Abstract
Strong pinning depends on the pinning force strength and number density of effective defects. Using the hydrostatic pressure method, we demonstrate here that hydrostatic pressure of 1.2 GPa can significantly enhance flux pinning or the critical current density (Jc) of optimally doped Ba0.6K0.4Fe2As2 crystals by a factor of up to 5 in both low and high fields, which is generally rare with other Jc enhancement techniques. At 4.1 K, high pressure can significantly enhance Jc from 5 × 105A/cm2 to nearly 106A/cm2 at 2 T, and from 2 × 105A/cm2 to nearly 5.5 × 105A/cm2 at 12 T. Our systematic analysis of the flux pinning mechanism indicates that both the pinning centre number density and the pinning force are greatly increased by the pressure and enhance the pinning. This study also shows that superconducting performance in terms of flux pinning or Jc for optimally doped superconducting materials can be further improved by using pressure.
Similar content being viewed by others
Introduction
Flux pinning has been a topic of much interest in the field of superconductivity because of its importance for applications and aspects of fundamental physics. This interest stems from the significance of flux pinning for high critical current density (Jc) in superconductors, which is the defining property of a superconductor. Generally, various types of random imperfections, such as cold-work-induced dislocations, secondary-phase precipitates, defects induced by high energy ion irradiation, etc., can be used to enhance flux pinning. Unfortunately, it is difficult to discern the maximum potential of a superconductor from these techniques, and the outcomes hold up only to a certain level. Furthermore, the critical current is only enhanced, in most cases, either in low or high fields, but not in both, while degradation of the superconducting critical temperature (Tc) is another drawback. For instance, proton irradiation can only enhance flux pinning in high fields by inducing point defects in K:Ba122 1. Similarly, light ion C4+ irradiation of Ba122:Ni crystals can only enhance Jc in low fields at high temperatures2. High energy particle irradiation can also decrease the critical superconducting temperature (Tc) by more than 5 K for cobalt and nickel doped Ba-122 3,4.
As is well known, Jc is mostly limited by weak links (in the case of polycrystalline bulks), and thermally activated flux creep (an intrinsic property) emerges from weak pinning5,6,7,8,9,10,11. Strong pinning can be achieved by inducing effective pinning centres with strong pinning force. Our previous results show that Jc is enhanced significantly under hydrostatic pressure in high fields (i.e., over one order of magnitude) in comparison to low fields, along with enhancement of the closely related Tc by more than 5 K in Sr4V2O6Fe2As2 polycrystalline bulks and NaFe0.97Co0.03As single crystals12,13. Until now, however, it has been unclear whether the observed Jc enhancement under pressure is correlated with improved Tc or flux pinning. The primary motivation for the present work is to use optimally doped single crystal samples (which have an unchanged Tc under hydrostatic pressure) to elucidate the contributions of flux pinning to Jc enhancement in Fe-based superconductors. The secondary motivation is to investigate further the contributions from both the pinning centre number density (Np) and the pinning force (Fp) to strong pinning.
The argument is as follows: Hydrostatic pressure can induce pinning centres, which, in turn, enhance the pinning force. The total pinning force and the pinning centres are correlated by Fp = Npfp where Np is the number density of pinning centres and fp is the elementary pinning force, defined as the maximum pinning strength of an individual pinning centre, with a value that depends on the interaction of the flux line with the defect. According to the flux pinning theory, strongly interacting defects can contribute to Fp individually, provided that Fp ∝ Np, and weakly interacting defects can contribute only collectively; the collective theory therefore gives Fp ∝ (Np)2 for small defect numbers14.
K:Ba122 compound is believed to be the most technologically suitable because of its isotropic nature and high Tc, upper critical field (Hc2), and Jc values (Jc > 106 A/cm2 at 2 K and 0 T)15,16,17,18,19. According to the Ginzburg-Landau theory, the depairing current density (Jd) is the maximum current density that superconducting electrons can support before de-pairing of Cooper pairs, and is given as
where Φo is the flux quantum and μo is the permeability constant. The Jd value that is found is roughly 0.3 GA/cm2 by using the following values of the penetration depth, λ = 105 nm and the coherence length, ξ = 2.7 nm20,21. Our estimation indicates that there is a considerable potential to further enhance flux pinning in (Ba,K)Fe2As2.
