In this letter, we describe quantitative magnetic imaging of superconducting vortices in RbEuFe$_4$As$_4$ in order to investigate the unique interplay between the magnetic and superconducting sublattices. Our scanning Hall microscopy data reveal a pr
onounced suppression of the superfluid density near the magnetic ordering temperature in good qualitative agreement with a recently-developed model describing the suppression of superconductivity by correlated magnetic fluctuations. These results indicate a pronounced exchange interaction between the superconducting and magnetic subsystems in RbEuFetextsubscript{4}Astextsubscript{4} with important implications for future investigations of physical phenomena arising from the interplay between them.
The iron-based superconductors are characterized by strong fluctuations due to high transition temperatures and small coherence lengths. We investigate fluctuation behavior in the magnetic iron-pnictide superconductor $mathrm{Rb}mathrm{Eu}mathrm{Fe}_
{4}mathrm{As}_{4}$ by calorimetry and transport. We find that the broadening of the specific-heat transition in magnetic fields is very well described by the lowest-Landau-level scaling. We report calorimetric and transport observations for vortex-lattice melting, which is seen as a sharp drop of the resistivity and a step of the specific heat at the magnetic-field-dependent temperature. The melting line in the temperature/magnetic-field plane lies noticeably below the upper-critical-field line and its location is in quantitative agreement with theoretical predictions without fitting parameters. Finally, we compare the melting behavior of $mathrm{Rb}mathrm{Eu}mathrm{Fe}_{4}mathrm{As}_{4}$ with other superconducting materials showing that thermal fluctuations of vortices are not as prevalent as in the high-temperature superconducting cuprates, yet they still noticeably influence the properties of the vortex matter.
We present a study of the upper critical field, H$_{c2}$, of pristine and proton-irradiated RbEuFe$_4$As$_4$ crystals in pulsed magnetic fields of up to 65 T. The data for H$_{c2}$ reveal pronounced downwards curvature, particularly for the in-plane
field orientation, and a superconducting anisotropy that decreases with decreasing temperature. These features are indicative of Pauli paramagnetic limiting. For the interpretation of these data, we use a model of a clean single-band superconductor with an open Fermi surface in the shape of a warped cylinder, which includes strong paramagnetic limiting. Fits to the data reveal that the in-plane upper critical field is Pauli paramagnetic limited, while the out-of-plane upper critical field is orbitally limited and that the orbital and paramagnetic fields have opposite anisotropies. A consequence of this particular combination is the unusual inversion of the anisotropy, $H_{c2}^{ab} < H_{c2}^c$, of the irradiated sample at temperatures below 10 K. The fits also yield an in-plane Maki parameter, $alpha_M^{110} approx$ 2.6, exceeding the critical value for the formation of the Fulde-Ferrell-Larkin-Ovchinnikov state. Nevertheless, the current measurements did not reveal direct evidence for the occurrence of this state.
We show on a few examples of one-band materials with spheroidal Fermi surfaces and anisotropic order parameters that anisotropies $gamma_H$ of the upper critical field and $gamma_lambda$ of the London penetration depth depend on temperature, the feat
ure commonly attributed to multi-band superconductors. The parameters $gamma_H$ and $gamma_lambda$ may have opposite temperature dependencies or may change in the same direction depending on Fermi surface shape and on character of the gap nodes. For two-band systems, the behavior of anisotropies is affected by the ratios of bands densities of states, Fermi velocities, anisotropies, and order parameters. We investigate in detail the conditions determining the directions of temperature dependences of the two anisotropy factors.
We report an unusual enhancement of the magnetic induction in single crystals of the magnetic superconductor RbEuFe$_4$As$_4$ , highlighting the interplay between superconducting and magnetic subsystems in this material. Contrary to the conventional
Meissner expulsion of magnetic flux below the superconducting transition temperature, we observe a substantial boost of the magnetic flux density upon approaching the magnetic transition temperature, Tm. Direct imaging of the flux evolution with a magneto-optical technique, shows that the magnetic subsystem serves as an internal magnetic flux pump, drawing Abrikosov vortices from the surface, while the superconducting subsystem controls their conveyance into the bulk of the magnetic superconductor via a peculiar self-organized critical state.
