Vortex Glass Research Articles

Signature of vortex glass and non-Fermi liquid state in a magnetic superconductor Pr2Pt3Ge5

A comprehensive study on a magnetic superconductor (Pr2Pt3Ge5) has been presented here. Superconducting state is well described through modified model of thermally activated flux flow (TAFF) motion of vortices which shows that consideration of temperature dependence of the prefactor as well as non-linear variation of thermally activated energy (TAE) of vortices provides more reliable value of TAE in different fields. A clear signature of vortex glass (VG) state in this superconductor has been observed with a crossover from 3-dimensional (3D) to 2-dimensional (2D) critical behaviour in field. In addition, the dimensionality analysis using different models like modified TAFF, obtained critical exponent (s) from VG state and Lowest Landau Level (LLL) scaling reveals that Pr2Pt3Ge5 has a tendency towards 2D behaviour. Moreover, normal state study shows a clear signature of non-Fermi liquid (NFL) behaviour in this superconductor which shifts to Fermi liquid (FL) state at higher fields.

Smectic vortex glass

We show that in type-II superconductors a magnetic field applied transversely to correlated columnar disorder, drives a phase transition to a distinct "smectic" vortex glass (SmVG) state. SmVG is characterized by an infinitely anisotropic electrical transport, resistive (dissipationless) for current perpendicular to (along) columnar defects. Its positional order is also quite unusual, long-ranged with true Bragg peaks along columnar defects and logarithmically rough vortex lattice distortions with quasi-Bragg peaks transverse to columnar defects. For low temperatures and sufficiently weak columnar-only disorder, SmVG is a true topologically-ordered "Bragg glass", characterized by a vanishing dislocation density. At sufficiently long scales the residual ever-present point disorder converts this state to a more standard, but highly anisotropic vortex glass.

Tuning superconductivity in Ge:Ga using Ga+ implantation energy

High-fluence gallium $({\mathrm{Ga}}^{+})$ implantation at medium energies is proven to be an effective tool in forming superconducting (SC) thin films in germanium (Ge). By changing the post-implantation annealing conditions nanocrystalline to single-crystalline Ge matrices have been produced. Irrespective of crystallinity, such processes have mostly led to supersaturated Ge:Ga films where superconductivity is controlled by the extent of coherent coupling between Ga precipitates. Here we use ${\mathrm{Ga}}^{+}$ implantation energy as a means to tailor the spatial distribution and the coupling energy of the Ga precipitates. By systematic structural and magneto-transport studies, we unravel the complex connection between the internal structure of Ge:Ga films and their global SC parameters. At the shallowest implantation depth, we observe the strongest coupling leading to a robust superconductivity that sustains parallel magnetic fields as high as 9.95 T, above the conventional Pauli paramagnetic limit and consistent with a quasi-2D geometry. Further measurements at mK temperatures revealed an anomalous upturn in perpendicular critical field ${\mathrm{B}}_{\ensuremath{\perp}}$ vs temperature whose curvature and thus origin may be tuned between weakly coupled SC arrays and vortex glass states with quenched disorder. This warrants future investigations into Ge:Ga films for applications where tunable disorder is favorable, including test-beds for quantum phase transitions and superinductors in quantum circuits.

Emergence of dynamic vortex glasses in disordered polar active fluids

In equilibrium, disorder conspires with topological defects to redefine the ordered states of matter in systems as diverse as crystals, superconductors, and liquid crystals. Far from equilibrium, however, the consequences of quenched disorder on active condensed matter remain virtually uncharted. Here, we reveal a state of strongly disordered active matter with no counterparts in equilibrium: a dynamical vortex glass. Combining microfluidic experiments and theory, we show how colloidal flocks collectively cruise through disordered environments without relaxing the topological singularities of their flows. The resulting state is highly dynamical but the flow patterns, shaped by a finite density of frozen vortices, are stationary and exponentially degenerated. Quenched isotropic disorder acts as a random gauge field turning active liquids into dynamical vortex glasses. We argue that this robust mechanism should shape the collective dynamics of a broad class of disordered active matter, from synthetic active nematics to collections of living cells exploring heterogeneous media.

