Unique defect structure and advantageous vortex pinning properties in superconducting CaKFe4As4

The lossless current-carrying capacity of a superconductor is limited by its critical current density (Jc). A key to enhance Jc towards real-life applications is engineering defect structures to optimize the pinning landscape. For iron-based superconductors considered as candidate materials for high-field applications, high Jc values have been achieved by various techniques to introduce artificial pinning centres. Here we report extraordinary vortex pinning properties in CaKFe4As4 (CaK1144) arising from the inherent defect structure. Scanning transmission electron microscopy revealed the existence of nanoscale intergrowths of the CaFe2As2 phase, which is unique to CaK1144 formed as a line compound. The Jc properties in CaK1144 are found to be distinct from other iron-based superconductors characterized by a significant anisotropy with respect to the magnetic field orientation as well as a remarkable pinning mechanism significantly enhanced with increasing temperature. We propose a comprehensive explanation of the Jc properties based on the unique intergrowths acting as pinning centres.


INTRODUCTION
Loss-free electrical transport is a unique property of superconductors that is utilized in various superconductivity applications. The figure of merit for the current-carrying capacity of a superconductor is J c , which is determined by the material's ability to trap vortices, namely, vortex pinning. 1 Consequently, J c strongly depends on the defect structure where superconductivity is locally suppressed, and the vortices have smaller energy and are therefore pinned. Thus, how to design and introduce defects is one of the key issues towards real-life applications. To date, various techniques have been developed to control defect structures, particularly through the research on high-transitiontemperature (high-T c ) cuprate superconductor YBa 2 Cu 3 O 7 (YBCO) thin films. [2][3][4][5] For example, nanoparticles/nanorods can be incorporated by alternately depositing YBCO and a nonsuperconducting (non-SC) secondary phase (e.g., Y 2 BaCuO 5 ) 6 or by adding appropriate impurities (e.g., BaZrO 3 ) to the deposition target. 7 Moreover, stacking faults and intergrowths (e.g., extra Y or CuO planes) are frequently generated near the inclusions. 8,9 Additionally, controlled artificial defects can be created by particle irradiation, 10-12 although this technique needs complex and dedicated facilities. In any case, in order to achieve suitable defect structures, the optimization of fabrication conditions such as starting chemical composition, substrate, growth temperature, growing rate, and atmosphere is indispensable, which requires tremendous efforts. Similarly, various techniques have been exploited to introduce artificial defects in iron-based superconductors (IBSs) since their discovery. 13,14 As in the case of YBCO, J c has been enhanced particularly for AEFe 2 As 2 -based (AE: alkaline-earth element) superconductors, the so-called 122 materials, by particle irradiation, 15 addition of BaZrO 3 , 16,17 fabrication of superlattices, 18 and introduction of stacking faults. 19,20 By devising the fabrication process, a significant progress has been achieved in improving J c of bulks and thin films so far, while further J c enhancement is required towards real-life applications.
Among the 122 materials, AE 1-x A x Fe 2 As 2 (A: alkali metal element) possesses the highest T c up to 38 K and largest upper critical fields (H c2 ) over 100 T with low anisotropy (γ)~1-2. These properties are advantageous for high-field applications. [21][22][23] In AE 1-x A x Fe 2 As 2 (e.g., Ba 1-x K x Fe 2 As 2 (BaK122), Fig. 1a), superconductivity is induced by substituting AE with A (hole doping), where AE and A randomly occupy the same crystallographic site in an arbitrary ratio x. Therefore, the superconducting properties, particularly J c , of AE 1-x A x Fe 2 As 2 significantly depend on x. 24 Note that the significant doping dependence of J c is common to other 122 materials with different dopant elements. [25][26][27] As a result, a fine adjustment of x is required to achieve better properties of bulks and thin films. In this study, we focus on the recently discovered 1144 materials, 28,29 AEAFe 4 As 4 , which possess T c and H c2 comparable to 122 materials. In the 1144 structure (Fig. 1b), AE and A do not occupy the same site owing to the large difference in the ionic radii (e.g., 1.21 and 1.51 Å for Ca 2+ and K + , respectively); hence, AE and A layers stack alternately along the c axis. Therefore, the 1144 material is a line compound where the Fe valence state is fixed at 2.25+. This characteristic is advantageous for applications because fluctuations in chemical composition is, in principle, not allowed. Meanwhile, for such an ordered-layered structure, 122 phases (AE122 and A122) intergrow in the CaK1144 matrix if excess of AE or A prevails during the synthesis process. Since AE122 are non-SC parent materials and A122 are superconductors with low T c < 4 K (practically non-SC), such intergrowths possibly act as vortex-pinning centres. In fact, recent studies on vortex pinning properties of CaK1144 reported unusually high J c 30 as well as vortex dynamics distinct from 122 materials, 31 while the relevant pinning mechanisms remain unsolved. This motivated us to explore the microstructure and the vortex pinning mechanisms in CaK1144. Here we demonstrate the unique defect structure in CaK1144, which provides comprehensive explanations of the sublime vortex pinning properties.

