Introduction

A high superconducting transition temperature (Tc), upper critical field (Hc2) and critical current density (Jc) are the three major requirements for large current and/or high magnetic field applications of superconductivity. Iron (Fe)-based superconductors discovered in 20081 are considered to satisfy these requirements because of their relatively high Tc reaching 56 K at highest2, as well as their high Hc2 exceeding 100 T3,4. In particular, materials derived from AEFe2As2 (AE = alkaline earth elements), so-called 122 – type materials, were regarded as the most promising candidates, since they possess further attractive properties, such as the small anisotropy factor (Hc2//ab/Hc2//c = γ  = 1~2)5,6, superior inter-grain connectivity7,8 and easiness in the sample synthesis etc. Various thin-films and bulk wires have been fabricated (mostly by powder-in-tube (PIT) methods) using 122-based materials9,10. To date, Jc values reach up to 106 A/cm2 for a BaFe2(As1−xPx)2 thin film (4 K, 9 T)11 and 105 A/cm2 for a Ba1−xKxFe2As2 (or Sr1−xKxFe2As2) PIT wire (4.2 K, 10 T)12,13, respectively.

While Tc and Hc2 are intrinsic material parameters and thus more or less determined by the microscopic superconducting mechanism, Jc is effectively determined by vortex pinning in single crystals or films, which is either of intrinsic or extrinsic origin. In general, the pinning force is not strong in homogeneous high-quality single crystals without defects, while introduction of artificial disorder results in enhancement of Jc. From the same point of view, in the case of Fe-based superconductors, many efforts have been paid to develop suitable materials with defect structures which give rise to strong vortex pinning, as well as to understand the fundamental pinning mechanism. As for the former, the introduction of columnar defects by irradiation with high energy particles14,15,16 or self-assembling BaFeO2 nanorods17,18 has been proven to be effective in increasing Jc. As for the latter, it is recognized that the Fe-based superconductors exhibit a second magnetization peak (SMP) in Jc19,20,21,22,23,24,25, which is associated with a peak at the finite magnetic field (H) appearing in the magnetization hysteresis loop (MHL). Thus, the study of the SMP effect is of great interest, from both academic and technological points of view.

So far, systematic doping (x) dependent studies of the Ba(Fe1−xCox)2As2 and BaFe2(As1−xPx)2 single crystals have been reported26,27,28,29. It has been shown that a doping dependence of SMP and Jc are observed and the Jc tends to be high at particular doping concentrations. As for the source of pinning, various mechanism have been proposed, including domain boundary26,30,31, compositional disorder21,29, etc., as shall be discussed later. Still, a consensus has not been reached so far. Similarly, Ba1−xKxFe2As2, the highest Tc and Hc2 material among the 122-type superconductors32,33, is also known to show SMP20,22. However, to the best of our knowledge, there has been no systematic study on the x-dependence of Jc in spite of its highest potential as a material for future applications. In this work, we report the systematic evolution of the vortex pinning behavior and Jc in the Ba1−xKxFe2As2 single crystals ranging from under- (x = 0.25) to over-doped (x = 0.52) compositions. We established a detailed x - Jc phase diagram, which is characterized by a spike-like peak at the slightly under-doped composition around x ~ 0.30. The behavior contrasts with the moderate dome-like x-dependence of the Tc with a broad maximum at x ~ 0.3 to 0.5. High Jc is apparently related to existence of the SMP which disappears at optimal- and over-doping composition. Possible mechanisms to account for the origin of the enhanced Jc will be discussed.

Results

Figure 1(a) shows the temperature (T)-dependence of the magnetic susceptibility (χ) for the Ba1−xKxFe2As2 single crystal samples measured under zero-field-cooling (ZFC) conditions with H = 10 Oe applied along the c-axis. (For a better comparison, the data are normalized by the magnitude at 5 K). The superconducting transition is sharp with ΔTc < 0.5 K except for x = 0.25, indicative of good sample quality. With increasing x, Tc increases from 27.5 K for x = 0.25 to 38.5 K for x = 0.36, then gradually decreases with further doping, down to 33 K for x = 0.52. We also performed the in-plane resistivity (ρ) measurements on these samples. The results are plotted in Fig. 1(b) (28 K ≤ T ≤ 42 K) and (c) (0 K ≤ T ≤ 300 K), respectively. We used the same color code as in Fig. 1(a). In Fig. 1(b), the superconducting transition of Ba1−xKxFe2As2 is very sharp (ΔTc < 0.5 K) and shows a x-dependence. Tc’s defined as the zero resistance T ′s are in good agreement with those defined by χ, which exhibits a dome-like shape with the broad maximum spanning from x ~ 0.3 to 0.5.