Evolution of vortex matter, phase diagram, and upper critical field in the FeSe1−x S x system

We present a comprehensive study of vortex matter in the FeSe1−x S x system with various doping degree. The influence of sulphur substitution on peak effect occurrence is studied. Additionally, we study a possible vortex liquid–vortex glass/lattice transition and find an evidence that the vortex liquid–vortex glass phase transition in FeSe1−x S x has a quasi two–dimensional nature. We investigate the upper critical field behaviour in FeSe1−x S x system, and found that the upper critical field is higher than that predicted by the Werthamer–Helfand–Hohenberg (WHH) model, whereas its temperature dependence could be fitted within a two-band framework. Finally, a detailed H–T phase diagram is presented.

The activation energy U(T,B) in high temperature superconductor

It is reported in this paper on the thermally assisted flux flow in epitaxial YBa2Cu3O7-δ deposited by Laser ablation method on the SrTiO3 substrate. The resistivity measurements ρ (T, B) of the sample under various values of the magnetic field up to 14T in directions B∥ab-plane and B∥c-axis with a dc weak transport current density were investigated in order to determine the activation energy and then understand the vortex dynamic phenomena and therefore deduce the vortex phase diagram of this material. The apparent activation energy U0 (B) calculated using an Arrhenius relation. The measured results of the resistivity were then adjusted to the modified thermally assisted flux flow model in order to account for the temperature-field dependence of the activation energy U (T, B). The obtained values from the thermally assisted activation energy, exhibit a behavior similar to the one showed with the Arrhenius model, albeit larger than the apparent activation energy with ∼1.5 order on magnitude for both cases of the magnetic field directions. The vortex glass model was also used to obtain the vortex-glass transition temperature from the linear fitting of [d ln ρ/dT ] −1 plots. In the course of this work thanks to the resistivity measurements the upper critical magnetic field Hc2 (T), the irreversibility line Hirr (T) and the crossover field HCrossOver (T) were located. These three parameters allowed us to establish a phase diagram of the studied material where limits of each vortex phase are sketched in order to optimize its applicability as a practical high temperature superconductor used for diverse purposes.

Second magnetization peak, rhombic-to-square Bragg vortex glass transition, and intersecting magnetic hysteresis curves in overdoped BaFe2(As1\u2212xPx)2 single crystals

The second magnetization peak (SMP) in the fourfold symmetric superconducting single crystals (such as iron pnictides and tetragonal cuprates) has been attributed to the rhombic-to-square transition (RST) of the quasi-ordered vortex solid (the Bragg vortex glass, BVG). This represents an alternative to the pinning-induced BVG disordering as the actual SMP mechanism. The analysis of the magnetic response of BaFe2(As1−xPx)2 specimens presented here shows that the SMP is not generated by the RST. However, the latter can affect the pinning-dependent SMP onset field if this is close to the (intrinsic) RST line, through the occurrence of a “shoulder” on the magnetic hysteresis curves m(H), and a maximum in the temperature variation of the DC critical current density. These features disappear in AC conditions, where the vortex system is dynamically ordered in the RST domain, emphasizing the essential role of vortex dislocations for an efficient accommodation of the vortex system to the pinning landscape and the SMP development. The m(H) shoulder is associated with a precipitous pinning-induced proliferation of dislocations at the RST, where the BVG elastic “squash” modulus softens. The DC magnetization relaxation indicates that the pinning-induced vortex system disordering continues above the RST domain, as the basic SMP mechanism.

