Origin of the fast magnetization relaxation at low temperatures in HTS with strong pinning

The temperature T variation of the normalized magnetization relaxation rate S in high-temperature superconductors (HTS) with strong vortex pinning exhibits a maximum in the low-T range. This was reported for various HTS, and the origin of the faster relaxation at low T appearing in standard magnetization relaxation measurements was usually related to specific pinning properties of the investigated specimens. Since the observed behaviour seems to be characteristic to all HTS with enhanced pinning (generated by random and/or correlated disorder), we show that the S(T) maximum can be explained in terms of classic collective vortex creep. The influence of thermo-magnetic instabilities in the low-T range is also evidenced. The collective (elastic) creep regime is generated by the T dependent macroscopic currents induced in the sample during standard magnetization measurements.     

Two-Dimensional Coulomb Glass as a Model for Vortex Pinning in Superconducting Films

A glass model of vortex pinning in highly disordered thin superconducting films in magnetic fields B ≪ H_c2 at low temperatures is proposed. Strong collective pinning of a vortex system realized in disordered superconductors that are close to the quantum phase transition to the insulating phase, such as InO_x, NbN, TiN, MoGe, and nanogranular aluminum, is considered theoretically for the first time. Utilizing the replica trick developed for the spin glass theory, we demonstrate that such vortex system is in non-ergodic state of glass type with a large kinetic inductance per square L_K. The distribution function of local pinning energies is calculated, and it is shown that it possesses a wide gap; i.e., the probability to find a weakly pinned vortex is extremely low.

     

Vortex lattice ordering in the flux flow state of Nb thin films

We measure current–voltage characteristics at high driving currents for different magnetic fields and temperatures in Nb thin films of rather strong pinning. In a definite range of the B–T phase diagram we find that a current induced transition occurs in the flux flow motion of the vortex lattice, namely a dynamic ordering (DO). Contrary to the case of weaker pinning materials, DO is observed only at low fields, due to the stronger intrinsic disorder that can deform plastically the moving vortex lattice even for small applied fields.     

Bi2Sr2CaCu2O8 crystal with a region of periodic blind antidots – transition between bulk and interface vortex pinning

This work focuses on differential magneto-optical two-dimensional imaging of the current distribution in a high-T_c superconducting Bi₂Sr₂CaCu₂O₈ crystal having a region of 170 × 170 μm² patterned with periodic blind antidots. By measuring the self-induced field of an applied current, we can map the current flow distribution within and at the edges of the patterned region. We detected three separate types of current flow within the patterned region, which correspond to three different arrangements of pancake vortices within and at the edges of the patterned region. At high temperatures the vortices delocalize from the antidots, presumably due to thermal fluctuations. However, at lower temperatures vortex pinning mechanisms become prominent, lowering the vortex mobility in the patterned region. There are two contributing mechanisms: bulk pinning by the patterned antidots and interface pinning due to an entry barrier into the patterned region. Each mechanism is dominant at different temperatures. From our experiments we see that the T–H transition line from the bulk to the interface pinning and the vortex melting line in the pristine region coincide.     

Vortex pinning in bulk-processed Y–Ba–Cu–O with ZrO2 nano-particles: Optimum pinning center size

Crystalline defects on the nano-scale were successfully introduced into YBCO high-temperature superconductors (HTS) by ZrO₂ nanometer particles addition in order to strongly pin the quantized vortices. Three batches of ZrO₂ nano-particles with different particle size distributions were used. The corresponding mean nano-particle diameters are respectively, 287, 536 and 764 nm. Serving as artificial pinning centers (APC), non-superconducting nano-particles cause a remarkable enhancement of critical current density (J_c) at T = 77 K. This improvement has been shown to depend on the size of APC. The pinning strength of nano-particles inclusions has been found to be greater with wide size dispersed nano-particles. Our results indicate that pinning properties and vortex dynamics depend on the size of APCs. The introduction of APCs with controlled size is indispensable to achieve a high J_c.     

