The detailed investigation of a superconducting spin-triplet valve is presented. This spin valve consists of a superconducting film covering a metal with intrinsic spiral magnetic order, which may be the result of a competitive exchange or of an asymmetric Dzyaloshinsky-Moriya exchange following from the central symmetry breaking of the crystal lattice. Depending on the anisotropy, this metal may change its magnetization either from a spiral to uniform order, as in Ho and Er, or in the direction of the spiral itself, as in B20 family crystals. Very recently, a new way of controlling the superconducting spin valve has been developed: the change of the magnetic order may also be triggered by magnonic relaxation processes, thus merging superconducting spintronics and magnonics. The nonuniform magnetic order controls the appearance of long-range triplet superconducting correlations (LRTC), which change the conditions of the proximity effect, enabling an external magnetic control of the superconducting critical temperature. We show that magnetic control of the spin-valve behavior can also be obtained for moderately low exchange energies thanks to an orientation-dependent averaging mechanism of the magnetic inhomogeneity on the scale of the Cooper pairs. The competition between these two mechanisms yields different behaviors of the spin-valve effect. Our numerical calculations show that at low exchange fields (as in MnSi) the spin valve effect may be quite significant. They suggest the switching behavior of the superconducting spin valve to be better optimized for B20 family compounds allowing magnonic control.

Transport properties of bulk indium-opal and indium-porous glass superconducting nanocomposites possessing moderate and strong disorder are investigated. A strongly nonmonotonous dependence of the global critical temperature T-c versus normal state conductivity of samples is found. The maximum, which is observed at moderate disorder, has T-c higher than that of clean bulk indium. The increasing part can be explained by the Eliashberg equations with disorder and an additional mechanism of interaction between superconducting and dielectric granules. The descending part of the maximum at higher disorder can be explained by the increasing of long-range Coulomb repulsion due to diffusion of charges. Negative slope in magnetic field dependence of resistivity and a peak in the temperature dependence of resistivity, observed in the sample near the proximity to the disorder-induced superconductor-insulator transition (SIT). A large difference between the onset temperature of superconducting fluctuations, T-c(on) and global critical temperature T-c is found and considered in the framework of the weak multifractal theory. Slow time-logarithmic relaxation of the resistivity between T-c and T-c(on) is observed, which assumes existence of the precursor state near the SIT. This unusual state is discussed in the scope of the many-body localization theory.

We propose a superconducting spin-triplet valve, which consists of a superconductor and an itinerant magnetic material, with the magnet showing an intrinsic non-collinear order characterized by a wave vector that may be aligned in a few equivalent preferred directions under control of a weak external magnetic field. Re-orienting the spiral direction allows one to controllably modify long-range spin-triplet superconducting correlations, leading to spin-valve switching behavior. Our results indicate that the spin-valve effect may be noticeable. This bilayer may be used as a magnetic memory element for cryogenic nanoelectronics. It has the following advantages in comparison to superconducting spin valves proposed previously: (i) it contains only one magnetic layer, which may be more easily fabricated and controlled, (ii) its ground states are separated by a potential barrier, which solves the "half-select" problem of the addressed switch of memory elements.

A finite-size scaling of the nanoscale magnetization m on size averaging R of a single vortex in d-wave bulk superconductor is developed using quasiclassical Eilenberger equations. Nanoscaling is anchoring around the linear London approximation for bulk superconductors. Comparing the results with those obtained in local nonlinear approach demonstrated the importance of the nonlocal contribution. Temperature dependences of two-point correlation function chi(T, R1, R2) - m (T, R2)/m (0, R2) - (T, R1)/m (0, R1) with R2 > R1 and one-point function chi(T, R1 -> infinity, R2) are calculated. It is found that.(T, R1, R ), R2 > R1, is a nonmonotonous function of temperature and changes sign at high temperatures. This nonmonotonous temperature dependence can be understood as a result of competition between various effects i) Volovik effect and nonlocal corrections to superconducting electron density dominating in low temperature range, and ii) current-induced suppression of the order parameter dominating at high temperatures. The introduced nonmagnetic disorder greatly suppresses the low temperature nonlocal and nonlinear effects, leaving the order parameter effects to prevail in the whole temperature range. Nonlocal pairing and tunneling effects are investigated at the superconductor-normal metal border by considering a d-wave superconducting dot (d-dot) inside a normal diffusive metal. These effects result in a suppression of the supercurrent in the vortex core and are essential in nanodots with relatively small sizes. At sizes larger than a temperature dependent characteristic length the nanoscale physics transforms into bulk solution. (C) 2016 Elsevier B.V. All rights reserved.