Vortex phase diagram in 12442-type RbCa2Fe4As4F2 single crystal revealed by magneto-transport and magnetization measurements

The recently discovered 12442-type ACa2Fe4As4F2 (A = K, Rb, Cs) compounds are the only iron-based superconductors (IBSs) with double FeAs layers between neighboring insulating layers, analogous to the double CuO2 layers in some high-T c cuprates. Here, we report the study of vortex phase diagram of RbCa2Fe4As4F2 single crystal via magneto-transport and magnetization measurements. The resistive transition under magnetic fields shows a foot-like kink at a characteristic temperature, T s, followed by a resistive tail in nearly zero resistivity region. Such behavior is ascribed to a vortex slush transition at T s, below which the vortex state has short-range vortex lattice correlation, and then a second-order transition into the vortex glass phase occurs with further decreasing temperature. Above T s, the Arrhenius plot of resistivity shows two linear regions that are separated by a crossover line T cr(B), which is associated with a crossover from collective to plastic pinning or different flux pinning behaviors resulted from different types of defect. In addition, the magnetic hysteresis loops reveal a second magnetization peak (SMP), which is shifted to lower fields with increasing temperature for T< 12 K. However, the SMP unexpectedly moves back to a higher field at T= 12 K, and then gradually turns into a shoulder or kink that moves to higher fields at high temperatures, such anomalous behavior has never been observed in IBSs. According to the magneto-transport and magnetization data, the vortex phase diagram of RbCa2Fe4As4F2 is finally constructed. Details on the different vortex phase transitions and relevant physical scenarios are given and discussed.

Thermally activated flux motion in optimally electron-doped (Ca0.85La0.15)10(Pt3As8)(Fe2As2)5 and Ca10(Pt3As8)((Fe0.92Pt0.08)2As2)5 single crystals

The temperature dependence of the electric resistivity measured in various magnetic fields was analyzed by the vortex glass theory and the thermally activated flux motion (TAFM) theory. The vortex glass-to-vortex liquid (GTL) transition Tg obtained from the analysis shows a temperature dependence of BgT=B01-T/Tcm. The vortex liquid region is divided into the critical region existing in a finite temperature region just above Tg and the TAFM region present in the finite temperature region above it. In the critical region, the activation energy is expressed as Ueff=kBTTc-T/(Tc-Tg), whereas in the TAFM region, the activity energy is expressed as temperature-nonlinear UT,B=U0B1-tq. In the GTL transition, (Ca0.85La0.15)10(Pt3As8)(Fe2As2)5 maintains the 3D vortex structure without exhibiting dimension crossover of the vortex, but Ca10(Pt3As8)((Fe0.92Pt0.08)2As2)5 exhibits the dimension crossover from the 3D vortex glass to the 2D vortex liquid.

Flux pinning and the vortex phase diagram in optimized CaKFe4As4 single crystals fabricated by a one-step method

We have synthesized CaKFe4As4 single crystals by a simple one-step method. X-ray analysis suggests that the single crystals are c-axis orientation and no obvious impurity phase can be detected. The onset transition temperature is about 35 K with the ΔTc ∼ 1 K. By measuring the magnetoreistance, the vortex liquid-to-glass transitions of the CaKFe4As4 single crystals have been investigated. The effective flux pinning potential U0(B, T) and well scaling of the resistivity (B, T) were achieved. The vortex phase diagrams have been established on the basic of vortex glass temperature Tg and upper critical field Hc2. We have compared the vortex glass phase diagram of CaKFe4As4 with Ba1−xKxFe2As2 single crystals, and found that both samples have narrow vortex liquid region. The analysis on flux pinning indicates that the flux pinning ability of CaKFe4As4 is very strong and only slightly smaller than Ba1−xKxFe2As2 single crystals. The dependence of flux pinning energies UB of CaKFe4As4 on magnetic induction is UB B−0.265 and B−0.177 for the H//c and H//ab, respectively. Taking the structural difference between CaKFe4As4 and Ba1−xKxFe2As2 into account, the origin of the flux pinning in CaKFe4As4 may have close relationship with itself electronic inhomogeneity and accompanying nanosized-intercalation of CaFe2As2 as well as distorted FeAs4-tetrahedrons.