Orientation-induced crossover in pinning force density and peak effect in Bi2Sr2CaCu2O8+x single crystal

Magnetization–hysteresis measurements on single crystal of Bi₂Sr₂CaCu₂O_8+x (Bi-2212) at various temperatures (20–40 K) are reported for different applied field orientations (θ) relative to the unit cell's c-axes. An orientation-induced crossover in the magnitude of the volume pinning force density F_p around θ≥20° is observed which does not conform with predictions of the existing 2D-pancake model. The results further indicate that the `peak-effect' in Bi-2212 is associated with the crossover in the vortex matter from a quasi-lattice to a disordered vortex solid.     

Anomalous magnetization jumps in granular Pb superconducting films

In granular superconductors, the grain boundaries are closely related to the vortex dynamics and the macroscopic superconducting properties. In our research, Pb films with different grain sizes were prepared by tuning the substrate temperature. With the grain size decreasing, Pb films are prone to feature the anomalous magnetization jumps in the M − T curves, while in the M − H curves flux avalanche happens. Both phenomena appear in the same region of the H − T phase diagram and thus are considered to have the same origin. The further theoretical analysis shows that with grain size decreasing the pinning mechanism evolves from a mixed δT_c and δl pinning to the δl pinning mechanism. The results shed light on the study of pinning mechanism for granular superconductors and is beneficial to the potential application of manipulating vortex pinning by regulation of intrinsic defects.     

Vortex pinning: A probe for nanoscale disorder in iron-based superconductors

The pinning of quantized flux lines, or vortices, in the mixed state is used to quantify the effect of impurities in iron-based superconductors (IBS). Disorder at two length scales is relevant in these materials. Strong flux pinning resulting from nm-scale heterogeneity of the superconducting properties leads to the very disordered vortex ensembles observed in the IBS, and to the pronounced maximum in the critical current density j_c at low magnetic fields. Disorder at the atomic scale, most likely induced by the dopant atoms, leads to “weak collective pinning” and a magnetic field-independent contribution j_c^coll. The latter allows one to estimate quasiparticle scattering rates.     

Direct visualization of the vortex distributions in a superconducting film with a Penrose array of magnetic pinning centers: Symmetry induced giant vortex state

Using scanning Hall probe microscopy a direct visualization of the flux distribution in a Pb film covering a fivefold Penrose array of Co dots is obtained. We demonstrate that stable vortex configurations can be found for fields H ∼ 0.8H₁, H₁ and 1.6H₁, where H₁ corresponds to one flux quantum per pinning site. The vortex pattern at 0.8H₁ corresponds to one vacancy in one of the vertices of the thin tiles whereas at 1.6H₁ the vortex structure can be associated with one interstitial vortex inside each thick tile. Strikingly, for H = 1.6H₁ interstitial and pinned vortices arrange themselves in ring-like structures (“vortex corrals”) which favor the formation of a giant vortex state at their center.     

Geometrical surface vortex pinning in superconducting films

A model is proposed for vortex pinning in a superconducting film with a rough surface. The model relates the critical current to the steepness of the surface relief and, at a high vortex concentration, to the distance between neighboring steepness maxima on the paths of vortex motion. The dependence of the critical current density on the thickness of a high-T_c superconducting film is measured in a weak magnetic field. Its behavior can be explained by the pinning at the stepped surface relief.     

The effect of pinning centers in Zn-doped CuBa2Ca3Cu4O12−y high-temperature superconductors

CuBa₂Ca₃Cu₄O_12−y (Cu:1234) high-temperature superconductors (HTS) doped with up to 2% Zn were grown using the high-pressure synthesis technique. Magnetization loops of the samples were measured at various temperatures between 5 and 77.3 K and magnetic fields up to 14 T. Critical current densities J_c of the samples were estimated using the critical state model. The results show that Zn-induced pinning centers increase J_c of Cu:1234 several times, depending on field and temperature. From the experimentally determined field-temperature region in which a higher Zn concentration lead to a higher J_c, we suggest the existence of a cross-over from quite efficient, extended (in the c-axes direction) pinning centers to point-like (inefficient) pinning centers at a certain temperature, depending on field. This effect can be attributed to the fact that, unlike other HTS, in Cu:1234 there is a second critical temperature T_c2 of about 70–80 K (in zero field, and 50–60 K in 15 T), related to the over-doping of pyramidal basal plane (outer CuO₂ plane).     