Microstructure of CaKFe4As4 single crystal
The crystal structure of the CaK1144 matrix and the unique defect structure can be directly observed by high-resolution scanning transmission electron microscopy (STEM) experiments. Figure 1c shows a low-magnification annular-dark-field (ADF)-STEM image taken along the [100] axis. Overall, the STEM image shows a uniform contrast, indicative of good homogeneity of the matrix region. Notably, characteristic bright stripes in the horizontal direction with typical lengths of~1 μm can be identified. These structures are regarded as planar defects along the ab plane, while no other defects are detected. Figure 1d shows the ADF-STEM image around one of the bright stripes. The upper right panel shows the magnified view of the CaK1144 matrix. The brightest zig-zag arrangements of dumbbells indicated by green arrows are assigned to FeAs layers. The Fe-Fe interplane distance across the two kinds of relatively dark layers (the brighter and the darker ones indicated by blue and orange arrows, respectively) was determined to be 6.1 and 7.0 Å, respectively. These values are in good agreement with the reported ones (6.12 and 6.70 Å, see Fig. 1b), indicating that the brighter and darker layers correspond to Ca and K layers, respectively. Thus, we confirmed that the alternating stacking of Ca and K layers is indeed realized in the matrix.
Next, we focus on the bright stripe magnified in the right lower panel in Fig. 1d. It reveals that the alternation of Ca and K layers is violated, while the local FeAs-layer structure is maintained. There are nine FeAs-to-FeAs units with a total thickness of about 55 Å, and each Fe-Fe interplane distance is found to be 6.1 Å, which is identical to that across the Ca layer. The chemical composition analysis shows that Ca is rich around the defect without significant changes for Fe and As (see Supplementary information). Based on the results, we conclude that the defect is a Ca122 intergrowth with dimensions of~5.5 nm (~5 unit cells) along the c axis and 1 μm along the ab-plane, which is coherently grown in the CaK1144 matrix.
Furthermore, when the microstructure of CaK1144 was carefully investigated, we found much smaller defects. In Fig. 1e, there is a thin bright line indicated by a black arrow. This defect is identified to be a monolayer Ca122 intergrowth, as shown in the right panel. Typically, such thin intergrowths have dimensions of 1-2 nm in thickness (along the c-axis) and 50-100 nm in length (along the ab-planes). Thus, the existence of Ca122 intergrowths with various sizes is revealed. Such intergrowths should have significant influence on the vortex pinning properties in CaK1144.  . The unusual T dependence of J c , namely, the 'peak effect' in J c -T, highlights a remarkable enhancement of pinning with increasing T even at temperatures well below T c , which is unique to CaK1144. It is evident that the T dependence of J c H//c of CaK1144 is distinct from that of the 122 materials. In Fig.  2e, the T dependence of J c H//c at 6 T for CaK1144 is compared with those for various 122 materials 27 ; Ba 1-x K x Fe 2 As 2 , Ba(Fe 1-x Co x ) 2 As 2 , and BaFe 2 (As 1-x P x ) 2 with different x values. Although J c H//c of CaK1144 is relatively small at low T, the maximum J c H//c = 0.17 MA/cm 2 at 20 K is comparable to the highest one reported for 122 materials. Such high J c demonstrates that the T-enhanced pinning centres trap vortices very efficiently.
Next, we show MHLs with H along the ab plane to evaluate J c for H // ab (J c H//ab ). Figure 3a shows the MHLs for CaK1144. The shape of the MHL is clearly different from that for H // c in that it shows a dip structure around self-field, which will be discussed later. Moreover, the size of the MHL monotonically decreases with increasing T in contrast to the case of H // c, suggesting a significant anisotropy in the vortex pinning properties with respect to the H orientation. Figure 3b shows the H dependence of J c H//ab derived from the MHLs. Here, we applied a simplified calculation procedure following the previous work 30  The unusually high J c H//ab in CaK1144 can be confirmed by comparing with the results of BaK122 obtained by the same procedure. Figure 3c shows the MHLs for BaK122 (x = 0.4). In contrast to the case of CaK1144, the MHLs show a peak around self-field, similar to that for H // c. Figure 3d (T p ) is almost H-independent, suggestive of a unique origin of the enhanced pinning with increasing T. At high T region (approximately above T p ), the peak in MHLs (H p ) appears in the observable H range (<7 T) similarly to BaK122, which is in general associated with the order-disorder transition of the vortex lattice. It is evident that T p and H p are well-separated in the H-T phase diagram, suggestive of the different mechanisms underlying the two types of peak effect. Now we return to the defect structure in CaK1144 to understand the anomalous J c properties. The Ca122 intergrowths observed by the STEM are schematized in Figs. 1f, g. The colour gradation indicates the difference in T c between the matrix and the defects. The intergrowths are considered