Using μSR to investigate the vortex lattice in high-temperature superconductors

We review some of the properties of the vortex lattice in type II superconductors and the use of muon spin rotation (μSR) to investigate high temperature superconducting oxides. As a microscopic probe of the field distribution inside the bulk of materials, μSR is shown to be a powerful tool with which to study the magnetic properties of superconductors. We also discuss how understanding the complex phenomenology of the vortex lattice in these materials is necessary in order to correctly determine fundamental parameters of the superconducting state.     

Composite to tilted vortex lattice transition in Bi2Sr2CaCu2O8+delta in oblique fields

Precision measurements of the vortex phase diagram in single crystals of the layered superconductor Bi2Sr2CaCu2O8+delta in oblique magnetic fields confirm the existence of a second phase transition, in addition to the usual first-order vortex-lattice melting line Hm(T). The transition has a strong first-order character, is accompanied by strong hysteresis, and intersects the melting line in a tricritical point (Hm perpendicular, Hcr parallel). Its field dependence and the changing character of the melting line at the tricritical point strongly suggest that the ground state for magnetic fields closely aligned with the superconducting layers is a lattice of uniformly tilted vortex lines.     

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)     

Superconducting vortex pinning with artificial magnetic nanostructures

This review is dedicated to summarizing the recent research on vortex dynamics and pinning effects in superconducting films with artificial magnetic structures. The fabrication of hybrid superconducting/magnetic systems is presented together with the wide variety of properties that arise from the interaction between the superconducting vortex lattice and the artificial magnetic nanostructures. Specifically, we review the role that the most important parameters in the vortex dynamics of films with regular array of dots play. In particular, we discuss the phenomena that appear when the symmetry of a regular dot array is distorted from regularity towards complete disorder including rectangular, asymmetric, and aperiodic arrays. The interesting phenomena that appear include vortex-lattice reconfigurations, anisotropic dynamics, channeling, and guided motion as well as ratchet effects. The different regimes are summarized in a phase diagram indicating the transitions that take place as the characteristic distances of the array are modified respect to the superconducting coherence length. Future directions are sketched out indicating the vast open area of research in this field.     

Intrinsic pinning of vortices as a direct probe of the nonuniform Larkin-Ovchinnikov-Fulde-Ferrell state in layered superconductors

Previously the search for the modulated superconducting Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) state was performed by means of measurements which do not give direct information on spatial modulation of the superconducting state. We propose to measure interlayer conductivity in Josephson-coupled layered superconductors as a function of the strength and the orientation of the parallel magnetic field. We show that interlayer critical current and the conductivity have peaks when the magnetic field is perpendicular to the in-plane wave vector of the LOFF state and when the period of the Josephson vortex lattice induced by the magnetic field is commensurate with the LOFF period.     

Structure of the mixed state in type II superconductors and its connection with Josephson effects in long superconducting bridges

The interaction energy between vortices and the structure of the vortex lattice in superconducting layers is calculated. It is shown that the one-dimensional vortex lattice (with vortices in the centre of the layer) is stable in a relatively large interval of magnetic fields above the flux penetration field. This result is true not only for very thin layers (with dimensions smaller than the penetration depth), but also for layers withd>. The results can be helpful at explaining some unusual experimental results on Josephson effects in long superconducting bridges.     

Excitation of plasma oscillations during the motion of Josephson vortices in layered superconductors

The electric and magnetic fields arising during uniform motion of a vortex lattice in a magnetic field oriented parallel to the conducting layers are calculated in an exactly solvable model. For low temperatures and high velocities of the lattice, features due to the excitation of plasma oscillations of the superconducting electrons appear in the current-voltage characteristic. Peaks associated with plasmon excitation and the Cherenkov effect are present in the radiation spectrum. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 12, 811–816 (25 December 1997)     

Magnetic-field effects on the size of vortices below the surface of NbSe2 detected using low energy beta-NMR

A low energy radioactive beam of polarized 8Li has been used to observe the vortex lattice near the surface of superconducting NbSe2. The inhomogeneous magnetic-field distribution associated with the vortex lattice was measured using depth-resolved beta-detected NMR. Below Tc, one observes the characteristic line shape for a triangular vortex lattice which depends on the magnetic penetration depth and vortex core radius. The size of the vortex core varies strongly with the magnetic field. In particular, in a low field of 10.8 mT, the core radius is much larger than the coherence length. The possible origin of these giant vortices is discussed.     