Study of TAFF and vortex phase of FexTe0.60Se0.40 (0.970 ≤ x ≤ 1.030) single crystals

Single crystalline samples with starting compositions FexTe0.60Se0.40 (x = 0.970, 0.985, 1, 1.015 and 1.030) have been grown using the self-flux method to study the effect of Fe variation (x) on the structural and superconducting properties of the grown single crystalline samples. All the grown samples are found superconducting and among all, the FeTe0.60Se0.40 (x = 1) sample shows the highest superconducting transition temperature (TC). For the samples with x other than 1, a decrease in the superconducting properties, such as TC, activation energy (U0) and upper critical field (HC2(0)), has been observed. The thermal activation energy (TAE) of the flux flow has been calculated using the conventional method and modified thermally activated flux flow (TAFF) model. The values of U0(H) show transition from the single vortex pinning regime to the collective vortex pinning regime at 2T. Also, the presence of planer defects has been estimated via both models. Furthermore, the modified TAFF model suggests three dimentional (3D) behaviour for all the grown single crystals. The vortex phase diagrams have been established by analysing the magnetoresistance data. The analysis reveals the transitions from unpinned to pinned vortex liquid region and also from the pinned vortex liquid state to vortex glass state. In the vortex phase diagram, below the critical temperature (T*), the critical exponent (s) is in a good agreement with the ‘q’ values for the 3D behaviour of vortex states for all the grown samples.

Transport characterization and pinning analysis of BaFe1.9Ni0.1As2.05 thin films

We report on the vortex-glass transition and superconducting performance of BaFe1.9Ni0.1As2.05 thin films with Tc = 17.8 K on CaF2(00l) single crystals by pulsed laser deposition. Atomic force microscopy characterization indicates the volumes of droplets appearing on the film surface increase with thickness and Magneto-optical imaging proves slight inhomogeneities in the current flow within the ab-plane of thin film. The thin films show a transport current density Jc of ∼1.14 MA cm−2 in self-field, and 0.34 and 0.28 MA cm−2 for H//c and H//ab up to 9 T at 4.2 K. Pinning mechanism associated with the fluctuations in the mean free path of the charge carries is found to be dominant in the thin films. The vortex-glass (VG) to vortex-liquid phase transition is identified in terms of the plots of the logarithmic derivative of the resistivity curves under different fields, allowing us to deduce the values of the VG transition temperature Tg, and the critical exponent s. The ρ–T curves are well scaled by VG theory. A phase diagram combining the VG transition temperature, irreversibility field and upper critical field is constructed.

Effect of the proton irradiation on the thermally activated flux flow in superconducting SmBCO coated conductors

We investigate changes in the vortex pinning mechanism caused by proton irradiation through the measurement of the in-plane electrical resistivity for H//c in a pristine and two proton-irradiated (total doses of 1 × 1015 and 1 × 1016 cm−2) SmBa2Cu3O7-δ (SmBCO) superconducting tapes. Even though proton irradiation has no effect on the critical temperature (Tc), the resulting artificial point defect causes an increase in normal state electrical resistivity. The electrical resistivity data around Tc shows no evidence of a phase transition to the vortex glass state but only broadens with increasing magnetic field due to the vortex depinning in the vortex liquid state. The vortex depinning is well interpreted by a thermally activated flux flow model in which the activation energy shows a nonlinear temperature change {boldsymbol{U}}{boldsymbol{(}}{boldsymbol{T}},{boldsymbol{H}}{boldsymbol{)}}{boldsymbol{=}}{{boldsymbol{U}}}_{{boldsymbol{0}}}{boldsymbol{(}}{boldsymbol{H}}{boldsymbol{)}}{{boldsymbol{(}}{bf{1}}-{boldsymbol{T}}{boldsymbol{/}}{{boldsymbol{T}}}_{{boldsymbol{c}}}{boldsymbol{)}}}^{{boldsymbol{q}}} (q = 2). The field dependence of activation energy shows a {{boldsymbol{U}}}_{{bf{0}}}{boldsymbol{ sim }}{{boldsymbol{H}}}^{-{boldsymbol{alpha }}} with larger exponents above 4 T. This field dependence is mainly due to correlated disorders in pristine sample and artificially created point defects in irradiated samples. Compared with the vortex pinning due to correlated disorders, the vortex pinning due to the appropriate amount of point defects reduces the magnitude of Uo(H) in the low magnetic field region and slowly reduces Uo(H) in high magnetic fields.