Dynamics of vortices in type-II superconductors with periodic square columnar pins

The dynamics of a two-dimensional vortex system with strong periodic square columnar pins is investigated. For the case vortex number matching pinning number, we find that the vortex liquid is frozen into square lattice via a continuous transition, and the freezing (melting) temperature T_m is the same as the thermal depinning temperature of vortices, which are different from the first-order phase transition at weak pinning. The zero-temperature critical depinning force F_c0 is exactly the same as the maximum pinning force, and the depinning property at T = 0 can be expressed by scaling v ～ (F ? F_c0)^β with the exponent β close to 0.5. The v–F curves at temperatures below T_m show that vortices are pinned at small driving force.     

Pinning,thermally activated depinning and their importance for tuning the nanoprecipitate size and density in high Jc YBa2Cu3O7−x films

YBa₂Cu₃O_7?x (Y123) films with quantitatively controlled artificial nanoprecipitate pinning centers were grown by pulsed laser deposition (PLD) and characterized by transport over wide temperature (T) and magnetic field (H) ranges and by transmission electron microscopy (TEM). The critical current density J_c was found to be determined by the interplay of strong vortex pinning and thermally activated depinning (TAD), which together produced a non-monotonic dependence of J_c on c-axis pin spacing d_c. At low T and H, J_c increased with decreasing d_c, reaching the very high J_c ～ 48 MA/cm² ～20% of the depairing current density J_d at 10 K, self-field and d_c ～ 10 nm, but at higher T and H when TAD effects become significant, J_c was optimized at larger d_c because longer vortex segments confined between nanoprecipitates are less prone to thermal fluctuations. We conclude that precipitates should extend at least several coherence lengths along vortices in order to produce irreversibility fields H_irr(77 K) greater than 7 T and maximum bulk pinning forces F_p,max(77 K) greater than 7–8 GN/m³ (values appropriate for H parallel to the c-axis). Our results show that there is no universal pin array that optimizes J_c at all T and H.     

Systematic Study of Vortex Pinning and a Liquid–Glass Phase Transition in BaFe<Subscript>2–<Emphasis Type="Italic">x</Emphasis></Subscript>Ni<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>As<Subscript>2</Subscript> Single Crystals

The vortex pinning and liquid-glass transition have been studied in BaFe_2–xNi _x As₂ single crystals with different doping levels (x = 0.065, 0.093, 0.1, 0.14, 0.18). We found that Ni-doped Ba-122 has rather narrow vortex-liquid state region. Our results show that the temperature dependence of the resistivity as well as I?V characteristics of Ni-doped Ba-122 is consistent with 3D vortex-glass model. It was found that -pinning gives the main contribution to overall pinning in 122 Ni-doped system. The vortex phase diagrams for different doping levels were built based on the obtained data of temperature of the vortex-glass transition T_g and the upper critical magnetic field H_c2.     

Effect of vortex pinning by point defects on the lower critical field in layered superconductors

The lower critical field H _c1 in layered superconductors is calculated under the assumption that vortex pinning by point defects is strong in these materials. We consider the case of a purely electromagnetic coupling of vortex pancakes and the case of both the electromagnetic and Josephson couplings of the pancakes in a vortex line. In the latter case, singularities in the temperature dependence of H _c1 are predicted at certain characteristic temperatures.     

Inhomogeneous superconducting state in the overdoped regime of La2−xSrxCuO4: Comparison with the superconducting state of NbSe2

We have measured the temperature dependence of the magnetic susceptibility, χ vs. T, and the magnetization curve, M vs. H, for NbSe₂ single crystals, in order to compare the superconducting (SC) state in the overdoped regime of La_2−xSr_xCuO₄ (LSCO) with the SC state of the layered conventional superconductor NbSe₂. While a plateau in χ vs. T in a moderate magnetic field and a so-called second peak in M vs. H, which is due to the marked enhancement of vortex pinning, have been observed in the overdoped regime of LSCO, these behaviors have not been observed in NbSe₂. The present results indicate that the anomalously marked enhancement of vortex pinning is a characteristic feature in the overdoped LSCO where a microscopic phase separation into SC and normal-state regions takes place.     