Figure 1
figure 1

(a) Temperature dependence of the magnetic susceptibility of Ba1−xKxFe2As2 (x = 0.25–0.52). (b,c) Temperature dependence of the in-plane resistivity, ρ(T), for the temperature range of 28 K to 42 K and 0 K to 300 K, respectively, with the same color cord used in (a). In (c), 30 μΩcm offset is applied for every doping increment and x dependence of room temperature resistivity, ρ(300 K), is shown in the inset. (d) Residual resistivity ρ0 and exponent n extracted from ρ(T) of the low temperature region by using a power-law fitting, ρ(T) = ρ0 + AT n.

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In Fig. 1(c), each ρ curve is shifted by 30 μΩcm to avoid an overlap. In the inset, the absolute value of ρ at 300 K, ρ(300 K), is plotted, which shows gradual decrease from 320 μΩcm (x = 0.25) to 290 μΩcm (x = 0.52). The overall shape of ρ(T) is similar with each other, which shows the saturating behavior at the high T region, in other words, S-shaped T-dependence. For x = 0.25, anomaly in ρ is observed at around 65 K due to the anti-ferromagnetic/orthorhombic phase transition. In the low-T region, ρ(T)s are well fitted by a power-law function, ρ(T) = ρ0 + AT n (the details of fitting procedure are described in Method section). The estimated residual resistivity ρ0 and exponent n are shown in Fig. 1(d), which will be discussed later.

Figure 2(a–d) show typical MHLs measured at various T with H along the c axis. Each sample represents under-doped (x = 0.25, Tc = 27.5 K), slightly under-doped (x = 0.30, Tc = 36.5 K), optimally doped (x = 0.36, Tc = 38 K) and slightly over-doped (x = 0.41, Tc = 37 K) concentration, respectively. Qualitatively, the overall features measured at T = 5 K are more or less similar to each other in that they are characterized by a sharp peak centered at H = 0 and almost symmetric shapes with respect to H. The latter property indicates the dominant contribution of bulk pinning instead of a surface barrier34. These behaviors are also seen in various Fe-based superconductors. The width of the irreversible magnetization ΔM tends to shrink with increasing x. Moreover, at higher temperatures (T > 15 K), for x = 0.25 and 0.30, M increases with H after the initial decrease in the low H region, indicative of the SMP. The broad peaks are evident above 19 K for x = 0.25 and 30 K for x = 0.30, respectively. The position of the SMP moves towards higher H as T decreases and eventually goes beyond the accessible field range, H = 7 T in the present case. In contrast, for x = 0.36 and 0.41, M decreases monotonically with H at all T.

Figure 2
figure 2

(a–d) Magnetization hysteresis loops (MHL) of Ba1−xKxFe2As2 with x = 0.25, 0.30, 0.36 and 0.41 measured at several temperatures. (e,f) Magnetic field and temperature dependence of the critical current density Jc determined by the Bean model from the MHL shown in (a–d), respectively. Dashed horizontal lines indicate the practical-level of Jc = 105 A/cm2.

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To determine Jc from the MHLs, we employed the extended Bean model35, Jc = 20▵M/[w(1 − w/3l)], where w and l are the dimensions of the rectangular sample (w < l). Figure 2(e–h) show the H-dependent Jc corresponding to the compositions shown in Fig. 2(a–d). The dashed lines indicate Jc = 105 A/cm2, which is a threshold value for practical applications. At T = 5 K, Jc is the order of 106 A/cm2 at zero field, 1.6 × 106 A/cm2 (x = 0.25), 3.0 × 106 A/cm2 (x = 0.30), 1.4 × 106 A/cm2 (x = 0.36) and 0.9 × 106 A/cm2 (x = 0.41), respectively. Among the four samples, Jc is the highest at x = 0.30. This crystal is slightly under-doped in terms of Tc, since Tc of the x = 0.30 sample is 36.5 K, lower than the highest Tc of 38 K at x = 0.36. The result shows that the highest Jc composition does not match the highest Tc composition in Ba1−xKxFe2As2. With increasing H, Jc decreases monotonically, while keeping high values above 105 A/cm2 up to H = 6 T, 4.6 × 105 A/cm2 (x = 0.25), 6.8 × 105 A/cm2 (x = 0.30), 2.3 × 105 A/cm2 (x = 0.36) and 1.3 × 105 A/cm2 (x = 0.41), respectively, indicating the high current-carrying ability of this system at low T.

