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 report detailed specific heat measurements on the recently discovered magnetic superconductor RbEuFe$_4$As$_4$. We investigated the superconducting transition at 37K and extract the phase boundary for in and out-of plane fields resulting in an ani
sotropy ratio of 1.8. An unusual cusp-like feature in the calorimetric data near 14.9K marks the onset of a magnetic phase. Studying the effect of small fields along the crystallographic $c$ axis, we resolve a shift in the cusp position moving to lower temperatures. For in-plane fields the cusp rapidly disappears and a broad shoulder that shifts to higher temperatures. We are able to reproduce our measured calorimetry data quantitatively by Monte-Carlo simulations of an anisotropic easy-plane 2D Heisenberg model. We can thus show that (i) the spins are preferably in plane, (ii) the cusp in specific heat is due to a Berezinskii-Kosterlitz-Thouless (BKT) transition, and (iii) the high-temperature hump in higher fields marks a crossover from a paramagnetically disordered to an ordered state. The extracted phase and crossover boundaries from experiment and simulations agree very well.
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.
Type-II superconductors owe their magnetic and transport properties to vortex pinning, the immobilization of flux quanta through material inhomogeneities or defects. Characterizing the potential energy landscape for vortices, the pinning landscape (o
r short, pinscape), is of great technological importance. Besides measurement of the critical current density $j_c$ and of creep rates $S$, the $ac$ magnetic response provides valuable information on the pinscape which is different from that obtained through $j_c$ or $S$, with the Campbell penetration depth $lambda_{rm scriptscriptstyle C}$ defining a characteristic quantity well accessible in an experiment. Here, we derive a microscopic expression for the Campbell penetration depth $lambda_{rm scriptscriptstyle C}$ using strong pinning theory. Our results explain the dependence of $lambda_{rm scriptscriptstyle C}$ on the state preparation of the vortex system and the appearance of hysteretic response. Analyzing different pinning models, metallic or insulating inclusions as well as $delta T_c$- and $delta ell$-pinning, we discuss the behavior of the Campbell length for different vortex state preparations within the phenomenological $H$-$T$ phase diagram and compare our results with recent experiments.
