Incommensurateness effects in a lattice Ginzburg-Landau model

This paper discusses the effect of magnetic translational symmetry on the vortex structure in superconducting crystals with a large basis in artificial Josephson media (regular lattices of superconducting clusters) prepared with opal as the base material. For external magnetic fields lower than the upper critical field, the lattice Ginzburg-Landau model reduces to the two-dimensional Frenkel’-Kontorova model which in some cases is exactly solvable, in which the crystal lattice plays the role of an “hard sublattice” while the deformable vortex lattice plays the role of a “soft sublattice.” It is shown that static shear waves in the vortex lattice are solutions to the two-dimensional sine-Gordon equation with an additional condition of incompressibility implied by flux quantization. The pinning energy is found as a function of the magnetic field, nearness to the transition line, and the crystal lattice constant. Fiz. Tverd. Tela (St. Petersburg) 39, 1158–1162 (July 1997)     

Features of the melting dynamics of a vortex lattice in a high-T c superconductor in the presence of pinning centers

The phase transition “triangular lattice-vortex liquid” in layered high-T _c superconductors in the presence of pinning centers is studied. A two-dimensional system of vortices simulating the superconducting layers in a high-T _c Shubnikov phase is calculated by the Monte Carlo method. It was found that in the presence of defects the melting of the vortex lattice proceeds in two stages: First, the ideal triangular lattice transforms at low temperature (≃3 K)into islands which are pinned to the pinning centers and rotate around them and then, at a higher temperature (≃8 K for T _c 584 K), the boundaries of the “islands” become smeared and the system transforms into a vortex liquid. As the pinning force increases, the temperatures of both phase transitions shift: The temperature of the point “triangular lattice-rotating lattice” decreases slightly (to ≃2 K)and the temperature of the phase transition “rotating lattice-vortex liquid” increases substantially (≃70 K). Pis’ma Zh. éksp. Teor. Fiz. 66, No. 4, 269–274 (25 August 1997)     

Pinning of planar vortices and magnetic field penetration in a three-dimensional Josephson medium

The behavior of planar (laminar) vortices in a three-dimensional, ordered Josephson medium as a function of the parameter I, which is proportional to the critical junction current and the cell size, is investigated with allowance for pinning due to the cellular structure of the medium. The minimum possible distances between two isolated vortices are calculated. A system of vortices formed in a sample in a monotonically increasing external magnetic field is analyzed. The minimum distance from the outermost vortex to the nearest neighbor is proportional to I ^−1.1. For I⩽1.3 each vortex contains a single flux quantum Φ₀, and the distance between them does not decrease in closer proximity to the boundary but remains approximately constant, implying that the magnetic field does not depend on the coordinate in the region penetrated by vortices. These facts contradict the generally accepted Bean model. The sample magnetization curve has a form typical of type II superconductors. Allowance for pinning raises the critical field H _c and induces a sudden jump in the curve at H=H _c. Zh. Tekh. Fiz. 67, 38–46 (September 1997)     

Vortex structure in FeTeSe single crystals

Vortex structure in FeTe_0.66Se_0.44 and FeTe_0.6Se_0.4 single crystals with T _c ∼ 11.7 and 14.5 K, respectively, has been studied using the decoration technique. It has been found that in single crystals with the simplest crystalline structure of 11-family iron-containing superconductors (without interlayers), no regular vortex lattice is observed, similar to the case of the previously studied 122 and 1111 families. Using transmission electron microscopy, the dislocation structure with a density of ∼10⁹ cm⁻² has been observed. The problem of pinning in iron-containing superconductor single crystals is discussed.     

Influence of the pinning of Abrikosov vortices on the propagation of surface magnetostatic waves in a ferromagnet-superconductor structure

The influence of surface-layer vortex pinning in a type-II superconductor on the propagation of surface magnetostatic waves in a ferromagnet-superconductor structure is analyzed. The pinning is assumed to be strong enough to prevent vortex displacement under the influence of the Lorentz force generated by the surface magnetostatic waves, so that the ground state of the superconductor is determined by the elastic properties of the vortex lattice and by pinning. In the given model the problem reduces to the analysis of the wave spectrum in the scattered field created by the disordered vortex surface layer. A calculation shows that the influence of this field on the surface magnetostatic-wave spectrum is slight and, hence, degradation of the shielding properties of the superconductor does not take place in the presence of strong vortex pinning (as opposed to the ferromagnet-ideal superconductor structure). Fiz. Tverd. Tela (St. Petersburg) 40, 32–35 (January 1998)     

Optical quenching of the magnetoplastic effect in NaCl crystals

Observations indicate that illuminating NaCl crystals by ultraviolet light (λ=350 nm) suppresses the magnetoplastic effect. The processes induced by illumination take place in a subsystem of point defects and are related to a change in the state of magnetically sensitive dislocation pinning sites. Fiz. Tverd. Tela (St. Petersburg) 39, 1389–1391 (1996)     