to be categorized  ); and H c2 , the upper critical field along the c axis obtained from the resistivity measurements (orange circles). The dashed lines are guide for the eye into two types; (i) intergrowths which are thick (5-10 nm) along c axis and large (~1 μm) along the ab plane (Fig. 1f), and (ii) thin (1-2 nm) and small (~100 nm) ones (Fig. 1g). For the former case, the thickness is typically~5 nm, as represented by Fig. 1d, which is much larger than the c-axis coherence length (ξ c~1 nm) 36 of CaK1144. Such intergrowths are regarded as non-SC planar defects because the inner part of the intergrowths is considered to be undoped Ca122. In general, these defects act as efficient pinning centres for H // ab while they do not contribute to pinning for H // c. On the other hand, for the latter case, when the thickness is~1-2 nm, i.e., 1-2 Ca layers are inserted (Fig. 1e), holes can be supplied to the inner FeAs layers from the K layers, hence such intergrowths are considered to be SC defects. It is expected that T c of the SC defects (T c defect ) is lower than that of the CaK1144 matrix due to the depleted carrier density as in the case of underdoped BaK122. Then, T c defect is determined by the number of Ca layers in the defect, hence it likely takes discrete values. In addition, these defects terminate in a short range (<~100 nm); hence, T c abruptly changes along the ab plane around their ends. Therefore, they act as effective pinning centres not only for H // ab but also for H // c.
Among those two types of defects, the former one is considered to give rise to the unusually large J c H//ab as well as J c anisotropy as in the case of artificial superlattices in thin films. In addition, such defects can account for the dip feature in the MHLs, which has been reported for irradiated IBSs where J c is significantly enhanced. For the dip feature, two explanations have been considered: a highly inhomogeneous field distribution 37 and the anisotropy of J c . 38 Both are compatible with the properties of CaK1144. The self-field is in general inhomogeneous with strongly curved flux lines, hence the local field can not be parallel to the intergrowths in the entire sample, and thus pinning by the intergrowths is less effective at low fields. where H c is thermodynamic critical field), which is the difference of the ground state energies between the normal state and the SC state, depends on T. Because the thin intergrowths are superconducting at low T (E c defect > 0), ΔE c is likely small hence the pinning is weak. When the intergrowths turn into the normal state (E c defect = 0) with increasing T, the pinning becomes stronger owing to the larger energy gain. Thus, the thin intergrowths, i.e., the SC defects, are regarded as T-enhanced pinning centres, which possibly give rise to the increase in J c H//c with increasing T. To our knowledge, the idea of SC defects has been well-known, while the T dependence of J c in the presence of SC defects has not been sufficiently investigated. Here, we calculate the pinning force density f p using a simple model;  (Fig. 5a). Next, an example result for SC defects is shown in Fig. 5b. Here, T c defect = 25 K (corresponding to underdoped BaK122 with x~0. 25) and E c defect (0)/E c 1144 (0) = 0.6 were chosen (for the results using other parameters, see Supplementary information). In this case, ΔE c shows a weak T dependence below T c defect owing to the increase of E c defect . As a result, f p increases with increasing T, showing a peak around 20 K, which qualitatively agrees with the present observations (Fig. 2d). Note that the peak position in f p -T depends on T c defect (see Supplementary information), hence T c defect is likely correlated with T p in the H -T phase diagram (Fig. 4). In addition, the vortex lattice softens with increasing T which allows for a better accommodation of the lattice to the defect structure and hence triggers an order-disorder transition of the vortex lattice. This tendency is compatible with the appearance of second magnetization peak at higher temperatures in CaK1144. Thus, the unusual T dependence of J c in CaK1144 can be qualitatively understood by considering the SC defects unique to this material. In the present case, the feature is pronounced possibly because (i) CaK1144 is essentially a clean system as indicated by the relatively low J c at low T and (ii) Ca122 intergrowths take discrete T c defect values determined by the number of Ca layers, resulting in a single peak in T dependence of J c . However, to quantify the influence of the Ca122 intergrowths on the unusual T dependence of J c , further experimental investigations such as determination of defect density as well as more detailed theoretical calculations are desired.
To summarize, we demonstrated a clear correlation between the microstructure and the vortex pinning properties of CaK1144. The nanoscale Ca122 intergrowths inherent to CaK1144 single crystals result in an unusual T dependence of J c H//c as well as extremely large J c H//ab , distinct from other IBSs. The advantageous vortex pinning properties will offer a new route for further

