Introduction

Significant advances towards high performing Fe-based superconducting materials (FeSCs) have been made so far, because the combination of reasonable value of critical temperature (Tc), extremely high upper critical field (Hc2) on the order of 100 T, high intrinsic pinning potential, low anisotropy (generally between 1-8) and high irreversible field (Hirr) makes this class of superconductors particularly attractive for large current and high field applications, where the critical current density (Jc) is a major limiting factor1,2,3,4,5,6,7,8,9,10,11,12,13,14. Therefore, improvement in Jc by using various methods has also been one of the most important topics in the superconductivity research field. Texturing procedures, ion implantation/irradiation and chemical doping are the most common approaches to enhancing Jc in different superconductors. Although Jc values can be improved by these methods, the major drawbacks are that Jc decays rapidly in high fields, especially at high temperatures. Therefore, the Jc values of the Fe-based superconductors at high fields and temperatures need to be improved. Furthermore, Tc and low field Jc deteriorate significantly for various types of superconductors under these approaches, which make them rather impractical for application. The reported enhancement in Jc values at high fields and temperatures is still not more than one order of magnitude.5,15,16,17,18,19,20,21,22. Generally, the requirements for enhancing Jc in superconductors include Tc enhancement, which can increase the effective superconducting volume and the formation of more effective point pinning centres (related to the pinning mechanism).

Hydrostatic pressure has many significant impacts on Fe-based superconductors. For instance, pressure can raise the onset Tc up to 50 K at 1.5 Gpa for LaFeAsOδ23. The application of pressure on BaFe1.92Co0.08As2 results in a very strong enhancement of Tc from 11 to 21 K at 2.5 Gpa24. For Co-doped NaFeAs, enhancement in Tc is more than 14 K at 2.5 GPa due to optimization of the structural parameters of the FeAs layers25. The Tc of FeSe is enhanced up to 37 K at 7 Gpa26. Furthermore, pressure can induce reduction in anisotropy, more effective point pinning centres and enhancement in Tc. We already anticipated in our previous case study that the most significant approach to enhancing Jc, particularly at high fields and temperatures, without degradation of Tc, is the use of hydrostatic pressure27.

Most recent research regarding Jc enhancement and pinning mechanisms is mainly focused on the 1111 system (RFeAsO, where R is a rare earth element), the 122 system (BaFe2As2, Ba0.5K0.5Fe2As2) and the iron chalcogenide 11 system. Only one report has revealed the nature of the pinning mechanism in LiFeAs (111 type FeSCs) so far, despite its simple structure and reasonable Tc value as compared to the 1111 and 122 types28. NaFeAs (Tc ≈ 10 K) experiences three successive phase transitions around 52, 41 and 23 K, which can be related to structural, magnetic and superconducting transitions, respectively29,30,31. Bulk superconductivity in NaFeAs with Tc of ~ 20 K can be achieved by the substitution of Co on Fe sites, which can suppress both magnetism and structural distortion25,32. The Tc of NaFe0.97Co0.03As single crystal is more sensitive to hydrostatic pressure as compared to other 11 and 111 Fe-based superconductors and it has a large positive pressure coefficient25. In addition, Jc values for Co-doped NaFeAs compounds have not been reported so far. Therefore, it is very interesting to see if the hydrostatic pressure can significantly improve the flux pinning for such compounds. High-quality NaFe0.97Co0.03As single crystals were grown by the conventional high temperature solution growth method using the NaAs self-flux technique30. In this communication, we report that hydrostatic pressure can enhance the Jc by more than 100 times at high fields at 12 K and 14 K in NaFe0.97Co0.03As single crystal. This is a giant enhancement of Jc and a record high to the best of our knowledge. The Hirr is improved by roughly 6 times at 14 K under P = 1 GPa.

The temperature dependence of the magnetic moment for zero-field-cooled (ZFC) and field-cooled (FC) curves at different pressures are shown in Fig. 1. The Tc increases with pressure, from 17.95 K for P = 0 GPa to 24.33 K for P = 1 GPa, with a huge pressure coefficient, i.e. dTc/dP ~ 6.36 K/GPa, which is nearly same to what we have already reported for NaFe0.97Co0.03As single crystal i.e. dTc/dP = 7.06 K·GPa−125. Interestingly, this pressure coefficient is more than two times greater than that of FeSe (3.2 K·GPa−1)33. The pressure-induced enhancement of Tc in NaFe0.97Co0.03As can be associated with the optimization of the structural parameters of the FeAs layers, including the As–Fe–As bond angle and anion height25,34.