Pinning of vortices and penetration of the magnetic field into a periodically modulated long Josephson contact

The upper field of the Meissner regime, H _up, and overheat field H′_c1, above which vortices start penetrating into a Josephson contact, are calculated throughout the range of pinning parameter I. The stability of likely configurations is investigated. It is shown that H _up = H′_c1 at any I. The existence of a single vortex centered at the extreme cell in the contact is demonstrated to be a possibility. At I > 3.69, such a vortex may exist even in a zero magnetic field. At 1.48 < I < 3.69, this vortex can exist in an external field in the range from some H _v to H _up. At I < 1.48, the vortex cannot exist under any conditions. From the equality of H _up and H′_c1 at any I, the conclusion is drawn that penetration of vortices into any Josephson medium is conditioned by the need to satisfy flux quantization conditions. Here, not the forces of vortex pinning at defects in the medium but quantization requirements are of major importance, which are satisfied in specific quantum ways rather than by meeting equilibrium conditions for vortices, forces, etc.     

Effective pinning barriers of NdFeAsO0.88F0.12 superconductor

Resistivities of polycrystalline iron-based NdFeAsO_0.88F_0.12 superconductors prepared via solid-state reaction in ambient pressure (AP) and high pressure (HP) were measured in various magnetic fields ranging from 0 to 9 T. Different resistivity broadening behaviors of the AP and HP samples, which may originate from the anisotropic superconductivity, the vortex motion, or the connectivity, were investigated in detail. The effective pinning barriers of both the AP and HP samples were obtained from the Arrhenius plot of the resistivity data by two analytic methods of which one assuming the prefactor 2ρ_cU/T of the thermally activated ?ux ?ow (TAFF) resistivity ρ=(2ρ_cU/T)exp(−U/T) is a constant, while the other assuming the prefactor is temperature dependent. The results determined from the two methods were compared and analysed, and the true effective pinning barriers were obtained. The origin of different pinning barriers of the AP and HP samples is discussed.     

Distribution of the current density in the cylindrical sample of the type II superconductor

Deviation from a homogeneous distribution of the vortex line lattice and magnetic field induced by transport current near H_c2 in the cylindrical sample of type II superconductor in the mixed state without pinning is determined. The dependence of the critical current density on the position in the sample is calculated.     

Effect of pinning and driving force on the metastability effects in weakly pinned superconductors and the determination of spinodal line pertaining to order—disorder transition

We explore the effect of varying drive on metastability features exhibited by the vortex matter in single crystals of 2H-NbSe₂ and CeRu₂ with varying degree of random pinning. The metastable nature of vortex matter is reflected in the path dependence of the critical current density, which in turn is probed in a contact-less way via AC-susceptibility measurements. The sinusoidal AC magnetic field applied during AC susceptibility measurements appears to generate a driving force on the vortex matter. In a nascent pinned single crystal of 2H-NbSe₂, where the peak effect (PE) pertaining to the order—disorder phenomenon is a sharp first-order-like transition, the supercooling feature below the peak temperature is easily wiped out by the reorganization caused by the AC driving force. In this paper, we elucidate the interplay between the drive and the pinning which can conspire to make the path-dependent AC-susceptibility response of different metastable vortex states appear identical. An optimal balance between the pinning and driving force is needed to view the metastability effects in typically weakly pinned specimen of low temperature superconductors. As one uses samples with larger pinning in order to differentiate the response of different metastable vortex states, one encounters a new phenomenon, viz., the second magnetization peak (SMP) anomaly prior to the PE. Supercooling/superheating can occur across both the PE and the SMP anomalies and both of these are known to display non-linear characteristics as well. Interplay between the path dependence in the critical current density and the non-linearity in the electromagnetic response determine the metastability effects seen in the first and the third harmonic response of the AC susceptibility across the temperature regions of the SMP and the PE. The limiting temperature above which metastability effects cease can be conveniently located in the third harmonic data, and the observed behavior can be rationalized within the Bean’s critical state model. A vortex phase diagram showing different vortex phases for a typically weakly pinned specimen has been constructed via the AC susceptibility data in a crystal of 2H-NbSe₂ which shows the SMP and the PE anomalies. The phase space of coexisting weaker and stronger pinned regions has been identified. It can be bifurcated into two parts, where the order and disorder dominate, respectively. The former part continuously connects to the reentrant disordered vortex phase pertaining to the small bundle pinning regime, where the vortices are far apart, interaction effects are weak and the polycrystalline form of flux line lattice prevails.