In this paper, we investigate the flux pinning of optimally doped (Ba,K)Fe2As2 under hydrostatic pressure. We demonstrate that hydrostatic pressure causes little change in Tc, but leads to significant enhancement in flux pinning or Jc by a factor of 5 in both low and high fields in optimally doped Ba0.6K0.4Fe2As2 crystals. At 4.1 K, high pressure can significantly enhance Jc from 5 × 105A/cm2 to nearly 106A/cm2 at 2 T and from 2 × 105A/cm2 to nearly 5.5 × 105A/cm2 at 12 T. Our systematic analysis shows that the both Np and Fp are increased by the pressure and contribute to strong pinning.
Figure 1 shows the temperature dependence of the magnetic moments for zero-field-cooled (ZFC) and field-cooled (FC) measurements at different pressures. Tc remains almost unchanged at different pressures. Tc ≈ 37.95 K was found at P = 0 GPa and P = 1 GPa. Similar results were also reported for Ba0.6K0.4Fe2As2 thin film22. Furthermore, a temperature independent magnetic moment at low temperatures was observed, along-with a small transition width, indicating the high quality of the crystals.
The field dependence of Jc at different temperatures (4.1, 16, and 24 K) and pressures (0 and 1.2 GPa), obtained from the magnetic hysteresis (M-H) curves by using Bean’s model, are shown in Fig. 2. Nearly five-fold Jc enhancement can be seen at 16 K and 24 K in both low and high fields at P = 1.2 GPa. It is noteworthy that Jc is enhanced for the Ba0.6K0.4Fe2As2 crystal at 1.2 GPa in both low and high fields. This has not been found with the other approaches for pinning enhancement reported so far. At 16 K and self-field, the Jc is 2 × 105A/cm2 and it increases up to 6 × 105A/cm2 under pressure of 1.2 Gpa, with as high a value as 3 × 105A/cm2 retained at 12 T. At 24 K, Jc at zero field is 9 × 104A/cm2 which increases to 2.5 × 105A/cm2 at P = 1.2 Gpa, with the same value retained at 12 T. At 4.1 K, the Jc is nearly 1 × 106A/cm2 at 2 T and 5 × 105A/cm2 at 12 T under P = 1.2 GPa.
The pinning force (Fp = Jc × B) as a function of field at 8 K, 12 K, 24 K, and 28 K is shown in Fig. 3 23. At high fields and pressures, the Fp is found to be nearly 5 times higher at 8, 12, 24, and 28 K as compared to the corresponding value at P = 0 GPa, which agrees nicely with the Jc enhancement results. Figure 4 shows a comparison of Fp obtained in our Ba0.6K0.4Fe2As2 under pressure with those of several other low and high temperature superconducting materials24,25,26,27. The (Ba,K)Fe2As2 shows better in-field performance under pressure. Pressure can significantly improve Fp values to greater than 60 GN/m3 at H > 10 T, which are even superior to those of Nb3Sn and NbTi.
With respect to the Np, pressure can also increase the number of point pinning centres (point defects), which can suppress thermally activated flux creep, leading to Jc enhancement12. Np is calculated by using the following equation28:
where ∑Fp is the accumulated pinning force density, is the maximum elementary pinning force (fp), which is the interaction between a flux line and a single defect, and η is an efficiency factor. η = 1 corresponds to a plastic lattice, and the η value is otherwise where B is the bulk modulus of the sample. We assume to a second order of approximation that the interaction between a flux line and a single defect is nearly the same under pressure. Therefore, we can use ≈ 3 × 10−13N for a similar superconductor (i.e., Ba122:Co) to estimate Np 29. At 4.1 K, Np ≈ 7.3 × 1024m−3 at P = 0 Gpa, which increases to Np ≈ 1.2 × 1025m−3 for P = 1.2 GPa, while at 24 K, Np ≈ 6.6 × 1023m−3 at P = 0 Gpa, which increases to Np ≈ 3.8 × 1024/m3 for P = 1.2 GPa.
