μ _t to a Gaussian translation-invariant measure as t→∞. The proof is based on the long time asymptotics of the Green function and on Bernstein's “room-corridor” argument. The application to the case of the Gibbs measures μ _±=g _± with two different temperatures T _± is given. Limiting mean energy current density is ?(0,...,0,C(T ₊?T _?)) with some positive constant C>0 what corresponds to Second Law.     

Structural transition of Ti3SiC2 under high hydrostatic pressure: A first-principles study

We theoretically studied the phase transformation, electronic and elastic properties of Ti₃SiC₂ ceramic by using the pseudopotential plane-wave method within the density functional theory. Our results demonstrate that there exists a structural phase transition from α‐Ti₃SiC₂ to β‐Ti₃SiC₂ under pressure up to 384 GPa, and α‐Ti₃SiC₂ is the most stable phase at zero pressure. The calculated electronic band structure and density of states reveal the metallic behavior for the polymorphs of Ti₃SiC₂. The mechanical stability of α‐Ti₃SiC₂ at zero pressure is confirmed by the elastic constants, and is analyzed in terms of electronic level. By analyzing the ratio between bulk and shear moduli, we conclude that α‐Ti₃SiC₂ is brittle in nature.     

Stochastic dynamics and Parrondo’s paradox

The Spanish physicist Juan Parrondo has provided two stochastic losing games such that for certain stochastic combinations one may obtain a winning game. If a large number of players are involved and if they try to play such that their gain in the next round is maximized one arrives at the problem of investigating a random walk on a certain space of measures.The appropriate abstract setting is as follows. There is given a compact metric space (M,d), and M is written as the union of certain closed subsets A₁,…,A_r. For every ρ=1,…,r there is prescribed a strict contraction Γ_ρ:A_ρ→M. A random walk (X_m)_m∈N0 on M is then defined as follows. The starting position is X₀=x₀, where x₀∈M is fixed, and if the walk at the m’th step is at position X_m∈M, then one chooses a ρ among the ρ with X_m∈A_ρ (with equal probability, say) and defines X_m+1 as Γ_ρ(X_m). Associated with the walk is a gainφ(X_m) in every round, where φ:M→R is a continuous function.The aim of the present investigations is the study of the expectation G_m of φ(X_m) as a function of m. Our main result states that the sequence (G_m) is “eventually approximately periodic” provided that all A_ρ are not only closed but also open in M: for every ε there is an l₀∈N such that (G_m) is l₀-periodic up to an error of at most ε for sufficiently large m. In fact it turns out that the behaviour of our process can be described well with a finite Markov chain.In the general case, however, the process might behave rather chaotically. We give an example where M is the unit interval. M is written as the union of two closed subsets A₁,A₂, the contractions Γ₁,Γ₂ are rather simple, but the expectations of the gains are not even Cesáro convergent.     

The estimation of equilibrium molecular structures from zero-point rotational constants

The approximate equation I_e = 2I₈ - I₀, where I_e, I₈, and I₀ are, respectively, the equilibrium, substitution and zero-point moments of inertia of a molecule, can be derived from a first order treatment of isotope effects, and is valid for linear, symmetric or asymmetric tops. By means of this equation it is possible to estimate the equilibrium structure of a molecule from the zero-point rotational constants of several isotopes. The advantage of this “mass-dependence” (r_m) method over the conventional r_e method is that it is insensitive to the perturbations and resonances that frequently affect excited vibrational states. The main disadvantages are that a large number of isotopic molecules may be necessary and that the above equation is not sufficiently accurate for hydrogen-deuterium isotope effects.A detailed comparison between r_m and r_e of CO shows that the slight difference of about 2 × 10^?4Å between the two bond lengths is due mainly to the difference in the contributions of the electrons. The r_m method has also been applied to the triatomic molecules N₂O, OCS, SO₂ and HCN. For N₂O and SO₂ the results are in excellent agreement with the most recent r_e structures. For OCS there is a significant difference between the r_m structure and the present r_e structure. This difference is as yet unexplained. The poor results for HCN confirm the general expectation that the r_m method cannot be applied to hydrides without further modification.     

Magnetization reversal dynamics in La0.65Sr0.28Mn1.07O3 ceramics and NixZn1−x Fe2O4 nickel-zinc ferrite placed in complicated pulsating fields

The magnetization reversal dynamics in La_0.65Sr_0.28Mn_1.07O₃ ceramics and Ni_xZn_1?x Fe₂O₄ nickel-zinc ferrite placed in a magnetic field is studied experimentally. The field is a superposition of quasi-static field H, rf field h _ω cosωt, and low-frequency field h _ΩcosΩt with H ∥ h _ω ∥ h _Ω. The low-frequency response is found to be nonlinear in h _Ω. A procedure discriminating between the linear and nonlinear components of this response is proposed. Unlike the linear component, the nonlinear component is an essentially anharmonic function of time. The results are analyzed in detail using the high-frequency and low-frequency magnetization reversal curves of the materials.     