Pinning by twin boundaries and peak effect in YBaCuO high-T c superconductors

Measurements of the imaginary part of the ac magnetic susceptibility of single crystals and melt-textured samples of YBa₂Cu₃O_x (YBCO) at T=77 K in a magnetic field ranging between 1 and 20 kOe are reported. If the dc magnetic field H _dc is rotated in the ab plane of the sample, the magnetic susceptibility and critical current density j _c have peaks corresponding to the magnetic field aligned with twin boundaries. Peaks in the curve of j _c versus magnetic field are observed at angles corresponding to these peaks, where AH _dc in a wide range of magnetic fields. The results have been interpreted in terms of the theory describing twin boundaries as a system of quasi-planar pinning sites. The pinning is strong if the elastic displacements of flux lines are of the order of the vortex lattice constant d _f. These displacements decrease with the magnetic field because of the decrease in d _f, and the contribution of the elastic energy to the Gibbs potential is reduced accordingly, which is the cause of the peak effect. Zh. éksp. Teor. Fiz. 111, 2158–2174 (June 1997)     

Dislocation unpinning model of acoustic emission from alkali halide crystals

The present paper reports the dislocation unpinning model of acoustic emission (AE) from alkali halide crystals. Equations are derived for the strain dependence of the transient AE pulse rate, peak value of the AE pulse rate and the total number of AE pulse emitted. It is found that the AE pulse rate should be maximum for a particular strain of the crystals. The peak value of the AE pulse rate should depend on the volume and strain rate of the crystals, and also on the pinning time of dislocations. Since the pinning time of dislocations decreases with increasing strain rate, the AE pulse rate should be weakly dependent on the strain rate of the crystals. The total number of AE should increase linearly with deformation and then it should attain a saturation value for the large deformation. By measuring the strain dependence of the AE pulse rate at a fixed strain rate, the time constantτ _s for surface annihilation of dislocations and the pinning timeτ _p of the dislocations can be determined. A good agreement is found between the theoretical and experimental results related to the AE from alkali halide crystals.     

Commensurability oscillations and a new phase transition in YBa2Cu3Oy single crystals

Magnetization oscillations due to the commensurability of the vortex and crystal lattice periods in YBa₂Cu₃O_y (y=6.97±0.02) single crystals are investigated using a high angular resolution magnetometer. A sharp peak in the temperature dependence of the oscillation amplitude as well as other features in the behavior of the oscillation amplitude and of the irreversible magnetization are observed at T _f ∼60 K. It is inferred that T _f is the temperature of a transition of the solid vortex state to a smectic phase. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 11, 832–837 (10 June 1999)     

Pinning in a porous high-temperature superconductor Bi2223

The current-voltage characteristics of a porous superconductor Bi₂Sr₂Ca₂Cu₃O _x (Bi2223) have been measured at temperatures in the range from 10 to 90 K in magnetic fields of 0–80 kOe. The experimental dependences have been analyzed within the model allowing for pinning by clusters of a normal phase with fractal boundaries, as well as the model taking into account phase transformations of vortex matter. It has been found that the electrical resistance of the superconductor material significantly increases at temperatures of 60–70 K over the entire range of magnetic fields under consideration without changing in the sign of the curvature of the dependence R(I). It has been assumed that this behavior is associated with the specific feature of the pinning in a highly porous high-temperature superconductor, which lies in the fractality of the distribution of pinning centers in a wide range of self-similarity scales. The studied material at the aforementioned temperatures is characterized by the melting of the vortex structure.     

Nonlinear dynamics of vortices pinned to unidirectional twins

The nonlinear resistive properties of superconductors in the mixed state in the presence of a system of unidirectional planar defects (twins) have been investigated theoretically within the framework of the two-dimensional stochastic model of anisotropic pinning based on the Fokker-Planck equations with a concrete form of the pinning potential. These equations allow one to obtain an exact analytical solution of the problem. Formulas are obtained for experimentally observable even and odd (relative to reversal of the direction of the external magnetic field) nonlinear longitudinal and transverse magnetoresistivities ρ _‖,⊥ ^± ( j,t,α,ε) as functions of the transport current density j, temperature t, the angle α between the directions of the current and the twins, and the relative volume fraction ε occupied by the twins. In light of the great variety of types of nonlinear resistive dependences contained in these expressions for ρ _‖,⊥ ^± the most characteristic of them are presented in the form of graphs with commentary. The desired nonlinear dependences ρ _‖,⊥ ^± are linear combinations of the even and odd parts of the function v(j,t, α,ε), which has the sense of the probability of overcoming the potential barrier of the twins; this makes it possible to give a simple physical treatment of the nonlinear regimes. New scaling relations for the Hall conductivity are obtained and investigated which differ from the previously known relations for isotropic pinning. The interaction of vortex motion directed along the twins and the Hall effect is considered for Hall constants which are arbitrary in magnitude and sign, and it is shown that in the case of small Hall viscosity vortex motion directed along the twins has an effect on the odd magnetoresistivities ρ _‖ ⁻ and ρ _⊥ ⁻ , whereas the reverse effect can be neglected. It is shown that pinning anisotropy is sufficient to manifest the new nonlinear (in the current) magnetoresistivities ρ _⊥ ⁺ and ρ _‖ ⁻ . Zh. éksp. Teor. Fiz. 116, 2103–2129 (December 1999)     