At higher T, Jc of the x = 0.25 and 0.30 samples exhibit a non-monotonic H dependence reflecting the SMP effect. As a consequence, the x = 0.30 sample sustains Jc exceeding 105 A/cm2 even at T = 25 K and H = 6 T, showing the possibility of high magnetic field applications with an operation temperature above 20 K even without introducing artificial pinning center. On the other hand, the optimal- (x = 0.36) and over-doped (x = 0.41) samples always exhibit a monotonic decrease of Jc with H, resulting in a much lower Jc under high H.

For a more detailed comparison, H-dependence of Jc for various x’s (x = 0.25, 0.29, 0.30, 0.33, 0.36, 0.40, 0.41, 0.52) at 5 K, 15 K and 25 K are plotted in Fig. 3(a–c). For each T, Jc changes more than tenfold with changing x. At T = 5 K (Fig. 3(a)), crystals with x = 0.29 and 0.30 possess the highest Jc among all compositions. On the other hand, Jc rapidly decreases either with increasing or decreasing x. The resultant x-dependence is shown in Fig. 3(e), in which the Jc values at H = 1 and 6 T for 26 samples are plotted. A peak in Jc is observed around x = 0.30. The peak is sharp with its full width half maximum as small as 0.08. Therefore, the Jc-x phase diagram turns out to be very different from the Tc-x phase diagram which is shown in Fig. 3(d). First, the peak position is x = 0.30 for the former, while x = 0.36 for the latter. Second, Jc shows salient x-dependence, while Tc changes mildly with x.

Figure 3
figure 3

(a–c) Doping dependence of Jc as a function of magnetic field at 5 K, 15 K and 25 K for x = 0.25, 0.29, 0.30, 0.33, 0.36, 0.40, 0.41 and 0.52. (d) Doping dependence of Tc for 26 samples. (e) Jc of the 26 samples at T = 5 K, H = 1 and 6 T. (f,g) Doping dependence of Jc at T = 15 and 25 K, respectively, with H = 1, 2 and 6 T extracted from (b,c). The shaded region in panels (d–g) indicates the optimal doping region, x ~ 0.36, showing maximum Tc ~ 38.5 K.

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At 15 K (Fig. 3(b)), non-monotonic H-dependence is seen for x = 0.25, x = 0.29 and x = 0.30. For these samples, Jc first decreases with H, then increases at high H. This behavior reflects the SMP observed in the MHL. In detail, the minimum Jc value of x = 0.25 at H = 1.8 T is smaller than that of x = 0.29 and 0.30 at H = 1.5 T and 2.2 T, respectively. On the contrary, the enhancement of Jc at high field is more prominent for x = 0.25 than that of x = 0.29 and 0.30, presumably because of the strong SMP effect of x = 0.25. Consequently, for the H = 6 T result shown in Fig. 3(f), the x = 0.25 sample exhibits the highest Jc, which is due to the steep increase of Jc with field. Meanwhile, as x increases above 0.33, Jc at H = 0 becomes smaller with x and decreases monotonically with H (Fig. 3(b)). As a result, Jc remains low (typically below 105 A/cm2) in the entire H-region.

At 25 K (Fig. 3(c)), with disappearance of the SMP, Jc becomes significantly lower for x = 0.25 compared to x = 0.29 and x = 0.30. This is because the measurement T is close to Tc of the x = 0.25 sample (Tc = 27.5 K). For x = 0.29 and 0.30, non-monotonic H-dependence persists and Jc’s above 105 A/cm2 are recorded up to H = 6 T except for the small H range around 0.5 T and 1 T, respectively. On the other hand, for x = 0.33 and above, Jc decreases down to the 104 A/cm2 range, although they possess Tc much higher than the measurement T.

Discussion

As shown in Fig. 3(d–g), Jc and Tc of the Ba1−xKxFe2As2 single crystal samples show contrasting x-dependence. A distinct x-dependence of Jc and Tc is also reported for the Ba(Fe1−xCox)2As2 and BaFe2(As1−xPx)2 single crystals26,27,28,29. In both cases, Jc exhibits marked x-dependence with a peak near the left end of the superconducting dome (under-doped region), while Tc gradually changes with x. Based on the Ba(Fe1−xCox)2As2 results, R. Prozorov et al.26 ascribed the characteristic Jc behavior to intrinsic pinning on the structural domains in the orthorhombic phase, which neighbors the superconducting phase on the under-doped side. On the other hand, based on the BaFe2(As1−xPx)2 single crystal results, S. Demirdiş et al.29 and L. Fang et al.28 proposed that the inhomogeneity in dopant distribution causes a spatial fluctuation of the superconducting condensation energy (δTc pinning) and/or the mean free path (δl pinning)36. To our knowledge, most of the precedent MHL studies take the latter stance.