Mathematical modeling of current-voltage characteristics of high-temperature superconductors with fractal boundaries of normal phase clusters

The fractality effect of the normal phase clusters' boundaries of a high-temperature superconductor YBa2Cu3O7−x (YBCO) on the magnetic flux creep is investigated. Experimental current-voltage and magnetoresistive characteristics of YBCO at the boiling point of nitrogen are obtained. Based on the model of intergranular clusters with fractal boundaries, an approximation of the experimental data is obtained after geometric-probability analysis of the photomicrographs of the samples. A model of the magnetoresistive state caused by flux creep is proposed for various transport currents, and experimental and empirical dependences of the fractal dimension of the normal YBCO phase cluster boundaries on the constant magnetic field are found. The magnetic field intensity is determined for a given fractal dimension, at which the vortex penetration into the granules begins. It is shown that the state of the samples corresponds to the metastable phase of the vortex glass. The connectivity index of the stall paths of the vortex bundles at the percolation threshold is calculated.

Vortex state study of superconducting Fe(Te, Se) thin films deposited on SrTiO3 substrate by pulsed laser deposition technique

Superconducting thin films of two thicknesses have been fabricated on (100) oriented SrTiO3 (STO) substrates using the target of composition Fe1.05Te0.50Se0.50 by pulsed laser deposition technique. The structural and transport properties of the fabricated thin films have been investigated and the results indicate the enhancement in the superconducting properties with increasing thickness of the thin films. The onset of the superconducting transition temperature of the grown thin films of thicknesses ∼78 nm and ∼177 nm are ∼12.10 and 12.62 K at 0 T magnetic field, respectively. To estimate the upper critical fields HC2(0), thermally activated energy (TAE) and vortex phase diagram, the magnetoresistance measurements have been performed in the magnetic field range of 0 - 8 T. HC2(0) have been calculated by Ginzburg Landau (GL) theory and Werthamer-Helfand-Hohenberg model by taking the criterion of 90%, 50% and 10% of normal state resistivity and the corresponding GL coherence lengths have also been calculated. In the present work, the TAE has been estimated by conventional Arrhenius relation and modified thermally activated flux flow (TAFF) theory. The power law dependence of TAE, shows prominently the possible planer defects in the system. From the modified TAFF model, the values of fitting parameter ‘q’ suggests the 3 dimensional behaviour of the vortices for both the grown thin films. The vortex phase diagram study reveals the transition from the vortex liquid to vortex glass state.

Study of Structural and Magnetotransport Properties of Fe(Te, Se) Single Crystals

Single‐crystalline samples of nominal compositions FeTe0.88 and FeTe1−xSex are synthesized using the self‐flux method. The activation energy of the flux flow is estimated using the Arrhenius relation as well as by the modified thermally activated flux flow (TAFF) model. The field dependence of U0 shows transition from single to collective vortex pinning at a magnetic field of ≈2 T. The analysis of field‐dependent U0 data reveals the planar and the point defect magnetic field regions for both the models. The modified TAFF model is used to study the 2D and 3D behavior of the vortex state for all the superconducting samples. The single‐crystalline FeTe0.80Se0.20 and FeTe0.60Se0.40 samples show 3D behavior, whereas the FeTe0.40Se0.60 crystal shows 2D behavior. The vortex phase diagrams of all the superconducting samples are obtained by analyzing the magnetotransport data. The vortex phase diagrams reveal transitions from the unpinned to pinned vortex liquid state and the vortex liquid to vortex glass state. Below T*, the critical exponent s is in good agreement with q values for 2D/3D behavior of vortex states of all the superconducting samples.

Unveiling the vortex glass phase in the surface and volume of a type-II superconductor

Order-disorder transitions between glassy phases are common in nature and yet a comprehensive survey on the entailed structural changes is challenging since the constituents are in the micro-scale. Vortex matter in type-II superconductors is a model system where some of these experimental challenges can be tackled. Samples with point disorder present a glassy transition on increasing the density of vortices. A glassy yet quasi-crystalline phase, the Bragg glass, nucleates at low densities. The vortex glass stable at high densities is expected to be disordered, however its detailed structural properties remained experimentally elusive. Here we show that the vortex glass has large crystallites with in-plane positional displacements growing algebraically and short-range orientational order. Furthermore, the vortex glass has a finite and almost constant correlation length along the direction of vortices, in sharp contrast with strong entanglement. These results are important for the understanding of disorder-driven phase transitions in glassy condensed matter.