In order to examine if the pinning force enhancement is the major factor responsible for the observed Jc enhancement in our crystal under pressure, we have calculated the differences in the ratios of and and plot the results in Fig. 5 as a function of field. Analysis of the data, acquired at different temperatures, leads to values of nearly zero. This result indicates that Jc enhancement is only related to pinning force enhancement.
To examine whether the observed Jc enhancement is likely to be affected by volume change of the samples under high pressure, we have performed the following analysis. According to the Wentzel-Kramers-Brillouin (WKB) approximation, high pressure can affect the grain boundaries by reducing the tunnelling barrier width (W) and the tunnelling barrier height (L) for polycrystalline bulks, in accordance with the following simple mathematical expression30,31,32:
here k = (2 mL)1/2/ corresponds to the decay constant, where is the reduced Planck constant, and Jc0 is the critical current density at 0 K and 0 T. The relative pressure dependence of Jc can be determined from Eq. (3) as33:
The reduction in the width and height of the grain boundaries can be written as and , respectively.
We can use this model for the (Ba,K)Fe2As2 single crystals, by assuming to a first approximation that κGB and κL can be nearly equated to the average linear compressibility values κa = −dlna/dP (κa ≈ 0.00318 GPa−1) and κc = −dlnc/dP (κc ≈ 0.00622 GPa−1), respectively, in the FeAs plane, where a and c are the in-plane and out-of-plane lattice parameters34. Consequently, Eq. (4) can be modified as
By using Jc ≈ 105A/cm2 at 24 K and Jc0 ≈ 106A/cm2, ≈ 0.0073 GPa−1 and (1/2 ) ≈ 0.0071 GPa−1, which contribute collectively not more than 2% of the experimentally obtained value, i.e., dlnJc/dP = 0.92 GPa−1 from the inset of Fig. 5. This illustrates that the source of the flux pinning under pressure is not the volume change.
The Jc value vs. reduced temperature (i.e. 1-T/Tc) at 0 and 10 T under different pressures is shown in Fig. 6. The data points in different fields and pressures follow a power law description [i.e. Jc ∝ (1 − T/Tc)β], where β is a critical exponent35,36,37. At specific fields, Ginzburg-Landau theory predicts distinct vortex pinning mechanisms, with different values of exponent β. For example β = 1 corresponds to non-interacting vortices and β ≥ 1.5 corresponds to the core pinning mechanism. Our value of β ~ 1.74 and 1.85 for zero field, and β ~ 1.20 and 1.43 at 10 T, at 0 and 1.2 GPa, respectively, reveal a robust dependence of Jc on pressure. The low β values at high pressure show the weak field dependences of Jc in contrast to its values at low pressure. Different values of exponent β have also been observed in MgB2 and yttrium barium copper oxide (YBCO)38,39.
The pinning mechanisms in Ba0.6K0.4Fe2As2 have been examined in the frame of collective pinning theory. Generally, core pinning comprises 1) δl pinning, which comes from spatial variation in the charge carrier mean free path, l, and 2) δTc pinning due to randomly distributed spatial variation in Tc.
Referring to the Griessen et al. approach:
corresponds to pinning, while
applies in the case of δTc pinning, where t = T/Tc 40. Figure 7 shows almost perfect overlapping of the experimentally obtained Jc values and the theoretically expected variation in the δl pinning mechanism at 0.05 T. This is in agreement with the observation of little change in Tc under high pressure. We also observed similar results in BaFe1.9Ni0.1As2 and SiCl4 doped MgB2 41,42. Furthermore, δl pinning has also been reported in FeTe0.7Se0.3 crystals43.
In conclusion, we have systematically examined the flux pinning in optimally doped Ba0.6K0.4Fe2As2 crystal under hydrostatic pressure, analyzing the critical current density that was determined experimentally. We have demonstrated that strong flux pinning in both low and high fields can be achieved by improving the pinning force under pressure. The pressure of 1.2 GPa improved the Fp by nearly 5 times at 8, 12, 24, and 28 K, which can increase Jc by nearly two-fold at 4.1 K and five-fold at 16 K and 24 K over a wide range of fields. This study also demonstrates that the performance of an optimally doped superconductor in both low and high fields can also be further enhanced by pressure.