Temperature dependence of single vortex magnetic moment in nanosize superconducting particles is investigated in the framework of quasiclassical Eilenberger approach. Such nanoparticles can be used for preparation of high-quality superconducting thin films with high critical current density. In contrast to bulk materials where the vortex magnetic moment is totally determined by flux quantum, in nano-sized specimens (with characteristic size, D, much less than effective penetration depth, lambda(eff)) the quantization rule is violated and magnetic moment is proportional to D-2/lambda(2)(eff)(T). Due to strong repulsion between vortices in nanoparticles only a single vortex can be trapped in them. Because of small size of particles the screening current of the vortex is located near the vortex core where the current is quite high and comparable to depairing currents. Therefore, the superconducting electron density, n(s) depends on the current value and the distance from the vortex core. This effect is especially important for superconductors having gap nodes, such as YBCO.The current dependence of n(s) in nanoparticles is analogous to the Volovik effect in flux-line lattice in bulk samples. The magnitude of the effect can be obtained by comparing the temperature dependence of magnetic moment in the vortex and in the Meissner states. In the last case the value of screening current is small and superconducting response to the external field is determined by London penetration depth. Because of importance of nonlinear and nonlocal effects, the quantum mechanical Eilenberger approach is applied for description of the vortex in nanoparticles. The flattening of 1/lambda(2)(eff)(T) dependence has been found. A comparison of the theoretical results with experimental magnetization data in Meissner and mixed states of YBCO nanopowders has been done. The presence of nonlinear and nonlocal effects in vortex current distribution is clearly visible. The obtained results are important for the description of pining in nanostructured high-T-c thin films.

Influence of the order parameter symmetries on the cutoff parameter ξh and vortex core size ξ2 (the distance from the vortex center at which the current density reaches the maximum value) in the mixed state are investigated in the framework of Eilenberger theory for unconventional superconductors. The cutoff parameter determines the field distribution in the generalized London equation obtained as a projection of the quasiclassical theory. It is used for the fitting of the μSR and small-angle neutron scattering experimental data. Anisotropic dx2−y2 and isotropic s±-wave superconducting pairings are studied. These pairing symmetries can be realized in iron pnictide superconductors. Conventional s++ pairing mediated electron-phonon interaction is also considered. Temperature, field, and impurity scattering dependences of ξh/ξc2 are obtained. It is found that normalized ξ2/ξc2(B/Bc2) dependence is increasing with pair breaking impurity scattering (interband scattering for s±-wave and intraband impurity scattering for d-wave superconductors). Here, ξc2 is the Ginzburg-Landau coherence length determined from the relation Bc2=Φ0/2πξc22, where Bc2 is an upper critical field and Φ0 is a flux quantum. Two types of ξ2/ξc2(B/Bc2) dependences are obtained for s± superconductors. It has minimum at low temperatures and small impurity scattering transforming in monotonously decreasing function at strong scattering and high temperatures. The second kind of this dependence was also found for d-wave superconductors at intermediate and high temperatures. In contrast, impurity scattering results in decreasing of ξ2/ξc2 field dependence in s++ superconductors.

