Local reorganisation of the intermediate mixed state in niobium below the critical depinning current

Brems X.S., Mühlbauer S., Cubitt R.

Small-angle neutron scattering is a widely used technique to study large-scale structures in bulk samples. The largest accessible length scale in conventional Bragg scattering is determined by the combination of the longest available neutron wavelength and smallest resolvable scattering angle. A method is presented that circumvents this limitation and is able to extract larger length scales from the low-q power-law scattering using a modification of the well known Porod law connecting the scattered intensity of randomly distributed objects to their specific surface area. It is shown that in the special case of a highly aligned domain structure the specific surface area extracted from the modified Porod law can be used to determine specific length scales of the domain structure. The analysis method is applied to study the micrometre-sized domain structure found in the intermediate mixed state of the superconductor niobium. The analysis approach allows the range of accessible length scales to be extended from 1 µm to up to 40 µm using a conventional small-angle neutron scattering setup.

Marychev P.M., Shanenko A.A., Vagov A.V.

Nonmagnetic impurity scattering is known to shift up the Ginzburg–Landau parameter κ of a superconductor. In this case, when the system is initially in type I, it can change its magnetic response, crossing the intertype domain with κ ∼ 1 between the two standard superconductivity types and arriving at type II. In the present work we demonstrate that the impact of disorder can be much more profound in the presence of the multiband structure of the charge carrier states. In particular, when the band diffusivities differ from each other, the intertype domain tends to expand significantly, including points with κ ≫ 1 that belong to deep type-II in conventional single-band superconductors. Our finding sheds light on the nontrivial disorder effect and significantly complements earlier results on the enlargement of the intertype domain in clean multiband superconductors.

Vagov A., Saraiva T.T., Shanenko A.A., Vasenko A.S., Aguiar J.A., Stolyarov V.S., Roditchev D.

AbstractIn many pnictides the superconductivity coexists with ferromagnetism in an accessible range of temperatures and compositions. Recent experiments revealed that when the temperature of magnetic ordering Tm is below the superconducting transition temperature Tc, highly non-trivial physical phenomena occur. In this work we demonstrate the existence of a temperature window, situated between Tm and Tc, where these intrinsically type-II superconductors are in the intertype regime. We explore analytically and numerically its rich phase diagram characterized by exotic spatial flux configurations—vortex clusters, chains, giant vortices and vortex liquid droplets—which are absent in both type-I and type-II bulk superconductors. We find that the intertype regime is almost independent of microscopic parameters, and can be achieved by simply varying the temperature. This opens the route for experimental studies of the intertype superconductivity scarcely investigated to date.

Backs A., Al-Falou A., Vagov A., Böni P., Mühlbauer S.

In the vicinity of the type-I/type-II crossover in conventional superconductors, vortices exhibit a nonmonotonic interaction, which leads to exotic vortex matter states. We perform molecular dynamics simulations on a model superconductor in the intertype regime. In a field cooled approach, we examine the transition of a homogeneous vortex lattice (VL) into a structure consisting of VL domains and Meissner-state domains. The results show extraordinary stability of the transition against vortex pinning and a strong dependence on the external magnetic field.

Reichhardt C., Regev I., Dahmen K., Okuma S., Reichhardt C.J.

Reversible to irreversible (R-IR) transitions have been found in a wide variety of both soft and hard matter periodically driven collectively interacting systems that, after a certain number of driving cycles, organize into either a reversible state where the particle trajectories repeat during every or every few cycles or into a chaotic motion state. An overview of R-IR transitions including recent advances in the field is followed by a discussion of how the general framework of R-IR transitions could be applied to a much broader class of nonequilibrium systems in which periodic driving occurs, including not only soft and hard condensed matter systems, but also astrophysics, biological systems, and social systems.

Campillo E., Bartkowiak M., Prokhnenko O., Smeibidl P., Forgan E.M., Blackburn E.

Bragg diffracted intensities and q values for crystalline structures with long repeat distances may be obtained by small-angle neutron scattering (SANS) investigations. An account is given of the methods, advantages and disadvantages of obtaining such data by the multichromatic time-of-flight method, compared with the more traditional quasi-monochromatic SANS method. This is illustrated with data obtained from high-magnetic-field measurements on magnetic vortex line lattices in superconductors on the former HFM/EXED instrument at Helmholtz-Zentrum Berlin. The methods have application to other mesoscopic crystalline structures investigated by SANS instruments at pulsed sources.

Maegochi S., Ienaga K., Okuma S.