Single crystal growth
Single crystals of CaK1144 were grown by the FeAs-flux method. 39 The FeAs precursor was prepared from Fe and As mixed at a ratio of 1: 1 and heated at 900 ℃ for 10 h in an evacuated quartz tube. Ca, K, and FeAs were weighed at a ratio of 1:1.1:10 and placed in a zirconia crucible, then sealed in a Ta container using an arc-welding chamber. The Ta container was sealed in an evacuated quartz tube to protect Ta from oxidation. The container was heated during 5 h to 650 ℃ and held there for 5 h. It was then heated to 1180 ℃ within 5 h and held there for another 5 h. Then, it was cooled over 5 h to 1050 ℃, followed by slow cooling to 930 ℃ for 80 h. For the single crystals used in this study, X-ray diffraction (XRD) patterns were measured at room temperature using a diffractometer with Cu Kα radiation (Rigaku, Ultima IV) to check 00 l peaks (see Supplementary information). No trace of Ca122 and K122 was observed within the resolution of XRD.

Scanning transmission electron microscopy
The microstructure of a CaK1144 single crystal was investigated using an aberration-corrected scanning transmission electron microscope (FEI, Titan cubed) at an acceleration voltage of 300 kV. The sample was prepared using a focused ion beam (Hitachi, FB-2000). The chemical composition was investigated by electron energy loss spectroscopy (EELS, Gatan, GIF Quantum ERS) and energy dispersive X-ray spectroscopy (EDS, Oxford Instruments, X-Max N 100TLE).

In-plane resistivity measurements
The in-plane resistivity ρ ab (T) (shown in the Supplementary information) was measured by a standard four-probe method using a physical property measurement system (Quantum Design). Magnetic fields up to 9 T were applied along the c axis and in the ab plane to evaluate the anisotropy of upper critical fields. As shown in the Supplementary information, the residual resistivity ratio (ρ ab (300 K)/ρ ab (40 K)) was~16, and no trace of magneto-structural phase transition of Ca122 phase was observed around 170 K. These properties meet the criteria for 'phase-pure' single crystals in ref. 39 .

Magnetization measurements
The samples for the magnetization measurements were cut into rectangular shapes. For CaK1144, the dimensions were l = 1.57 mm (length), w = 1.34 mm (width), and d = 0.035 mm (thickness). For BaK122, the dimensions were l = 1.59 mm, w = 0.764 mm, and d = 0.099 mm. The measurements were performed using a magnetic property measurement system (Quantum Design). For H // c, J c H//c was calculated using Bean's critical state model 40 ; J c H//c = 20ΔM/w(1-w/3 l) where ΔM is the width of the MHLs. For H // ab, two J c components (in-plane J c (J c H//ab ) and inter-plane J c (J c c )) contribute to M. Here, we used a simplified formula for the evaluation of J c H//ab by taking J c H//ab = J c c , i.e., J c H//ab = 20ΔM/d(1−d/3 l), following the previous study. 30 We confirmed that this simplified procedure does not alter the main conclusions in this study. For more details, see the Supplementary information where the evaluation of J c H//ab and J c c using the extended Bean's critical state model for anisotropic J c 41 is described.

DATA AVAILABILITY
The data that support the findings of this study are available from the corresponding author upon reasonable request.