Vortex-glass Transition Research Articles

Vortex-glass transition and vortex pinning behavior in three-dimensional NbTiN epitaxial films

In the present paper, the vortex dynamics in two NbTiN epitaxial films have been explored via analyzing the current–voltage (I–V) curves measured at different temperatures and fields. The thicknesses of the two films are ∼50 and ∼100 nm, respectively, and they are three-dimensional (3D) with respect to superconductivity. The films transform from normal state to superconducting state with decreasing temperature at zero field, and the values of superconducting transition temperature Tc are 8.73 and 12.03 K for the ∼50- and ∼100-nm-thick films, respectively. When a magnetic field with magnitude 0.5T≲μ0H≲7 T and perpendicular to the film plane is applied, the isothermal I–V data show a 3D vortex-glass (VG) scaling collapse at each field, suggesting that a 3D vortex-liquid phase to VG phase transition occurs in the NbTiN films. By analyzing the critical current density, we found that core pinning is the main pinning mechanism in the films. In addition, it is found that the normal point-like pinning dominates the pinning behavior at low field regime. While in the high field regime, besides the normal point-like pinning, other pinning mechanisms, such as Δκ pinning, also exist in the films. Our results not only provide strong experimental support for the occurrence of VG phase transition in conventional superconductors, but also provide fundamental information for the application of NbTiN films.

Vortex glass phase transition in two-dimensional Bi2Sr2Ca2Cu3O sub-microbridge

Vortex dynamics is crucial for practical applications and to understand the nature of the mixed state for high-T c superconductors. Mechanically exfoliated ultra-thin single crystals provide a unique platform for exploring vortex physics in the two-dimensional (2D) limit. Here, we systematically investigated the current–voltage (I–V) characteristics as functions of the temperature and magnetic field in a single-crystalline Bi2223 sub-microbridge of 2.5 unit cells thickness. The nonlinear I–V characteristics are excellently described by the scaling theory for a quasi-2D vortex glass (VG) phase transition, and a phase diagram revealing the VG and vortex liquid phase is drawn. The scaling parameter v is consistent with previous reports, while the critical exponent z is far smaller than that in most investigations. Moreover, the VG transition temperature T g of the present sample is higher than that in the reported Bi2223 epitaxial thin films and tapes. In addition, the pinning force density of our sample is calculated, which is stronger than that reported in Bi2223 epitaxial thin films and tapes. Our results indicate that a high pinning force density may suppress the dynamical critical exponent z and enhance the VG phase transition temperature, providing new insight into the flux dynamics in cuprates.

Scaling of current-voltage characteristics without and with finite superfluid phase stiffness below [formula omitted

Superfluid phase stiffness (SPS) of NCBCO superconductor as a function of T has been extracted by using the Ambegaokar–Halperin–Nelson–Siggia (AHNS) theory at the zero magnetic field. The Berezinskii–Kosterlitz–Thouless (BKT) phase transition temperature, TBKT has been extracted to be 54.0 K. The idea of the vortex glass (VG) transition has been applied to the resistive states of the BKT phase transition observed at 54.0 K. We have extracted the static exponent required in the Fisher, Fisher and Huse (FFH) scaling equation.The scaling of the current-voltage (IV) curves around 54.0 K with and without finite SPS is possible within the framework of the FFH theory.

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.

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.