Out-of-equilibrium systems exhibit various dynamic phases with different degrees of order. A moving smectic phase with transverse periodicity is one of the ordered states, which is theoretically expected to be generic to driven two-dimensional systems. However, a comprehensive dynamic phase diagram, including the moving smectic phase, has not been obtained because of lack of suitable experimental methods. Here we study dynamic phases of driven vortex matter in an amorphous ${\mathrm{Mo}}_{x}{\mathrm{Ge}}_{1\ensuremath{-}x}$ film by using two-step measurements of transient voltage in response to mutually perpendicular driving currents. We find dynamic orderings from the plastic flow to the anisotropic smectic flow and from the anisotropic smectic flow to the isotropic moving Bragg glass as a function of the current. Convincing evidence of the moving smectic phase is obtained from the first transverse mode locking (ML) with signals larger than those of longitudinal ML, indicating the higher transverse order than the longitudinal one. Transverse ML developed here is useful to detect the anisotropic periodicity in driven media.

Brems X.S., Mühlbauer S., Córdoba-Camacho W.Y., Shanenko A.A., Vagov A., Albino Aguiar J., Cubitt R.

Abstract Small-angle neutron scattering is used in combination with transport measurements to investigate the current-induced effects on the morphology of the intermediate mixed state (IMS) domains in the intertype superconductor niobium. We report the robust self-organisation of the vortex lattice domains to elongated parallel stripes perpendicular to the applied current in a steady-state. The experimental results for the formation of the superstructure are supported by theoretical calculations, which highlight important details of the vortex matter evolution. The investigation demonstrates a mechanism of a spontaneous pattern formation that is closely related to the universal physics governing the IMS in low-κ superconductors.

Wang W., Díaz-Méndez R., Wallin M., Lidmar J., Babaev E.

We study numerically the glass formation and depinning transition of a system of two-dimensional cluster-forming monodisperse particles in presence of pinning disorder. The pairwise interaction potential is nonmonotonic, and is motivated by the intervortex forces in type-$1.5$ superconductors. Such systems can form cluster glasses due to the intervortex interactions following a thermal quench, without underlying disorder. We study the effects of vortex pinning in these systems. We find that a small density of pinning centers of moderate depth has limited effect on vortex glass formation, i.e., formation of vortex glasses is dominated by intervortex interactions. At higher densities pinning can significantly affect glass formation. The cluster glass depinning, under a constant driving force, is found to be plastic, with features distinct from non-cluster-forming systems such as clusters merging and breaking. We find that in general vortices with cluster-forming interaction forces can exhibit stronger pinning effects than regular vortices.

Maegochi S., Ienaga K., Okuma S.

Random assemblies of particles subjected to cyclic shear undergo a reversible–irreversible transition (RIT) with increasing a shear amplitude d or particle density n, while the latter type of RIT has not been verified experimentally. Here, we measure the time-dependent velocity of cyclically sheared vortices and observe the critical behavior of RIT driven by vortex density B as well as d. At the critical point of each RIT, $$B_{\mathrm {c}}$$ and $$d_{\mathrm {c}}$$ , the relaxation time $$\tau $$ to reach the steady state shows a power-law divergence. The critical exponent for B-driven RIT is in agreement with that for d-driven RIT and both types of RIT fall into the same universality class as the absorbing transition in the two-dimensional directed-percolation universality class. As d is decreased to the average intervortex spacing in the reversible regime, $$\tau (d)$$ shows a significant drop, indicating a transition or crossover from a loop-reversible state with vortex-vortex collisions to a collisionless point-reversible state. In either regime, $$\tau (d)$$ exhibits a power-law divergence at the same $$d_{\mathrm {c}}$$ with nearly the same exponent.

Ooi S., Tachiki M., Konomi T., Kubo T., Kikuchi A., Arisawa S., Ito H., Umemori K.

Suppression of the occurrence of remanent vortices is necessary to improve the quality factor of superconducting resonators. In particular, the flux-expulsion dynamics in Nb during cooling has become of major interest to researchers focusing on superconducting cavities. To study the vortex states and their behavior in high-purity cavity-grade Nb, we used a magneto-optical imaging technique to perform real-space observations of the magnetic field distributions during the field-cooling and field-scanning processes. In the field-cooling process, the distributions were observed to undergo phase separation into vortex and Meissner regions, as would be expected in an intermediate mixed state (IMS). The vortex regions in the IMS, such as vortex bundles, tend to be larger in higher fields, in contrast to the Meissner regions, which experience shrinkage. In the field-scanning process, domelike field profiles, which indicate a geometrical barrier with very weak bulk pinning, were observed. The existence of the IMS suggests that cavity-grade Nb is in a type-II/1 superconductor regime, in which attractive interaction between vortices at a length scale of the penetration depth is crucial for the behavior of vortices.