Suppression of Tc by Zn impurity in the electron-type LaFe0.925−y Co0.075ZnyAsO system

The effect of non-magnetic Zn impurity on superconductivity in electron-type pnictide superconductor LaFe_0.925−yCo_0.075Zn_yAsO is studied systematically. The optimally doped LaFe_0.925Co_0.075AsO without Zn impurity exhibits superconductivity at T_c^mid of 13.2 K, where T_c^mid is defiend as the mid-point in the resistive transition. In the presence of Zn impurity, the superconducting transition temperature, T_c^mid, is severely suppressed. The result is consistent with the theoretic prediction on the effect of non-magnetic impurity in the scenario of s_± pairing, but it is in sharp contrast to the previous report on the effect of Zn impurity in the F-doped systems. The possible interpretation of the different effects of Zn impurity on superconductivity in different systems is discussed.     

On the renormalization of the quantum field theory of point-like monopoles and charges

The quantum field theory of point-like monopoles and charges is first formulated on a euclidean lattice for a convenient regularization. The regularization preserves the peculiar features of the theory, namely those related to the invariance and to the quantization condition. The partition function is expressed as a path integral over the particle's closed paths and the action is constructed in terms of arbitrary surfaces having those paths as boundaries. The possible divergences of the continuum limit are discussed, in particular the vacuum polarization ones. It is found that, although both the electric charge Q and the magnetic charge G are renormalized as Q = Z_QQ_R and G = Z_GG_R, the quantization condition is preserved by the renormalization i.e. Z_QZ_G = 1 so that QG = Q_RG_R = 2πn. Due to the dual symmetry of the theory, then, for Q = G we get Z_Q = Z_G = 1.     

The development of a new Morse-oscillator based rotation-vibration Hamiltonian for H3+

The rotation-vibration Hamiltonian for an equilateral triangular X₃ molecule is derived in terms of the three curvilinear stretching coordinates Δr_i, and expanded in the form of a power series in the variables y_i = 1 ? exp(-aΔr_i), where a is a molecular parameter obtained from the potential function. The reason for the use of the variable y_i is twofold: Stretching potentials exhibit a much stronger convergence in the y_i than in the Δr_i, and a Hamiltonian expressed in the y_i can be diagonalized in a straightforward fashion using a Morse-oscillator basis set as we do here. Using a published ab initio potential surface we have expanded it as a polynomial in the y_i, and have calculated variationally the rotation-vibration energies of H₃⁺ and D₃⁺ using a symmetry-adapted Morse-oscillator-rigid symmetric top basis set. The results indicate that an expansion of the potential function to quartic terms in the y_i might be adequate, and that satisfactorily converged energies can be obtained with a relatively small basis set. The molecule H₃⁺ is the simplest polyatomic molecule. Inspection of the Appendix of this paper shows that the rotation-vibration Hamiltonian used here is one of the more complicated ones.     

The ν7 vibrational states of C3O2: A least-squares fit of the rigid-bender model to the v7ν7l7 energies and rotational constants

The rigid-bender model is used to treat the large-amplitude, low-frequency, bending vibration ν₇ of C₃O₂. Different parameterizations of the bending potential function are considered, and a simple two-term power series is found to give the best fit. With this parameterization, using a least-squares fit to energies and B values, the ν₇ potential function is determined for the ground state as well as for the states in which ν₂, ν₃, ν₄, ν₆, 2ν₆, ν₁ + ν₃, ν₁ + ν₄, ν₂ + ν₃, and 2ν₂ + ν₄ are excited. The excitation of other vibrations has in some cases a drastic effect on the ν₇ potential. In the ground state the potential has a 29 cm^?1 barrier at the linear position, in ν₁ + ν₃ the barrier increases to 79 cm^?1, while in 2ν₂ + ν₄ the barrier vanishes. An equilibrium potential is determined by correcting the ground state potential for the effects of zero-point motion of the normal vibrations ν₁, …, ν₆. This potential has a 35.6-cm^?1 barrier with a minimum at α = 11.14°, where 2α is the angular deviation from linearity. The model accurately predicts the quartic and sextic centrifugal distortion terms for the low-lying v₇ν₇^l₇ states. Second-order l-type coupling is included in the calculations of the quartic terms. The effects of this coupling, which are most pronounced for the ν₇ ≥ 2 states, adequately explain the negative D term recently reported for the ν₂ + 4ν₇⁰ state.     

The theory of diffusion-limited recombination of donor—acceptor pairs

The asymptotics of the quasi-steady kinetics of diffusion-limited recombination of donor-acceptor (DA) pairs has been developed. The theory is based on the probability of DA pair recombination according to the relation w₀ exp [-(r/r_B)], where w₀ is constant, r is the separation between defects and r_B is the half Bohr radius of the more diffuse wavefunction. The reaction rate equation (for the thermal activation mechanism) includes the reaction constant as follows: k = 4πr_B[E_a/kT + ln (w₀r^2_B/D₀) + 1.54 + 2 K₀ (α)], α = 2r₀(w₀/D)$\text{1}\text{2}\text{,}$ where E_a is the activation energy, and K₀, I₀ are the modified Bessel functions. The quasi-steady recombination radius is introduced. The theory developed has been compared with the zone one. The interpretation of the activation energy and frequency factor have been presented for the diffusion model. An extension of the theory developed by taking into account Coulomb interaction between defects has also been presented. The applicability of the theory to the recombination of V_k centers with electronics centers is alkali halides has been shown. It is assumed that the theory is applicable to other centers of hole nature (H, proton, low symmetry exciton i.e. V_k + electron).