The generalized London equation in the mixed state of high-κ s-wave pairing superconductors with impurities is considered as a projection of the quasiclassical nonlocal nonlinear Eilenberger theory. Only one fitting parameter – the cutoff parameter ξh – is used in the theory. The distribution of the magnetic field is calculated self-consistently. Both nonlocal effects originated from extended states between the vortices and bound Andreev states in the vortex are taken into account. Comparison with different analytical nonlocal linear approaches (the Kogan–Gurevich, Amin–Franz–Affleck, Kogan–Zhelezina models) including only extended states is done. The importance of the Kramer–Pesch nonlinear effect and the field dependence of the cutoff parameter is emphasized and their strong influence on the variance of the magnetic field is found. The influence of the impurities on the ratio of the cutoff parameter ξh and the Ginzburg–Landau coherence length ξc2 is considered. Quasiparticle scattering by impurities and lowering of the temperature reduces the value of ξh to the values much less than ξc2. This is different from the prediction of the local Ginzburg–Landau theory where ξh is scaled by ξc2. It is found that impurities influence by different way on the cutoff parameter ξh and the order parameter coherence length ξ1. The ξh decreases monotonously with the impurity scattering time in contrast to the nonmonotonous behavior of ξ1. The results can be used for analysis of the μSR experimental data.

The effects of the pairing symmetries (s(+/-) and s(++)) on the cutoff parameter of field distribution, xi(h), in stoichiometric (like LiFeAs) and nonstoichiometric (like doped BaFe2As2) iron pnictides have been investigated using Eilenberger quasiclassical equations. Magnetic field, temperature, and impurity scattering dependencies of xi(h) have been calculated. Two opposite behaviors have been discovered. The xi(h)/xi(c2) ratio is less in s(+/-) symmetry when the intraband impurity scattering (Gamma(0)) is much larger than 1 and is much larger than the interband impurity scattering (Gamma(pi)), i.e., in nonstoichiometric iron pnictides. In contrast, the value xi(h)/xi(c2) is higher in the s(+/-) case and the field-dependent curve is shifted upward from the "clean" case (Gamma(0) = Gamma(pi) = 0) for stoichiometric iron pnictides (Gamma(0) = Gamma(pi) << 1). Results can be tested in muon spin rotation measurements.

Quasiclassical Eilenberger equations are solved for s±-wave superconductors in the mixed state. This symmetry has been proposed for multiband superconductors as pnictides. This mechanism can be realized because of Umklapp scattering between the electron and the hole Fermi surface pockets resulting in opposite sign of pairing gap in these pockets. The applicability of the phenomenological Hao-Clem theory is investigated. Magnetic, temperature and impurity scattering rate dependencies of vortex core size are calculated. It is found that the accuracy of the effective London model gets better with the presence of the impurity scattering and even near the second critical field it is below 6%. The model with the parameters of intraband and interband impurity scattering, describing well superfluid density in BaFe2As2, is also considered.

Hall effect and flux pinning in YBa2Cu3O6+x (YBCO) thin films doped with BaZrO3 (BZO) nanoparticles is investigated. The results show that sign reversal of the Hall coefficient from positive hole-like to negative electron-like occurs in vortex-liquid regime of undoped and BZO-doped YBCO films. With increasing BZO concentration the amplitude of the negative Hall effect is suppressed while the temperature position of the anomalous Hall effect does not depend significantly on doping level. In addition, it is shown that Hall conductivity increases non-monotonically with increasing BZO doping. These results support a model where BZO at low doping concentration induces point pinning centres turning to strong columnar pinning defects in films doped with 4% BZO. (c) 2009 Elsevier B.V. All rights reserved.

The resistivity of YBa2Cu3O7-delta (YBCO) films deposited by a pulsed laser from nanograined targets doped with various amounts of BaZrO3 (BZO) is investigated in the thermally activated flux-flow (TAFF) regime, where the activation energy, U, has a linear temperature dependence. It is found that the magnetic field dependence of the irreversibility temperature, T-irr(B), has a maximum at some optimal BZO concentration, which depends on the applied magnetic field. Our results show that the superconducting materials used in different magnetic fields need optimization of the dopant concentration to achieve the best properties for various applications.