Experimental
High quality 122 crystals were grown by the flux method. The pure elements Ba, K, Fe, As, and Sn were mixed in a mol ratio of Ba1−xKxFe2As2:Sn = 1:45–50. A crucible with a lid was used to control the evaporation loss of potassium along with that of arsenic during growth. The crucible was sealed in a quartz ampoule filled with Ar and loaded into a box furnace15. The M-H loops at different temperatures and pressures and the temperature dependence of the magnetic moments were measured on a Quantum Design Physical Properties Measurement System (QD PPMS 14 T) by using the Vibrating Sample Magnetometer (VSM) option. We used an HMD high pressure cell and Daphne 7373 oil as the medium for applying hydrostatic pressure on our samples. Further details can be found in pressure cell manual i.e. Quantum Design (QD) High Pressure Cell User Manual for use with the QD VSM, No. CC-Spr-Φ8.5D-MC4. The magnetic fields were applied parallel (H//ab) to the ab-plane of the samples.
Additional Information
How to cite this article: Shabbir, B. et al. Study of flux pinning mechanism under hydrostatic pressure in optimally doped (Ba,K)Fe2As2 single crystals. Sci. Rep. 6, 23044; doi: 10.1038/srep23044 (2016).
References
Kihlstrom, K. J. et al. High-field critical current enhancement by irradiation induced correlated and random defects in (Ba0.6K0.4)Fe2As2 . Appl. Phys. Lett. 103, 202601 (2013).
Shahbazi, M. et al. Simulation of Light C4+ Ion Irradiation and Its Enhancement to the Critical Current Density in BaFe1.9Ni0.1As2 Single Crystals. Science of Advanced Materials 6, 1650–1654 (2014).
Tamegai, T. et al. Effects of particle irradiations on vortex states in iron-based superconductors. Supercond. Sci. and Technol. 25, 084008 (2012).
Kim, H. et al. London penetration depth in Ba(Fe1−xTx)2As2 (T = Co and Ni) superconductors irradiated with heavy ions. Phys. Rev. B 82, 060518 (2010).
Yang, P. & Lieber, C. M. Nanorod-Superconductor Composites: A Pathway to Materials with High Critical Current Densities. Science 273, 1836–1840 (1996).
Chong, I. et al. High Critical-Current Density in the Heavily Pb-Doped Bi2Sr2CaCu2O8+δ Superconductor: Generation of Efficient Pinning Centers. Science 276, 770–773 (1997).
Dai, H., Yoon, S., Liu, J., Budhani, R. C. & Lieber, C. M. Simultaneous Observation of Columnar Defects and Magnetic Flux Lines in High-Temperature Bi2Sr2CaCu2O8 Superconductors. Science 265, 1552–1555 (1994).
Bishop, D. J. Flux Lattice Melting. Science 273, 1811 (1996).
Blatter, G., Feigel’man, M. V., Geshkenbein, V. B., Larkin, A. I. & Vinokur, V. M. Vortices in high-temperature superconductors. Reviews of Modern Physics 66, 1125–1388 (1994).
Wang, X., Ghorbani, S. R., Peleckis, G. & Dou, S. Very High Critical Field and Superior J c -Field Performance in NdFeAsO0.82F0.18 with T c of 51 K. Advanced Materials 21, 236–239 (2009).
Ma, Y. Progress in wire fabrication of iron-based superconductors. Supercond. Sci. and Technol. 25, 113001 (2012).
Shabbir, B. et al. Hydrostatic pressure: A very effective approach to significantly enhance critical current density in granular iron pnictide superconductors. Sci Rep 5, 8213 (2015).
Shabbir, B. et al. Giant enhancement in critical current density, up to a hundredfold, in superconducting NaFe0.97Co0.03 As single crystals under hydrostatic pressure. Sci Rep 5, 10606 (2015).