Spectroscopy of magnetic excitations in magnetic superconductors using vortex motion

In magnetic superconductors a moving vortex lattice is accompanied by an ac magnetic field which leads to the generation of spin waves. At resonance conditions the dynamics of vortices in magnetic superconductors changes drastically, resulting in strong peaks in the dc I-V characteristics at voltages at which the washboard frequency of the vortex lattice matches the spin wave frequency omegaS(g), where g are the reciprocal vortex lattice vectors. We show that if the washboard frequency lies above the magnetic gap, measurement of the I-V characteristics provides a new method to obtain information on the spectrum of magnetic excitations in borocarbides and cuprate layered magnetic superconductors.     

Local magnetic probes of superconductors

Investigations of the magnetic properties of high temperature superconductors (HTSs) have revealed the existence of striking new vortex phenomena due, in part, to their strong crystalline anisotropy, very short coherence lengths and the much larger thermal energies available at high temperatures. Some of these phenomena, for example vortex lattice 'melting', pose serious problems for technological applications of the most anisotropic HTS materials and a fuller understanding of them is of considerable importance. The most direct information regarding vortex structures and dynamics is obtained through local measurement of the magnetic field within or at the surface of a superconducting sample. A detailed review of such local magnetic probes is presented here including Lorentz microscopy, magnetic force microscopy, Bitter decoration, scanning Hall probe microscopy, magneto-optical imaging, and scanning superconducting quantum interference device microscopy. In each case the principles underpinning the technique are described together with the factors that limit the magnetic field and the spatial and temporal resolution. A range of examples will be given, emphasizing applications in the area of HTSs. In addition the ways in which the existing techniques can be expected to develop over the next few years will be discussed and new approaches that seem likely to be successful described.     

On the Effect of Boundary Conditions in the Ginzburg–Landau Theory on the Results of Calculations of the Critical State of Layered Structures

The effect of boundary conditions in the Ginzburg–Landau theory on the critical state of superconducting layered structures is studied. The method is based on the numerical solution of the Ginzburg–Landau nonlinear equations describing the behavior of a superconducting plate carrying a transport current in a magnetic field, provided the absence of vortices in it. The use of the general boundary condition for the Ginzburg–Landau system of equations leads to a change in the order parameter over the thickness of thin superconducting plates. The calculated dependences of the critical current of plates on the magnetic field applied in parallel to layers are used to determine the critical current of multilayered structures. It is assumed that the mutual influence of superconducting layers occurs only through the magnetic field induced by them.     

Vortices in superconducting bulk, films and SQUIDs

The properties of the ideal periodic vortex lattice in bulk superconductors and in films of any thickness can be calculated from Ginzburg-Landau theory by an iteration method using Fourier series. The London theory yields general analytic expressions for the magnetic field and energy of arbitrary arrangements of straight or curved vortex lines. The elasticity of the vortex lattice is highly nonlocal. The magnetic response of superconductors of realistic shapes like thin and thick strips and disks or thin rectangular plates or films, containing pinned vortices, can be computed within continuum theory by solving an integral equation. A useful example is a thin square with a central hole and a radial slit, used as superconducting quantum interference device (SQUID).     

Enhancement of nonlinear properties of superconducting films in low-frequency magnetic field

The effect of enhancement of nonlinear properties of superconducting films is found in low-frequency magnetic field. Harmonic mixing of the electromagnetic radiation is detected. These results provide an argument in support of a new approach to design the active superconducting elements. A low-frequency oscillating magnetic field directed perpendicularly to the film surface forms an unstable vortex structure in the film. The frequency multiplication is intensified in the vortex unstable state. A transition of the vortex structure into the ground state synchronized by an external resonant circuit causes the generation of the electromagnetic radiation. Main advantage of these oscillators over Josephson junctions is high power emitted into a broadband system.     

Universal behavior of the upper critical field in iron-based superconductors

The newly discovered iron-based high temperature superconductors have demonstrated rich physical properties. Here we give a brief review on the recent studies of the upper critical field and its anisotropy in a few typical series of the iron-based superconductors (FeSCs). In spite of their characters of a layered crystal structure, all the FeSCs possess an extremely large upper critical field and a weak anisotropy of superconductivity, being unique among the layered superconductors. These particular properties indicate potential applications of the FeSCs in the future. Based on the experimental facts of the FeSCs, we will discuss the possible mechanisms of pair breaking in high magnetic fields and its restrictions on the theoretical analysis of the superconducting pairing mechanisms.     