Figure 1
figure 1

Temperature dependence of magnetic moment at different applied pressures in both ZFC and FC runs for NaFe0.97Co0.03As.

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The field dependence of Jc at different temperatures obtained from the M-H curves by using Bean’s model, at P = 0 GPa, P = 0.45 GPa and P = 1 GPa are shown in Fig. 2. Remarkably, Jc is increased significantly at both low and high fields, especially with enhancement of more than 10 times and up to more than 100 times for low and high fields at both 12 and 14 K, respectively. The significant positive effect of hydrostatic pressure on the Jc at high fields and temperatures is further reflected in Fig. 3, which shows the Jc enhancement ratio (i.e. at 12 and 14 K over a wide range of fields. We have taken the Jc value at P = 0 GPa as a reference. The Jc ratio values at both temperatures show significant improvements at low and high fields. Although this result also suggests that hydrostatic pressure is more effective at high fields and temperatures, it is worth mentioning that Jc values are well improved at zero field at a significant rate, i.e. d(lnJc)/dP = 1.6 and 2.9 GPa−1 at 12 and 14 K, respectively, as can be seen from the inset of Fig. 3. The d(lnJc)/dP values that have been found are more significant than for yttrium barium copper oxide(YBCO)35.

Figure 2
figure 2

Field dependence of Jc at different pressures (0, 0.45 and 1 GPa) at different temperatures.

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Figure 3
figure 3

Plot of versus field at 12 K and 14 K. There is a giant enhancement in Jc values at P = 1 GPa. The inset shows the plot of d(lnJc)/dP versus temperature, which demonstrates enhancement in lnJc at a rate of nearly 3 GPa−1 at 14 K at zero magnetic field.

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We also found that Hirr of NaFe0.97Co0.03As is significantly increased by pressure. As shown in Fig. 4, the Hirr values improve gradually with pressure and the Hirr value at 14 K is increased from 2.6 T at P = 0 GPa up to 8.67 T at P = 0.45 GPa and roughly more than 13 T at P = 1 GPa (by nearly six times).

Figure 4
figure 4

Plot of Hirr versus temperature at different pressures. Inset shows Hirr as a function of reduced temperature.

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In Fig. 5, we show the temperature dependence of Jc at 0 and 12 T under different pressures. It follows power law [Jc ∝ (1-T/Tc)β] behaviour at different pressures. According to the Ginzburg-Landau theory, the exponent β is used to identify different vortex pinning mechanisms at specified fields. It was found that β = 1 refers to non-interacting vortices and β > 1.5 corresponds to the core pinning mechanism26. The exponent β (i.e. slope of the fitting line) is found to be 1.79 and 1.85 for zero field and 2.73 and 4.28 at 12 T, at 0 and 1 GPa, respectively, which shows strong Jc dependence on pressure. The low values of β at P = 1 GPa indicate that the Jc decays rather slowly in comparison to its values at P = 0 GPa. In addition, the differences between P = 0 GPa and P = 1 GPa scaling show a real pressure effect, the factor is roughly 2, which corresponds nicely to the low-T data in inset Fig. 3.

Figure 5
figure 5

Logarithmic plot of critical current density as a function of reduced temperature at different pressures and magnetic fields.

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For polycrystalline bulks, high pressure can modify grain boundaries through reduction of the tunnelling barrier width and the tunnelling barrier height. The Wentzel-Kramers-Brillouin (WKB) approximation applied to a potential barrier gives the following simple expression36,37,38:

Where W is the barrier width, k = (2 mL)1/2/ħ is the decay constant, which depends on the barrier height L, ħ; is the Planck constant and Jc0 is the critical current density at 0 K and 0T. The relative pressure dependence of Jc can be obtained from Eq. (1) as39:

Where the compressibility in the width and height of the grain boundary are defined by and , respectively. For single crystals, we assume to a first approximation that κGB and κL are roughly comparable, respectively,to the average linear compressibility values κa = –dlna/dP (κa≈–0.029 GPa−1) and κc = –dlnc/dP (κc≈–0.065 GPa−1) of NaFe0.97Co0.03As crystal in the FeAs plane, where a and c are the in-plane and out-of-plane lattice parameters, respectively26. Therefore, we can write Eq. (2) as

By using Jc≅1.3 × 103  A/cm2 at 14 K and Jc0 ~ 105 A/cm2, we find that () ≈ 0.12 GPa−1 and (1/2) ≈ 0.14 GPa−1, so that both of them together only contribute less than 10% to the already mentioned experimental value dlnJc/dP = 2.09 GPa−1 inset of Fig. 2b). This result suggests that the origin of the significant increase in Jc(T) under pressure does not arise from the reduction of volume but mainly due to the pressure induced pinning centre phenomenon.

To gain further insight into the pressure effect on the pinning mechanism in NaFe0.97Co0.03As, the experimental results have been analysed by using collective pinning theory. There are two predominant mechanisms of core pinning, i.e. pinning, which comes from spatial variation in the charge carrier mean free path, and δTc pinning due to randomly distributed spatial variation in Tc. According to the theoretical approach proposed by Griessen et al.40, in case of pinning, whereas corresponds to δTc pinning, where Fig. 6 (Top Panel) shows a comparison between the experimental Jc values and the theoretically expected variation within the and δTc pinning mechanisms at 0.1 T and 0 T (the so-called remanent state shown by the solid symbols). The Jc(t) values have been obtained from the Jc(B) curves at various temperatures. It is found that the experimental data at P = 0 and P = 1 GPa are in good agreement with theoretical pinning. It is more likely that pinning in NaFe0.97Co0.03As originates from spatial variation of the mean free path “”. We observed similar results in BaFe1.9Ni0.1As2 and SiCl4 doped MgB2 at low fields. In addition, pinning has also been reported in FeTe0.7Se0.3 crystal41,42,43. In order to understand the nature of the pinning mechanisms in more detail, it is useful to study the variation of the vortex pinning force density, with the field. The normalized pinning force density () as a function of reduced field (H/Hirr) at P = 0 GPa and P = 0.45 GPa at 14 K is plotted in lower panel of Fig. 6. Hirr is estimated by using the criterion of Jc ~100A/cm2. We can use the Dew-Hughes formula, i.e. Fp ∝ hm(1 − hn) to fit our experimental data, where m and n are fitting parameters to describe the nature of the pinning mechanism. We found that m = 1.15 and n = 2 at 0 GPa and m = 1.1 and n = 2.1 at 0.45 GPa. According to the Dew-Hughes model, in the case of pinning for a system dominated just by point pinning, the values of the fitting parameters are m = 1 and n = 2, with the maxima occurring at hmax = 0.33, while hmax occurs at 0.20 for surface/grain boundary pinning with m = 0.5 and n = 2. In case of δTc pinning, hmax shifts to higher values and the fitting parameters change accordingly. Further details can be found elsewhere44. The values of m and n that were found in the present study are almost the same at 0 GPa and 0.45 GPa, so normal core point pinning is dominant in our material.

Figure 6
figure 6

Top panel shows normalized temperature dependence (t = T/Tc) of normalized measured Jc at 0.1 T and 0 T, in good agreement with δl pinning. Lower panel shows plots of Fp vs H/Hirr at P = 0 GPa and P = 0.45 GPa at 14 K. The experimental data is fitted through the Dew-Hughes model and the parameters are given in inset.

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Pressure can enhance the pinning force strength by a significant amount in NaFe0.97Co0.03As single crystal. The pinning force density as a function of field at 12 K and 14 K is plotted in Fig. 7. At high field and pressures, the Fp is found to be over 20 and 80 times higher than at 0 GPa at 12 and 14 K, respectively. Furthermore, pressure induces more point pinning centres at 12 K and 14 K, especially at P = 1 GPa, as can be seen in the inset of Fig. 7. The number density of randomly distributed effective pinning centres (Np) can be calculated from the following relation:

Figure 7
figure 7

Pinning force density (Fp) as a function of field at P = 0 GPa and P = 1 GPa at 12 K and 14 K. The inset shows the temperature dependence of the pinning centre number density at the different pressures.