Kerchner, H. R., Christen, D. K., Klabunde, C. E., Sekula, S. T. & Coltman, R. R. Low-temperature irradiation study of flux-line pinning in type-II superconductors. Phys. Rev. B 27, 5467–5478 (1983).
Ni, N. et al. Effects of Co substitution on thermodynamic and transport properties and anisotropic H c2 in Ba(Fe1−xCox)2As2 single crystals. Phys. Rev. B 78, 214515 (2008).
Wang, X.-L. et al. Very strong intrinsic flux pinning and vortex avalanches in (Ba,K)Fe2As2 superconducting single crystals. Phys. Rev. B 82, 024525 (2010).
Weiss, J. D. et al. High intergrain critical current density in fine-grain (Ba0.6K0.4)Fe2As2 wires and bulks. Nat Mater 11, 682–685 (2012).
Fang, L. et al. High, magnetic field independent critical currents in (Ba,K)Fe2As2 crystals. Appl. Phys. Lett. 101, 012601 (2012).
Katase, T., Hiramatsu, H., Kamiya, T. & Hosono, H. High Critical Current Density of 4 MA/cm2 in Co-Doped BaFe2As2 Epitaxial Films Grown on (La,Sr)(Al,Ta)O3 Substrates without Buffer Layers. Appl. Phys. Exp. 3, 063101 (2010).
Ren, C. et al. Evidence for Two Energy Gaps in Superconducting (Ba0.6K0.4)Fe2As2 Single Crystals and the Breakdown of the Uemura Plot. Phys. Rev. Lett. 101, 257006 (2008).
Shahbazi, M. et al. Magnetoresistance, critical current density, and magnetic flux pinning mechanism in nickel doped BaFe2As2 single crystals. Journal of Applied Physics 109, 07E151 (2011).
Park, E., Hoon, L. N., Nam, K. W. & Park, T. Pressure effects on the superconducting thin film Ba1−xKxFe2As2 . Appl. Phys. Lett. 101, 042601 (2012).
Dew-Hughes, D. Flux pinning mechanisms in type II superconductors. Philosophical Magazine 30, 293–305 (1974).
Miura, M. et al. Strongly enhanced flux pinning in one-step deposition of BaFe2(As0.66P0.33)2 superconductor films with uniformly dispersed BaZrO3 nanoparticles. Nat Commun 4, 2499 (2013).
Godeke, A. A review of the properties of Nb3Sn and their variation with A15 composition, morphology and strain state. Supercond. Sci. Technol. 19, R68 (2006).
Cooley, L. D., Lee, P. J. & Larbalestier, D. C. Flux-pinning mechanism of proximity-coupled planar defects in conventional superconductors: Evidence that magnetic pinning is the dominant pinning mechanism in niobium-titanium alloy. Phys. Rev. B 53, 6638–6652 (1996).
Si, W. et al. High current superconductivity in FeSe0.5Te0.5-coated conductors at 30 tesla. Nat Commun 4, 1347 (2013).
Colliongs, E. W. Applied Superconductivity: Metallurgy, and Physics of Titanium Alloys Vol. 2: Applications. Springer: N. Y. (1986).
van der Beek, C. J. et al. Vortex pinning: A probe for nanoscale disorder in iron-based superconductors. Physica B: Condensed Matter 407, 1746–1749 (2012).
Halbritter, J. Pair weakening and tunnel channels at cuprate interfaces. Phys. Rev. B 46, 14861–14871 (1992).
Tomita, T., Schilling, J. S., Chen, L., Veal, B. W. & Claus, H. Pressure-induced enhancement of the critical current density in superconducting YBa2Cu3Ox bicrystalline rings. Phys. Rev. B 74, 064517 (2006).
Browning, N. D. et al. The atomic origins of reduced critical currents at [001] tilt grain boundaries in YBa2Cu3O7−δ thin films. Physica C: Superconductivity 294, 183–193 (1998).
Tomita, T., Schilling, J. S., Chen, L., Veal, B. W. & Claus, H. Enhancement of the Critical Current Density of YBa2Cu3Ox Superconductors under Hydrostatic Pressure. Phys. Rev. Lett. 96, 077001 (2006).