Vortex dynamics in (NiFe2O4)x/CuTl-1223 nanoparticles-superconductor composites

The effect of NiFe2O4 nanoparticles (NPs) addition on activation energy Uo(H,T) and vortex dynamics of Cu0.5Tl0.5Ba2Ca2Cu3O10-δ (CuTl-1223) superconducting phase was studied. Crystal structure and phase purity of CuTl-1223 matrix and NiFe2O4 NPs were determined by X-ray diffraction (XRD). There was no substantial variation observed in lattice parameters of CuTl-1223 phase with inclusion of NiFe2O4 NPs, which indicated the settlement of these NPs across the grain-boundaries of CuTl-1223 matrix. The broadening of superconducting resistive transition in infield resistivity versus temperature curves was linked to thermally activated flux flow (TAFF) generating dissipation in the system. Overall decrease in Uo(H,T) and vortex-glass phase transition temperature (Tg) with increasing content of NiFe2O4 NPs were associated to suppression of flux pinning strength in material. The values of Tg and TcOnset were shifted towards lower values with increasing content of these NPs, which was elaborated in the form of a vortex-phase diagram in H-T space.

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.

Thermally activated flux flow, vortex-glass phase transition and the mixed-state Hall effect in 112-type iron pnictide superconductors

The transport properties in the mixed state of high-quality Ca0.8La0.2Fe0.98Co0.02As2 single crystal, a newly discovered 112-type iron pnictide superconductor, are comprehensively studied by magneto-resistivity measurement. The field-dependent activation energy, U0, is derived in the framework of thermally activated flux flow (TAFF) theory, yielding a power law dependence U0~Hα with a crossover at a magnetic field around 2 T in both H⊥ab and H//ab, which is ascribed to the different pinning mechanisms. Moreover, we have clearly observed the vortex phase transition from vortex-glass to vortex-liquid according to the vortex-glass model, and vortex phase diagrams are constructed for both H⊥ab and H//ab. Finally, the results of mixed-state Hall effect show that no sign reversal of transverse resistivity ρxy(H) is detected, indicating that the Hall component arising from the vortex flow is also negative based on the time dependent Ginzburg-Landau (TDGL) theory. Meanwhile, the transverse resistivity ρxy(H) and the longitudinal resistivity ρxx(H) follow the relation |ρxy(H)|=Aρxx(H)β well with an exponent β~2.0, which is in line with the results in theories or experiments previously reported on some high-Tc cuprates.

Systematic Study of Vortex Pinning and a Liquid–Glass Phase Transition in BaFe2–xNixAs2 Single Crystals

The vortex pinning and liquid-glass transition have been studied in BaFe2–xNixAs2 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 Tg and the upper critical magnetic field Hc2.

Quasi-two-dimensional vortex–glass transition and the critical current density in TiO epitaxial thin films

There are many fascinating properties in titanium oxides such as the enhanced superconductivity in cubic TiO epitaxial thin films with the superconducting transition temperature of 7.65 K, which is much higher than that of the bulk polycrystalline TiO. To explore the superconductivity of the TiO thin films in more detail, we investigated the magnetic field and temperature dependences of the current–voltage (I–V) characteristics and the critical current density Jc in magnetic fields perpendicular to the film surface. The I–V curves show a quasi-two-dimensional vortex glass (VG) scaling collapse in different magnetic fields, and a vortex phase diagram is constructed from the VG and vortex liquid regions to the normal state. Through the critical current density investigation, we found that δl pinning dominates the pinning behavior, which is in accordance with the analyzed results of the vortex pinning force associated with defects in the film, such as grain boundaries. The findings of the magnetic phase diagram and critical current properties should be helpful for practical applications of the TiO family.

Thermally activated transport and vortex-glass phase transition of K0.78Fe1.70Se2 single crystals

The transport property () and flux motion together with the superconductivity of Fe Se2 single crystals are studied. In the transport measurement, contrasting behavior is observed under two different magnetic field orientations, i.e., and , which is ascribed to different vortex configurations. In the flux motion study, the tail of the well fits the description of the vortex-glass (VG) critical behavior, which is confirmed by VG scaling. The strong pinning nature of FeSe2 implies great sustainability under high magnetic fields and the potential for practical application of the system. The relation under Tc follows Arrhenius thermally activated flux flow (TAFF) behavior. The existence of a crossover behavior in a magnetic field is discovered via the magnetic dependence of the effective pinning barrier, which is related to the change in pinning strength of the point defects and the entanglements of the flux lines. Finally, a vortex phase diagram is proposed based on the evolution of upper critical field and other dynamic characteristics.