Study of the critical current in YBaCuO films under reactor-neutron irradiation in the low-temperature helium circuit in the 25–300 K range

Changes in the temperature and dose dependences of I-V characteristics and of the critical current j _c of YBaCuO films on MgO and SrTiO₃ substrates under neutron irradiation has been studied at 25–80 K. The transport properties of YBaCuO films on MgO (M1) and SrTiO₃ (S1) substrates were found to behave differently. It is shown that the M1 films have granular structure, and their transport properties were considered within the concept of percolation over weak intergranular links. The S1 are single-crystal films, and their properties are analyzed within a resistive-state theory associated with thermal activation of Abrikosov vortices. It is shown that the degradation rate of the critical temperature T _c of S1 films is 3.5 times smaller than that of the M1 films. The dose dependence of j _c has an exponential character, j _c=j _c(0)exp(−kΦ), where k is related to the number of displaced atoms per neutron and is the same for the M1 and S1 films, irrespective of the irradiation temperature. The pinning energy has been derived from the I-V characteristics and it has been found that the U/kT ratio lies within 20–25 and is independent of neutron flux. It is shown that the radiation-induced disorder changes the pinning mechanism, from pinning at the boundaries of misoriented crystals to that at spatial inhomogeneities, apparently radiation induced. Fiz. Tverd. Tela (St. Petersburg) 40, 1961–1967 (November 1998)     

Pinning of pancake vortices in a three-dimensional Josephson medium and structure of the vortex lattice in the “critical” state

A system of pancake vortices formed near the boundary of a sample in a monotonically increasing external magnetic field is calculated with allowance for pinning due to the cellular structure of the medium for various values of the pinning parameter I, which is proportional to the critical current of the junction and the cell diameter. The shortest distance from the outermost vortex to the nearest neighbor is proportional to I ⁻¹¹. It is shown that the pinning parameter has a critical value I _c separating two regimes with different types of critical states. For I<I _c the external magnetic field has a threshold value H _t(I), above which the field immediately penetrates the interior of the junction to an infinite distance. For I>I _c the magnetic field decays linearly from the boundary into the interior of the junction. The value obtained in the study, I _c=3.369, differs from the value of 0.9716 postulated by other authors. The dependence of the slope of the magnetic field profile near the boundary on I is determined. It is shown that the slope is independent of I in intervals 2πk<I<2πk+π. Fiz. Tverd. Tela (St. Petersburg) 39, 1958–1963 (November 1997)     

Anomalous vortex dynamics in

We report on measurements of current–voltage (I–V) characteristics for YNi₂B₂C single crystals with weak pinning in various fields at 7.6 K. We find nonmonotonic, N-shaped I–V curves in a certain field region deep in the vortex solid phase. This behavior is anomalous, since there exists an intermediate I region where flow voltage V shows a decrease with increasing I (a driving force). While the exact nature remains unknown, this phenomenon suggests vortex motion (driving I) induced pinning.     

Vortex pinning in YBa2Cu3O7?x films

Evidence that pinning on linear or planar defects dominates the vortex dynamics in YBa₂Cu₃O_7−x (YBCO) films is provided by complex impedance measurements at temperature 8 K<T<T _c and magnetic field 0<B<6 T. Below the vortex lattice melting transition B_g(T) but above a threshold field B_p≈8(1-T/T _c ) T, the inductance of vortices increases as B², much less rapidly than predicted for collective pinning of vortices by point defects. Above the vortex melting line, critical scaling persists over the region B_g(T<B<B^*(T) where the vortex correlation length ξ exceeds a characteristic length scale ξ^*≡ξ(B=B^*)≈450?. The value of ξ^* is not sensitive to Al-doping in the Cu sites in the lattice and is close to the size of twin domains in the film. The nature of the observed crossovers is discussed in terms of available theoretical models for a glass-liquid transition at B_g.     