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Where ΣFP is the aggregated pinning force density, is the maximum normalized elementary pinning force (fp) and η is an efficiency factor. The η value is 1 in the case of a plastic lattice and the η value is otherwise where B is the bulk modulus of the material45. We can assume that η = 1, as pressure can shrink lattice parameters. The inset of Fig. 7 shows the Np versus temperature plot at P = 0 and P = 1 GPa. The Np values are found to be much greater at 14 K at P = 1 GPa as compared to Np at P = 0 GPa (nearly six times as great). It is well known that hydrostatic pressure induces pinning centres which, in turn, leads to huge values of Jc and increase in Np at P = 1 Gpa is a direct evidence of that27,46,47,48. This is further verified in Fig. 8, which shows the plot of versus reduced field (i.e. H/Hirr) at P = 0 GPa and P = 1 GPa for 14 K and P = 0 GPa & P = 0.45 GPa for 12 K. Obviously, the hump or secondary peak effect observed at high pressures suggests that the Jc enhancement is due to induced pinning centres.

Figure 8
figure 8

Reduced field dependence of the normalized Jc at 14 K for different pressures. The inset shows the same plot for 12 K at P = 0 GPa and P = 0.45 GPa.

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Additionally, we found a pronounced reduction in the superconducting anisotropy at high temperatures, by almost 63% at P = 1 GPa. The pressure dependence of the Tc, volume (V) and anisotropy (γ) are interconnected through a relation49:.

At ΔP = 1 GPa, ΔV(Tc)/V(Tc) is estimated to be –0.02, as ΔV/V = –ΔP/B, where B is the bulk modulus. We can use the bulk modulus (B≈52.3 GPa) of a similar superconductor, i.e. Na1-xFeAs34. The value of γ at P = 1 GPa is found to be 63% less than its value at P = 0 GPa.

Hydrostatic pressure can significantly enhance Jc by up to 102 times in NaFe0.97Co0.03As single crystals, which is a record high enhancement. The most significant enhancement in in-field performance of NaFe0.97Co0.03As in terms of pinning force density (Fp) is found at P = 1 GPa in particular, where the Fp at high fields is over 20 and 80 times higher at 12 and 14 K, respectively, than at 0 GPa. The hydrostatic pressure induces more effective point pinning centres and Np at 1 GPa is almost two times higher at 12 K and over six times higher at 14 K compared to the value at 0 GPa. Moreover, a hump or secondary peak effect is found from the plot of the normalized Jc as a function of reduced field. Therefore, this giant enhancement in Jc values for NaFe0.97Co0.03As exists because of more pinning centres induced by pressure and the increase in pinning strength as well. The present study indicates that the supercurrent carrying ability in the Fe111 can be further and significantly increased by the proposed hydrostatic pressure technique. Our results were achived in single crystal samples, which means that the enhancement is intrinsic and more significant than other reported approaches. It gives us high expections that the tapes or wires made by the same compounds should carry higher supercurrents using the hydrostatic pressure than those at ambient pressure.

Experimental

High-quality single crystals of NaFe0.97Co0.03As have been grown by use of the NaAs flux method. NaAs was obtained by reacting the mixture of the elemental Na and As in anevacuated quartz tube at 200°C for 10 h. Then NaAs, Fe and Co powders were carefully weighed according to the ratio of NaAs:Fe:Co = 4:0.972:0.028 and thoroughly ground. The mixtures were put into alumina crucibles and then sealed in iron crucibles under 1.5 atm of highly pure argon gas. The sealed crucibles were heated to 950°C at a rate of 60 °C/h in the tube furnace filled with the inert atmosphere and kept at 950 °C for 10 h and then cooled slowly to 600 °C at 3 °C/h to grow single crystals.

The temperature dependence of the magnetic moments and the M-H loops at different temperatures and pressures were performed on Quantum Design Physical Property Measurement System (QD PPMS 14 T) by using Vibrating Sample Magnetometer (VSM). We have used HMD High Pressure cell and Daphne 7373 oil as a pressure transmitting medium to apply hydrostatic pressure on a sample. The critical current density was calculated by using the Bean approximation.

Additional Information

How to cite this article: 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; doi: 10.1038/srep10606 (2015).