Vortex–glass transformation within the surface superconducting state of β-phase Mo1-xRex alloys

We have performed an experimental study on the temperature dependence of electrical resistivity ρ(T) and heat capacity C(T) of the MoRex alloy superconductors in different magnetic fields. In the presence of applied magnetic field, the electrical resistivity of these alloys goes to zero at a temperature well above the bulk superconducting transition temperature obtained with the help of heat capacity measurements in the same magnetic field. Our study indicates the presence of a surface superconducting state in these alloys, where the flux lines are pinned in the surface sheath of the superconductor. The configuration of the flux lines (two-dimensional pancake-like) in the surface sheath is understood in the realm of the flux-spot model. Experimental evidence in support of the surface mixed-state state or ‘Kulik vortex-state’ and the occurrence of a vortex–liquid to vortex–glass transition is presented.

Thermally activated flux flow in superconducting epitaxial FeSe0.6Te0.4 thin film

The thermally activated flux flow effect has been studied in epitaxial FeSe0.6Te0.4 thin film grown by a PLD method through the electrical resistivity measurement under various magnetic fields for B//c and B//ab. The results showed that the thermally activated flux flow effect is well described by the nonlinear temperature-dependent activation energy. The evaluated apparent activation energy U0(B) is one order larger than the reported results and showed the double-linearity in both magnetic field directions. Furthermore, the FeSe0.6Te0.4 thin film shows the anisotropy of 5.6 near Tc and 2D-like superconducting behavior in thermally activated flux flow region. In addition, the vortex glass transition and the temperature dependence of the high critical fields were determined.

The magnetoresistance of YBCO/BZO composite superconductors

We study the effect of addition of BaZrO3 (BZO) on normal and superconducting state of YBa2Cu3O7-δ (YBCO). We find that in general both room temperature and residual resistivity increase with the addition of BZO except at low concentration of BZO. The temperature dependence of resistivity in presence of magnetic field also shows less resistivity broadening in composites containing low concentration of BZO below transition temperature (TC). The zero temperature upper critical field (Hc2(0)), estimated by using Werthamer, Helfand and Hohenberg theory and Ginzburg Landau theory, shows an increase by the finite addition of BZO in YBCO. Further, the activation energy (U0) determined from Arrhenius plots and vortex glass transition temperature (Tg) also increase with the limited addition of BZO. Such an enhancement in Hc2(0), Uo and Tg has been attributed to the increase in grain connectivity of YBCO . We conclude that the limited addition of BZO in YBCO significantly improves its superconducting performance in magnetic environment.

Magneto transport study of YBCO: Ag composites

We study the effect of Ag addition on the magnetoresistance and allied properties of YBCO. We find that the zero resistance temperature (TC0) shift is narrowed down by the addition of Ag as magnetic field (H) is increased from 0 to 13 T. The resistivity broadening of composites under magnetic field exhibits Arrhenius behavior due to thermally activated flux flow of vortices. The activation energy, determined from Arrhenius plot of resistivity, increases with the addition of Ag in YBCO and is found optimum for 15%Ag composite. The vortex glass transition temperature is found more in YBCO:Ag composites as compared to pristine YBCO. The zero temperature upper critical field Hc2(0) estimated by using Werthamer, Helfand and Hohenberg theory and Ginzburg Landau theory shows two fold enhancement by adding Ag in YBCO matrix. We find that the addition of Ag in YBCO leads to an enhancement in activation energy, an increases in Hc2(0) in addition to better grain connectivity.