Hall effect and flux pinning in YBa2Cu3O6+x (YBCO) thin films doped with BaZrO3 (BZO) nanoparticles is investigated. The results show that sign reversal of the Hall coefficient from positive hole-like to negative electron-like occurs in vortex-liquid regime of undoped and BZO-doped YBCO films. With increasing BZO concentration the amplitude of the negative Hall effect is suppressed while the temperature position of the anomalous Hall effect does not depend significantly on doping level. In addition, it is shown that Hall conductivity increases non-monotonically with increasing BZO doping. These results support a model where BZO at low doping concentration induces point pinning centres turning to strong columnar pinning defects in films doped with 4% BZO.

Influence of impurities on coherence length xi(h) in the mixed state of 8-wave superconductors is investigated in framework of quasiclassical Eilenberger theory. The increasing of impurity scattering rate results in decreasing of The obtained field dependence of xi(h) for clean superconductors has a minimum and it is similar to that in Hao-Clem and Miranovie-Ichioka-Machida theories for order parameter of coherence length. It is found that growing behavior of xi(h) with magnetic field in dirty superconductors is different from order parameter coherence length determining by pairing potential near with vortex core. The magnetic field dependence of coherence length in normalized units, xi(h)/xi(c2)(B/B-c2), is nonuniversal and depends on impurity scattering potential.

Angular dependence of the resistivity, the irreversibility field and the critical current of undoped and BaZrO3-(BZO)-doped YBa2Cu3O6+x (YBCO) thin films are investigated using pulsed magnetic fields up to 30T. Doping with BZO forms a dense network of anisotropic c-axis oriented columnar defects, which lead, in comparison with undoped material, to clearly improved values of the pinning potential, the critical current density and the irreversibility field in the whole angular range. The results are explained by point defect scaling theory using a renormalized anisotropy parameter in connection with linear defects. In oblique magnetic field a porous vortex matter is formed by means of kinks on the columnar defects. Our results demonstrate the efficiency of the columnar defects in thin YBCO films in magnetic fields much above the matching field, opening up a possibility to use this material in various high field applications.

Transport properties of YBa2Cu3O6+x films prepared by pulsed laser deposition from pure and BaZrO3- (BZO-)doped nanocrystalline targets and from a microcrystalline target are investigated in pulsed magnetic fields up to 30 T. As shown by transmission electron microscopy, doping by BZO creates columnar defects of diameter 5-10 nm traversing the films in the direction of the c axis. The irreversibility line, the delocalization line, and the high-field critical current density j(c) are strongly enhanced in the films deposited from a nanocrystalline target in comparison with those deposited from the microcrystalline target. Doping with BZO further improves the irreversibility and depinning lines and increases the value of j(c). The irreversibility fields of the films prepared from the pure and from the BZO-doped nanocrystalline targets exceed 10 T at 77 K, and at 65 K the value of j(c)approximate to 10(5) A/cm(2) is observed in fields up to 22 T.

The problem of transformation of the quasiclassical Eilenberger theory to the one-parameter London model is considered for the mixed state of clean type-II superconductors. Numerical computations demonstrate that introduction of a field dependent coherence length xi(h)(B) is enough for description of the magnetic field distribution in the vortex core of a superconductor. It is found that the shape of xi(h)(B) has strong temperature dependence. The comparison between s- and d-wave pairing symmetry is done. Different behavior of xi(h)(B) in triangular and square vortex lattices is found.