Kimber, S. A. J. et al. Similarities between structural distortions under pressure and chemical doping in superconducting BaFe2As2 . Nat Mater 8, 471–475 (2009).
Cyrot, M. Ginzburg-Landau theory for superconductors. Reports on Progress in Physics 36, 103 (1973).
Djupmyr, M., Soltan, S., Habermeier, H. U. & Albrecht, J. Temperature-dependent critical currents in superconducting YBa2Cu3O7-δ and ferromagnetic La2/3Ca1/3MnO3 hybrid structures. Phys. Rev. B 80, 184507 (2009).
Pan, V. et al. Supercurrent transport in YBCO epitaxial thin films in a dc magnetic field. Phys. Rev. B 73, 054508 (2006).
Albrecht, J., Djupmyr, M. & Brück, S. Universal temperature scaling of flux line pinning in high-temperature superconducting thin films. Journal of Physics: Condensed Matter 19, 216211 (2007).
Shabbir, B., Wang, X. L., Ghorbani, S. R., Dou, S. X. & Xiang, F. Hydrostatic pressure induced transition from δT c to δℓ pinning mechanism in MgB2 . Supercond. Sci. Technol. 28, 055001 (2015).
Griessen, R. et al. Evidence for mean free path fluctuation induced pinning in YBa2Cu3O7 and YBa2Cu4O8 films. Phys. Rev. Lett. 72, 1910–1913 (1994).
Wang, X.-L. et al. Enhancement of the in-field J c of MgB2 via SiCl4 doping. Phys. Rev. B 81, 224514 (2010).
Shahbazi, M., Wang, X. L., Choi, K. Y. & Dou, S. X. Flux pinning mechanism in BaFe1.9Ni0.1As2 single crystals: Evidence for fluctuation in mean free path induced pinning. Appl. Phys. Lett. 103, 032605 (2013).
Bonura, M., Giannini, E., Viennois, R. & Senatore, C. Temperature and time scaling of the peak-effect vortex configuration in FeTe0.7Se0.3 . Phys. Rev. B 85, 134532 (2012).
Acknowledgements
X.L.W. acknowledges the support from the Australian Research Council (ARC) through an ARC Discovery Project (DP130102956) and an ARC Professorial Future Fellowship project (FT130100778). Dr. T. Silver’s critical reading of this paper is greatly appreciated. This work is also partially supported by 111 project no. B13029.
Author information
Authors and Affiliations
Contributions
X.L.W. conceived the pressure effects and designed the experiments. B.S. performed high pressure measurements. Y.M. provided samples. X.L.W. and B.S. analysed the data and wrote the paper. S.X.D., S.Y. and L.M. contributed to the discussions of the data and the paper.
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing financial interests.
Rights and permissions
This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/
About this article
Cite this article
Shabbir, B., Wang, X., Ma, Y. et al. Study of flux pinning mechanism under hydrostatic pressure in optimally doped (Ba,K)Fe2As2 single crystals. Sci Rep 6, 23044 (2016). https://doi.org/10.1038/srep23044
Received:
Accepted:
Published:
DOI: https://doi.org/10.1038/srep23044
- Springer Nature Limited
This article is cited by
-
Effects of cobalt nanoparticles addition in Cu0.5Tl0.5-1223 superconductor composite
Journal of Electroceramics (2023)
-
Excess Conductivity Analysis of Y-Ba-Cu–O Superconductor Phases
Journal of Low Temperature Physics (2022)
-
Suppression of Superconductivity by Anharmonic Oscillations in Zn- or Ni-doped Cu0.5Tl0.5Ba2(CaMg)Cu1.5M1.5O10-δ (M=Zn, Ni) Superconductors; Evident by Magnetic Measurements
Journal of Electronic Materials (2021)
-
Study of Carrier Transfer Mechanism When Substituting Strontium at Barium Sites in CuTl-1223 Superconducting Phase
Journal of Electronic Materials (2021)
-
Thermoelectric properties of indium-doped zinc oxide sintered in an argon atmosphere
Journal of Materials Science: Materials in Electronics (2019)