Biswas P.K., Rybakov F.N., Singh R.P., Mukherjee S., Parzyk N., Balakrishnan G., Lees M.R., Dewhurst C.D., Babaev E., Hillier A.D., Paul D.M.

Superconductors usually display either type-I or type-II superconductivity and the coexistence of these two types in the same material, for example at different temperatures is rare in nature. We the employed muon spin rotation (muSR) technique to unveil the superconducting phase diagram of the dodecaboride ZrB12 and obtained clear evidence of both type-I and type-II characteristics. Most importantly, we found a region showing unusual behavior where the usually mutually exclusive muSR signatures of type-I and type-II superconductivity coexist. We reproduced that behavior in theoretical modeling that required taking into account multiple bands and multiple coherence lengths, which suggests that material has one coherence length larger and another smaller than the magnetic field penetration length (the type-1.5 regime). At stronger fields, a footprint of the type-II mixed state showing square flux-line lattice was also obtained using neutron diffraction.

Reichhardt C., Reichhardt C.J.

We examine driven superconducting vortices interacting with quenched disorder under a sequence of perpendicular drive pulses. As a function of disorder strength, we find four types of behavior distinguished by the presence or absence of memory effects. The fragile and jammed states exhibit memory, while the elastic and pinning dominated regimes do not. In the fragile regime, the system organizes into a pinned state during the first pulse, flows during the second perpendicular pulse, and then returns to a pinned state during the third pulse which is parallel to the first pulse. This behavior is the hallmark of the fragility proposed for jamming in particulate matter. For stronger disorder, we observe a robust jamming state with memory where the system reaches a pinned or reduced flow state during the perpendicular drive pulse, similar to the shear jamming of granular systems. We show signatures of the different states in the spatial vortex configurations, and find that memory effects arise from coexisting elastic and pinned components of the vortex assembly. The sequential perpendicular driving protocol we propose for distinguishing fragile, jammed, and pinned phases should be general to the broader class of driven interacting particles in the presence of quenched disorder.

Dobrovolskiy O.V., Vodolazov D.Y., Porrati F., Sachser R., Bevz V.M., Mikhailov M.Y., Chumak A.V., Huth M.

The ultra-fast dynamics of superconducting vortices harbors rich physics generic to nonequilibrium collective systems. The phenomenon of flux-flow instability (FFI), however, prevents its exploration and sets practical limits for the use of vortices in various applications. To suppress the FFI, a superconductor should exhibit a rarely achieved combination of properties: weak volume pinning, close-to-depairing critical current, and fast heat removal from heated electrons. Here, we demonstrate experimentally ultra-fast vortex motion at velocities of 10–15 km s−1 in a directly written Nb-C superconductor with a close-to-perfect edge barrier. The spatial evolution of the FFI is described using the edge-controlled FFI model, implying a chain of FFI nucleation points along the sample edge and their development into self-organized Josephson-like junctions (vortex rivers). In addition, our results offer insights into the applicability of widely used FFI models and suggest Nb-C to be a good candidate material for fast single-photon detectors. To realize ultra-fast dynamics of superconducting vortices one needs to overcome the practical issue of flux-flow instability (FFI). Here, Dobrovolskiy et al. demonstrate ultra-fast vortex motion at 10-15 km/s velocity in a Nb-C superconductor where the FFI is described by the edge-controlled FFI model.

Vagov A., Wolf S., Croitoru M.D., Shanenko A.A.

Experiments with the crossover superconductors between standard types I and II revealed exotic magnetic flux patterns where Meissner domains coexist with islands of the vortex lattice as well as with vortex clusters and chains. Until now a comprehensive theory for such configurations has not been presented. We solve this old-standing fundamental problem by developing an approach which combines the perturbation expansion of the microscopic theory with statistical simulations and which requires no prior assumption on the vortex distribution. Our study offers the most complete picture of the interchange of the superconductivity types available so far. The mixed state in this regime reveals a rich manifold of exotic configurations, which reproduce available experimental results. Our work introduces a pattern formation mechanism that originates from the self-duality of the theory that is universal and not sensitive to the microscopic details. Classification into type I and II reflects different responses of a superconductor to an applied magnetic field, however, there are intertype materials with unique properties and atypical vortex configurations. The authors study vortex patterns in this regime revealing that their properties are governed by a universal material independent mechanism, which amends the dual classification.