Investigation of fundamental and higher harmonic AC magnetic susceptibility of FeSe0.5Te0.5 superconductor

We present the complex harmonic magnetic susceptibilities χn = χ′n-iχ″n (n = 1, 3) of FeSe0.5Te0.5 polycrystalline superconducting sample. The ac magnetic susceptibility is measured as a function of various external perturbations such as temperature T, the ac magnetic field amplitude Hac, frequency υ, and the magnitude of dc bias field Hdc. The in-phase (χ′n) and out of phase (χ″n) components of the fundamental and third harmonics of ac susceptibility are found to vary as a function of ac driven field. Particularly, the curves shift toward lower temperatures with increasing Hac. Contrary to ac magnetic field (Hac), no noticeable change has been observed within the range of applied dc magnetic field (Hdc) of up to 20 Oe. At a fixed ac magnetic field of Hac = 0.5 Oe, both parts of the third harmonics show frequency dependence. The imaginary part of the third harmonics, χ″3 shows a small peak followed by a negative minimum at lower temperatures. The small peak diminishes as the frequency increases. The negative minimum suppresses and shifts towards the higher temperatures as we increase the frequency. To better understand the ac magnetic response under the influence of various perturbations, we have analyzed the polar plots (Cole-Cole) of the complex ac susceptibility for both the harmonics. Our analysis suggests that the studied sample is in a vortex glass state, characterized by a collective flux creep within Bean’s model, while the Kim–Anderson model is ruled out.

Frequency dependence of ac losses in a granular superconductor Lu2Fe3Si5

By using ac susceptibility measurements, the frequency dependence of ac losses was experimentally studied in a granular Lu2Fe3Si5 sample. Three types of temperature dependent ac loss peaks were observed which were attributed to the intergranular, intragranular and intrinsic bulk behaviors. It is found that the intergranular and intragranular peaks show clear frequency dependence while the intrinsic peak remains constant as the frequency changes. With increasing frequency the pinning difference between the intergranular and intragranular becomes small, and vanishes at high frequencies. The vortex glass temperature Tg was determined to be 5.97 K. The phase diagram was constructed by measuring the ac susceptibility under different magnetic fields.

Strain relaxation behaviour of vortices in a multiferroic superconductor

The elastic and anelastic properties of a single crystal of Co-doped pnictide Ba(Fe0.957Co0.043)2As2 have been determined by resonant ultrasound spectroscopy in the frequency range 10–500 kHz, both as a function of temperature through the normal-superconducting transition (Tc ≈ 12.5 K) and as a function of applied magnetic field up to 12.5 T. Correlation with thermal expansion, electrical resistivity, heat capacity, DC and AC magnetic data from crystals taken from the same synthetic batch has revealed the permeating influence of strain on coupling between order parameters for the ferroelastic (QE) and superconducting (QSC) transitions and on the freezing/relaxation behaviour of vortices. Elastic softening through Tc in zero field can be understood in terms of classical coupling of the order parameter with the shear strain e6, λe6, which means that there must be a common strain mechanism for coupling of the form λQE. At fields of ~5 T and above, this softening is masked by Debye-like stiffening and acoustic loss processes due to vortex freezing. The first loss peak may be associated with the establishment of superconductivity on ferroelastic twin walls ahead of the matrix and the second is due to the vortex liquid–vortex glass transition. Strain contrast between vortex cores and the superconducting matrix will contribute significantly to interactions of vortices both with each other and with the underlying crystal structure. These interactions imply that iron-pnictides represent a class of multiferroic superconductors in which strain-mediated coupling occurs between the multiferroic properties (ferroelasticity, antiferromagnetism) and superconductivity.