Transport properties of $\mathrm{Y}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6+x}$ films prepared by pulsed laser deposition from pure and $\mathrm{Ba}\mathrm{Zr}{\mathrm{O}}_{3}$- (BZO-)doped nanocrystalline targets and from a microcrystalline target are investigated in pulsed magnetic fields up to $30\phantom{\rule{0.3em}{0ex}}\mathrm{T}$. As shown by transmission electron microscopy, doping by BZO creates columnar defects of diameter $5--10\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ traversing the films in the direction of the $c$ axis. The irreversibility line, the delocalization line, and the high-field critical current density ${j}_{\mathrm{c}}$ are strongly enhanced in the films deposited from a nanocrystalline target in comparison with those deposited from the microcrystalline target. Doping with BZO further improves the irreversibility and depinning lines and increases the value of ${j}_{\mathrm{c}}$. The irreversibility fields of the films prepared from the pure and from the BZO-doped nanocrystalline targets exceed $10\phantom{\rule{0.3em}{0ex}}\mathrm{T}$ at $77\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, and at $65\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ the value of ${j}_{\mathrm{c}}\ensuremath{\approx}{10}^{5}\phantom{\rule{0.3em}{0ex}}\mathrm{A}∕{\mathrm{cm}}^{2}$ is observed in fields up to $22\phantom{\rule{0.3em}{0ex}}\mathrm{T}$.

We extend the Ginsburg-Landau solution for cutoff function in London equation to low temperatures by solving numerically the quasiclassical Eilenberger equations in mixed state of s-wave superconductors. As a result the nonlocal generalized London equation (NGLE) is obtained. The magnetic field and temperature dependence of the cutoff function parameter k(1)(B,T) are calculated. Due to Kramer-Pesch effect k(1) decreases strongly at low temperatures. It is also found that k(1) has a minimum at a value of magnetic field depending on temperature. We reduce the NGLE model to an effective local model and calculate the value of an effective penetration depth lambda(eff)(B,T). The sublinear field dependence of lambda(eff) is predicted that agrees with experimental mu SR results for the penetration depth of magnetic field in the s-wave superconductor V3Si and NbSe2.

Dependence of the critical current on applied magnetic field ${j}_{c}({B}_{a})$ is investigated in ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6+x}$ (YBCO) films prepared by pulsed laser deposition from pure YBCO target and from those doped with 2.9 or $9.0\phantom{\rule{0.3em}{0ex}}\mathrm{wt}.\phantom{\rule{0.2em}{0ex}}%$ ${\mathrm{BaZrO}}_{3}$. All targets were sintered from nanophase powders made by a citrate-gel process. Transmission electron microscopy images show distributions of ${\mathrm{BaZrO}}_{3}$ particles with typical diameters of $5\char21{}10\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ in the doped films. In comparison with the pure YBCO film the value of ${j}_{c}(0)$ is slightly smaller in the film deposited from the target doped with $2.9\phantom{\rule{0.3em}{0ex}}\mathrm{wt}.\phantom{\rule{0.2em}{0ex}}%$ ${\mathrm{BaZrO}}_{3}$ and only half in case of $9.0\phantom{\rule{0.3em}{0ex}}\mathrm{wt}.\phantom{\rule{0.2em}{0ex}}%$ doping. Two interesting phenomena in the behavior of ${j}_{c}({B}_{a})$ are observed for the doped films. First, the low-field plateau of ${j}_{c}$ is significantly lengthened and second, in fields above the accommodation field ${B}^{*}$ marking the end of this plateau the rate of decrease of ${j}_{c}$ is strongly reduced. These results are well fitted with a critical state model of superconductors taking into account the self field effects at low applied magnetic fields.

The cutoff function of the nonlocal generalized London equation (NGLE) describing the mixed state in a d-wave superconductor is found from comparison with a numerically obtained solution of the quasiclassical Eilenberger equations. A good agreement between these models is reached if the argument of the cutoff function of NGLE is taken to be temperature and field dependent, decreasing strongly at low temperatures. At high temperatures the field dependence of this argument is nonmonotonic and shows a minimum at a field which depends on the temperature. This result agrees with the prediction of the Hao-Clem theory.