The current-carrying capacity of type-II superconductors is decisively determined by how well material defect structures can immobilize vortex lines. In order to gain deeper insights into the fundamental pinning mechanisms, we have explored the case
of vortex trapping by randomly distributed spherical inclusions using large-scale simulations of the time-dependent Ginzburg-Landau equations. We find that for a small density of particles having diameters of two coherence lengths, the vortex lattice preserves its structure and the critical current $j_c$ decays with the magnetic field following a power-law $B^{-alpha}$ with $alpha approx 0.66$, which is consistent with predictions of strong-pinning theory. For a higher density of particles and/or larger inclusions, the lattice becomes progressively more disordered and the exponent smoothly decreases down to $alpha approx 0.3$. At high magnetic fields, all inclusions capture a vortex and the critical current decays faster than $B^{-1}$ as would be expected by theory. In the case of larger inclusions with a diameter of four coherence length, the magnetic-field dependence of the critical current is strongly affected by the ability of inclusions to capture multiple vortex lines. We found that at small densities, the fraction of inclusions trapping two vortex lines rapidly grows within narrow field range leading to a peak in $j_c(B)$-dependence within this range. With increasing inclusion density, this peak transforms into a plateau, which then smooths out. Using the insights gained from simulations, we determine the limits of applicability of strong-pinning theory and provide different routes to describe vortex pinning beyond those bounds.
The ability of high-temperature superconductors (HTSs) to carry very large currents with almost no dissipation makes them irreplaceable for high-power applications. The development and further improvement of HTS-based cables requires an in-depth unde
rstanding of the superconducting vortex dynamics in presence of complex pinning landscapes. We present a critical current analysis of a real HTS sample in a magnetic field by combining state-of-the-art large-scale Ginzburg-Landau simulations with reconstructive three-dimensional scanning transmission electron microscopy tomography of the pinning landscape in Dy-doped YBa$_2$Cu$_3$O$_{7-delta}$. This methodology provides a unique look at the vortex dynamics in the presence of a complex pinning landscape, responsible for the high current-carrying capacity characteristic of commercial HTS wires. Our method demonstrates very good functional and quantitative agreement of the critical current between simulation and experiment, providing a new predictive tool for HTS wires design.
Introducing nanoparticles into superconducting materials has emerged as an efficient route to enhance their current-carrying capability. We address the problem of optimizing vortex pinning landscape for randomly distributed metallic spherical inclusi
ons using large-scale numerical simulations of time-dependent Ginzburg-Landau equations. We found the size and density of particles for which the highest critical current is realized in a fixed magnetic field. For each particle size and magnetic field, the critical current reaches a maximum value at a certain particle density, which typically corresponds to 15-23% of the total volume being replaced by nonsuperconducting material. For fixed diameter, this optimal particle density increases with the magnetic field. Moreover, we found that the optimal particle diameter slowly decreases with the magnetic field from 4.5 to 2.5 coherence lengths at a given temperature. This result shows that pinning landscapes have to be designed for specific applications taking into account relevant magnetic field scales.
Understanding the interaction of vortices with inclusions in type-II superconductors is a major outstanding challenge both for fundamental science and energy applications. At application-relevant scales, the long-range interactions between a dense co
nfiguration of vortices and the dependence of their behavior on external parameters, such as temperature and an applied magnetic field, are all important to the net response of the superconductor. Capturing these features, in general, precludes analytical description of vortex dynamics and has also made numerical simulation prohibitively expensive. Here we report on a highly optimized iterative implicit solver for the time-dependent Ginzburg-Landau equations suitable for investigations of type-II superconductors on massively parallel architectures. Its main purpose is to study vortex dynamics in disordered or geometrically confined mesoscopic systems. In this work, we present the discretization and time integration scheme in detail for two types of boundary conditions. We describe the necessary conditions for a stable and physically accurate integration of the equations of motion. Using an inclusion pattern generator, we can simulate complex pinning landscapes and the effect of geometric confinement. We show that our algorithm, implemented on a GPU, can provide static and dynamic solutions of the Ginzburg-Landau equations for mesoscopically large systems over thousands of time steps in a matter of hours. Using our formulation, studying scientifically-relevant problems is a computationally reasonable task.
We consider the behaviour of the fluctuating specific heat and conductivity in the vicinity of the upper critical field line for a two-band superconductor. Multiple-band effects are pronounced when the bands have very different coherence lengths. The
transition to superconductive state is mainly determined by the properties of the rigid condensate of the strong band, while the weak band with a large coherence length of the Cooper pairs causes the nonlocality in fluctuation behaviour and break down of the simple Ginzburg-Landau picture. As expected, the multiple-band electronic structure does not change the functional forms of dominating divergencies of the fluctuating corrections when the magnetic field approaches the upper critical field. The temperature dependence of the coefficients, however, is modified. The large in-plane coherence length sets the field scale at which the upper critical field has upward curvature. The amplitude of fluctuations and fluctuation width enhances at this field scale due to reduction of the effective z-axis coherence length. We also observe that the apparent transport transition displaces to lower temperatures with respect to the thermodynamic transition. Even though this effect exists already in a single-band case at sufficiently high fields, it may be strongly enhanced in multiband materials.