Square vortex lattice at anomalously low magnetic fields in electron-doped Nd1.85Ce0.15CuO4

We report here on the first direct observations of the vortex lattice in the bulk of electron-doped Nd1.85Ce0.15CuO4 single crystals. Using small-angle neutron scattering, we have observed a square vortex lattice with the nearest neighbors oriented at 45 degrees from the Cu-O bond direction, which is consistent with theories based on the d-wave superconducting gap. However, the square symmetry persists down to unusually low magnetic fields. Moreover, the diffracted intensity from the vortex lattice is found to decrease rapidly with increasing magnetic field.     

三维介观超导环的涡旋结构

在Ginzburg-Landan理论的框架下, 运用有限差分法研究了在圆环电流产生磁场下的介观超导圆环内的涡旋结构, 讨论了超导圆环尺寸和不同空间分布的磁场对涡旋形成的影响, 得到在一般超导圆环体内的基态多是巨涡旋态、而多涡旋态多以激发态形式存在的结论, 说明磁场一般从超导圆环的环孔穿过, 而很难穿过超导圆环体.     

Current-voltage characteristics of a foamed Bi1.8Pb0.3Sr2Ca2Cu3O x high-temperature superconductor with fractal cluster structure

The influence of the structure of foamed polycrystalline bismuth-based superconductors on their critical currents and current-voltage characteristics is studied. It is found that superconducting foams have a fractal structure, and the fractal dimension of the boundary between the normal and superconducting phases is estimated. The magnetic and transport properties of superconducting foams are investigated, and the current-voltage characteristics are obtained in a wide range of currents. The effect of percolation phenomena on vortex pinning in a foamed superconductor is considered. The current-voltage characteristics of the superconducting foams at the beginning of the resistive transition are found to be in good agreement with a model in which a magnetic flux is assumed to be trapped in the fractal clusters of a normal phase.     

Transition between layered and filamentary types of anisotropy in layered superconducting structures

A model of layered superconducting structure consisting of alternating anisotropic superconducting layers S₁ and S₂ with different transition temperatures is considered. It is shown that due to competition between two origins of anisotropy - effective-mass anisotropy of individual layers and proximity-induced anisotropy the effective anisotropy of the whole system signficiantly varies temperature. The components of the effective-mass tensor m_c (along the anisotropy axis) and m_a (perpendicular to the anisotropy axis) strongly depend upon temperature. This may lead to transition between layered (m_c > m_a) and quasi one-dimensional (m_c < m_a) types of anisotropy as well as to biaxial-type anisotropy which is also temperature dependent. The field distribution in a tilted vortex in a biaxial superconductor is calculated. The change in the properties of the vortex lattice with temperature in such systems is also investigated. The properties of YBa₂Cu₃O_x/PrBa₂Cu₃O_y multilayers are discussed in this connection.     

The phase diagram of the superconducting state of superconductor-band-antiferromagnet superlattices

The formation of the superconducting phase in short-period proximity-effect layered superlattices of the superconductor-band-antiferromagnetic-metal (SC/AF) type is studied. The exact solution of the Usadel equations is used to discuss the possibility of formation in such structures of a ground state in which the order parameters of the adjacent superconducting layers have opposite signs (the “π-phase”). The dependence of the superconducting transition temperature and the upper critical field normal to the layers on the lattice period, the intensity of magnetic interaction in the antiferromagnetic layer, and the state of the interface between the layers is examined. It is found that there exists a nonlinear dependence of the conditions for the appearance of the superconducting state in a layered SC/AF system on the system’s parameters. Finally, the conditions for the appearance of the superconducting phase in proximity-effect superlattices consisting of a superconductor with nonmagnetic, ferromagnetic, and antiferromagnetic metals are compared. Zh. éksp. Teor. Fiz. 111, 547–561 (February 1997)     

Relaxation of the magnetic state of a ferromagnetic–superconducting layered structure

We have proposed a real-time method of neutron reflectometry. The magnetic state of the Ta/V/FM/Nb/Si ferromagnetic–superconducting system has been analyzed. Relaxation of the inhomogeneous magnetic state with a characteristic time of several hours, which depends on the magnetic field magnitude and temperature, has been observed. The relaxation of the domain structure has changed upon a transition of the V and Nb layers to the superconducting state. It has been concluded that real-time reflectometry data for polarized neutrons are important for determining the origin of magnetism in ferromagnetic–superconducting layered structures.