Study of vortex dynamics in single crystalline Ba0.54K0.46Fe2As2 superconductor using dc and ac magnetization

Due to relatively lower superconducting transition temperature(Tc), weaker anisotropy and larger coherence length, the overall strength of thermal fluctuations in iron-based superconductors seem to be intermediate between cuprates and more classical superconductors like Nb3Sn. A detailed linear and non-linear ac magnetic susceptibility technique has been used as a probe to investigate the vortex-glass melting transition and vortex dynamics in an optimally doped p-type Ba0.54K0.46Fe2As2 good quality single crystal (RRR≈10) under various fields and frequency range. Besides these, we have also constructed a vortex phase diagram in this compound using dc magnetization. Magnetic irreversibility temperature (Tirr) is the only temperature where solid vortex phase shows true zero resistance and has a great importance for technical applications of a superconductor. We have clearly observed that Tirr strongly depends on frequency and this dependency can be explained in the framework of vortex-glass phase transition model. From our experimental observations, we conclude that vortex-glass melting transition is second order in nature and vortex phase shows glassy character in this compound.

Thermally activated flux flow in Fe1.06Te0.6Se0.4 single crystal

Resistivity of Fe1.06Te0.6Se0.4 single crystal is investigated around superconducting transition region in different magnetic fields. The thermally activated energy (TAE) is analysed using the Arrhenius relation and modified thermally activated flux flow (TAFF) model. The results indicate that the Arrhenius curve slopes are directly related to but not equal to TAE. Therefore, use of the modified TAFF model is suggested, ρ(T,B) = ρ0f exp(−U/T), where the temperature dependence of the pre-factor ρ0f = 2ρcU/T and the nonlinear relation of the TAE should be considered. The modified TAFF method results are in good agreement with the very high critical current density values from the experimental data. It was found that the vortex glass has a narrow region, and it depends weakly on magnetic field. The vortex phase diagram was determined based on the evolution of the vortex-glass transition temperature with magnetic field and the upper critical field.

Nanoscale-phase-separation–enhanced critical current and vortex transition temperature in K0.62Fe1.71Se2 crystals

The critical current and vortex glass (VG) transition of K0.62Fe1.71Se2 crystal have been studied via measuring the current-voltage characteristics by rotating the crystal around its c-axis in magnetic fields parallel to the ab-plane. It is found that the curves show a good three-dimensional VG scaling collapse. The and VG transition temperature exhibit a distinct fourfold symmetry due to the in-plane fourfold superconducting stripe structure in the nanoscale phase-separated system. The is clearly enhanced for fields parallel to the superconducting stripe owning to the increased pinning associated with the nanoscale phase separation.

Unveiling of Bragg glass to vortex glass transition by an ac driving force in a single crystal of Yb3Rh4Sn13

We present here some striking discrepancies in the results of ac and dc magnetization measurements performed in a single crystal of a low-Tc superconductor, Yb3Rh4Sn13. The fingerprint of a transition from an ordered vortex lattice a la Bragg glass (BG) phase to a partially disordered vortex glass (VG)-like phase is unearthed under the influence of an ac driving force present inevitably in the isothermal ac susceptibility () measurements. In contrast to its well-known effect of improving the state of spatial order in the vortex matter, the ac drive is surprisingly found to promote disorder by helping the BG-to-VG transition to occur at a lower field value in this compound. On the other hand, the isothermal dc magnetization (M–H) scans, devoid of such a driving force, do not reveal this transition; they instead yield the signature of another order–disorder transition at elevated fields, i.e., peak effect (PE), located substantially above the BG-to-VG transition observed in runs. Further, the evolution of the PE feature with increasing field as observed in isofield ac susceptibility () plots indicates the emergence of an ordered vortex configuration (BG) from a disordered phase above a certain field, H* (∼4 kOe). Below H*, the vortex matter created via field cooling (FC) is found to be better spatially ordered than that prepared in zero field-cooled (ZFC) mode. This is contrary to the usual behavior anticipated near the high–field order-disorder transition (PE), wherein an FC state is supposed to be a supercooled disordered phase and the ZFC state is comparatively better ordered.