Existing phase diagrams of the Ba1−xKxFe2As2 system37,38 show that the orthorhombic phase disappears between x = 0.25 and 0.30, which approximately matches with the composition where the enhancement of Jc is found. In this regard, the present results are compatible with the idea that the orthorhombic structural domains are the main source of vortex pinning. On the other hand, comparing Fig. 3(d,e), one notices that the high Jc is realized where the x-dependence of Tc (defined by dTc/dx) is large. In such a situation, small compositional inhomogeneity results in large local variation in Tc, yielding δTc pinning. In addition, the possible role of δl pinning to the enhanced Jc is suggested from the x-dependence of the residual resistivity ρ0. In Fig. 1(d), exponent n decreases gradually with x from ~1.9 at x = 0.25 to ~1.6 at x = 0.40, then slightly increases to ~1.7 at x = 0.52. This result indicates that the T-linear contribution becomes large at around optimal x. However, the feature is not significant compared to BaFe2(As1−xPx)2 case39 which shows certain variation in n from 2 to 1. On the other hand, ρ0 rapidly decreases by more than twenty times from x = 0.25 to x = 0.40. In this doping range, carrier density is considered to evolve moderately, since the small change in the magnitude of ρ(300 K) as well as the small variation of n, ~1.6 < n < ~1.9, are observed. (see inset of Fig. 1(c)) Thus, it is natural to assume that the change in ρ0 comes from the change in the mean free path (l) of the carriers, not due to the change in the carrier number40. From the same point of view, the x-dependence of ρ0 in Fig. 1(d) reflects the x-dependence of l, which indicates that the δl pinning should be stronger in the under-doped samples, while it becomes weaker in the optimal- to over-doped samples. This tendency consistently explains the observed Jc behavior. Meanwhile, we should not rule out another possibility that some novel features such as quantum criticality and/or anti-ferromagnetic/orbital fluctuations are correlated with the origin of strong flux pinning of this system.

In any case, the present results clearly demonstrate that intra-grain Jc of the Ba1−xKxFe2As2 system takes the largest value at x = 0.30, which is different from the composition x = 0.40, commonly employed for fabricating PIT wires12. Although the real wires are composed of polycrystalline samples and their Jc’s are affected by the inter-grain connectivity, as well as by the presence of pinning centers introduced either intentionally or accidentally, the present results suggest that Jc of PIT wires can be further increased by tuning the composition towards the lower doping side. This highlights the importance of fine chemical tuning for establishing and broadening the application potential of the Ba1−xKxFe2As2 superconductor.

Methods

The Ba1−xKxFe2As2 single crystals with doping concentration x = 0.25–0.52 were grown by the KAs self-flux method using a stainless-steel container, following the method depicted in ref. 41. The doping concentration of the grown crystals was successfully controlled by tuning the mixing ratio of Ba and Fe in the starting compositions. In total, ten batches of Ba1−xKxFe2As2 single crystals (two batches for x ~ 0.25, two batches for x ~ 0.3, two batches for x ~ 0.33, one batch for x ~ 0.36, two batches for x ~ 0.4 and one batch for x ~ 0.5, respectively) were grown for this study in order to check the reproducibility carefully. The compositions of the single crystals were confirmed by energy-dispersive X-ray (EDX) analysis and X-ray diffraction using Cu Kα radiation. The c-axis lengths determined by the X-ray diffraction were consistent with the compositions determined by EDX. The samples were cut into rectangular shapes with typical dimensions of 1 mm (length) × 0.8 mm (width) × 0.02 mm (thickness) for the magnetization and resistivity measurements. The T- and H- dependence of the magnetization were measured using a magnetic property measurement system (MPMS, Quantum Design). The resistivity measurements were carried out by a standard four probe method using a physical property measurement system (PPMS, Quantum Design). The data are reproducible and independent of the sample batch. We therefore believe that the present results represent intrinsic property of Ba1−xKxFe2As2 system. We fitted the ρ(T) data using a power law function, ρ(T) = ρ0 + AT n, in the T range, Tc < T < Tup. The upper bound temperature (Tup) of fitting for each sample is taken well below the inflection point of S-shaped ρ(T) in order to avoid underestimation of exponent n. Since the inflection point shifts from T ~ 95 K to T ~ 80 K as x increases from x = 0.25 to x = 0.5242, Tup also gradually decreases from 80 K to 53 K.

Additional Information

How to cite this article: Song, D. et al. Distinct doping dependence of critical temperature and critical current density in Ba1−xKxFe2As2 superconductor. Sci. Rep. 6, 26671; doi: 10.1038/srep26671 (2016).