Effect of pinning and driving force on the metastability effects in weakly pinned superconductors and the determination of spinodal line pertaining to order—disorder transition

We explore the effect of varying drive on metastability features exhibited by the vortex matter in single crystals of 2H-NbSe₂ and CeRu₂ with varying degree of random pinning. The metastable nature of vortex matter is reflected in the path dependence of the critical current density, which in turn is probed in a contact-less way via AC-susceptibility measurements. The sinusoidal AC magnetic field applied during AC susceptibility measurements appears to generate a driving force on the vortex matter. In a nascent pinned single crystal of 2H-NbSe₂, where the peak effect (PE) pertaining to the order—disorder phenomenon is a sharp first-order-like transition, the supercooling feature below the peak temperature is easily wiped out by the reorganization caused by the AC driving force. In this paper, we elucidate the interplay between the drive and the pinning which can conspire to make the path-dependent AC-susceptibility response of different metastable vortex states appear identical. An optimal balance between the pinning and driving force is needed to view the metastability effects in typically weakly pinned specimen of low temperature superconductors. As one uses samples with larger pinning in order to differentiate the response of different metastable vortex states, one encounters a new phenomenon, viz., the second magnetization peak (SMP) anomaly prior to the PE. Supercooling/superheating can occur across both the PE and the SMP anomalies and both of these are known to display non-linear characteristics as well. Interplay between the path dependence in the critical current density and the non-linearity in the electromagnetic response determine the metastability effects seen in the first and the third harmonic response of the AC susceptibility across the temperature regions of the SMP and the PE. The limiting temperature above which metastability effects cease can be conveniently located in the third harmonic data, and the observed behavior can be rationalized within the Bean’s critical state model. A vortex phase diagram showing different vortex phases for a typically weakly pinned specimen has been constructed via the AC susceptibility data in a crystal of 2H-NbSe₂ which shows the SMP and the PE anomalies. The phase space of coexisting weaker and stronger pinned regions has been identified. It can be bifurcated into two parts, where the order and disorder dominate, respectively. The former part continuously connects to the reentrant disordered vortex phase pertaining to the small bundle pinning regime, where the vortices are far apart, interaction effects are weak and the polycrystalline form of flux line lattice prevails.     

Vortex structure in BaFe2(As1 − x P x )2 single crystals

Single crystals of iron-containing Ba(FeAs)₂ superconductors doped with phosphorus have been studied. The vortex structure has been studied by means of the decoration method. Large domains of the triangular vortex structures have been observed in the phosphorus-doped single crystals of iron-containing superconductors. The effect of doping on pinning in iron-containing superconductors has been discussed.     

Evolution of dislocation structure during deformation of γ-irradiated LiF crystals

The effect of γ irradiation on the mechanical characteristics and dislocation structure of slip bands in LiF crystals is studied at doses D⩽7.3×10⁸ R. Irradiation causes a substantial increase (up to a factor of 30) in the yield stress τ _y of the crystals, with τ _y ∝ D ^0.4 in the first approximation. The deformation shear increases in the slip bands of irradiated crystals, as do the densities of the screw and edge dislocation components, while the dislocation mean free paths decrease. Irradiation also raises the probability of twinning cross slip for screw dislocations. The observed effects are assumed to be related to the formation of a different kind of defects in the irradiated crystals, primarily clusters of implanted atoms. Fiz. Tverd. Tela (St. Petersburg) 39, 1072–1075 (June 1997)     

Generation of electromagnetic radiation in the motion of vortices in magnetically coupled superconducting films

We examine theoretically the generation of electromagnetic radiation in the relative motion of vortex lattices in magnetically coupled films in the dc transformer geometry. We establish the conditions under which the force of mutual pinning of the vortex lattices varies according to a harmonic law as a function of the relative displacement of the vortices in the films within a given range of magnetic field inductions. In this case the equation describing the viscous flow of vortex lattices in magnetically coupled films is the same as the equation of the resistively shunted Josephson junction model. We show that magnetically coupled superconductors exhibit the properties of a Josephson element without any restrictions on the geometrical size of such a system imposed by the coherence length ξ. The frequency f of the electromagnetic radiation generated by the relative motion of vortex lattices in magnetically coupled superconductors depends on the spatial period of the vortex lattices and the velocity of relative vortex motion, which means that the frequency of the radiation can be tuned by applying a magnetic field or a current. Zh. éksp. Teor. Fiz. 113, 1319–1338 (April 1998)     

Peak effect at microwave frequencies in swift heavy ion irradiated YBa2Cu3O7-δ thin films

The vortex dynamics at microwave frequencies in YBa₂Cu₃O_7-δ (YBCO) films have been studied. We observe a peak in the microwave (4.88 and 9.55 GHz) surface resistance in some films in magnetic fields up to 0.8 T. This is associated with the ‘peak-effect’ phenomenon and reflects the order-disorder transformation of the flux line lattice near the transition temperature. Introduction of artificial pinning centers like columnar defects created as a result of irradiation with 200 MeV Ag ion (at a fluence of 4×10¹⁰ ions/cm²) leads to the suppression of the peak in films previously exhibiting ‘peak effect’.