Artificially engineered nanostrain in FeSexTe1-x superconductor thin films for supercurrent enhancement

Although nanoscale deformation, such as nanostrain in iron-chalcogenide (FeSexTe1−x, FST) thin films, has attracted attention owing to its enhancement of general superconducting properties, including critical current density (Jc) and critical transition temperature, the development of this technique has proven to be an extremely challenging and complex process thus far. Herein, we successfully fabricated an epitaxial FST thin film with uniformly distributed nanostrain by injection of a trace amount of CeO2 inside an FST matrix using sequential pulsed laser deposition. By means of transmission electron microscopy and geometric phase analysis, we verified that the injection of a trace amount of CeO2 forms nanoscale defects, with a nanostrained region of tensile strain (εzz ≅ 0.02) along the c-axis of the FST matrix. This nanostrained FST thin film achieves a remarkable Jc of 3.5 MA/cm2 under a self-field at 6 K and a highly enhanced Jc under the entire magnetic field with respect to those of a pristine FST thin film. The maximum amount of current that can be carried by iron-based superconductors can be improved by introducing deliberate defects during fabrication. Iron–selenium–tellurium thin films have recently been identified as high-temperature superconductors that may pass large quantities of current. Sanghan Lee from the Gwangju Institute of Science and Technology in South Korea and co-workers have now used lasers to deposit small amounts of cerium oxide atoms between layers of an iron–selenium–tellurium thin film. The cerium oxide particles create defects, such as selenium-deficient sites, that slightly strain the crystal lattice and let more current move through the film. Mapping these nanostrain effects with electron microscopy enabled the team to find conditions needed to enhance superconductivity while minimizing cerium oxide by-products. To enhance supercurrent of iron-chalcogenide (FST) superconductor thin films, we induced nanostrain in FST thin films. The nanostrain was generated around nanoscale defects which were formed by the inserted a trace amount of oxide artificially inside FST matrix during the growth of FST thin film using sequential pulsed laser deposition. In particular, the critical current density (Jc) of the nanostrained FST thin films was significantly improved without dominant degradation of critical transition temperature.


Introduction
Superconductors are essential materials for high magnetic field applications, such as those in nuclear fusion energy devices, magnetic resonance imaging, and superconducting magnetic energy storage systems. In recent years, iron-based superconductors (FeSCs) have attracted attention for use in high magnetic field applications because of their high upper-critical field (H c2 ) and low magnetic anisotropy (γ) 1,2 . Moreover, FeSC epitaxial thin films have demonstrated enhanced overall superconducting properties compared with those of the corresponding bulk materials [3][4][5][6][7][8][9] . Among several FeSCs, iron chalcogenides (FeSe x Te 1−x , FST), which are simple PbO-type chalcogenides with layered-like structures 10 , are excellent candidates for use as practical superconducting materials for several reasons. First, the critical transition temperature (T c ) of FST abruptly increases due to an Se ratio that increases with the suppression of phase separation, which is generally observed in Se-rich FST bulk, when FST is fabricated as an epitaxial thin film 11,12 . In addition, an FeSe monolayer can achieve a T c of 100 K, which is the maximum T c for FeSCs 13 . Second, FST thin films exhibit promising critical current densities (J c ), greater than 1 MA/cm 2 , under self-field regardless of the substrate, including coated conductor substrates 5,14 . This result indicates that these films can potentially be used as superconductor tape. However, J c enhancement via an artificial pinning center is a critical requirement for use of FST in high magnetic field applications.
Several approaches have been used to improve the J c of FST to date, such as the use of a buffer layer 14 , oxygen annealing 15 , and ion irradiation 16,17 . In particular, low-energy proton irradiation (190 keV) is an effective method for this purpose because this method causes nanoscale cascade defects accompanied by nanostrain that simultaneously enhances both the T c and J c in an FST thin film 16 . However, proton irradiation is a complicated ex situ process that is not suitable for practical applications. Therefore, a straightforward in situ process for forming artificially controlled nanostrain is necessary to improve the J c of FSTs.
Nanostrain has been generated via the introduction of various defect formations to date. For example, the insertion of a desired material with a slightly different lattice constant can induce strain through the formation of a secondary phase 18,19 ; further, the doping of certain elements can generate lattice changes with nanoscale strain 20 . The formation of cascades 16 or point defects 21 by ion irradiation induces deformation of a lattice through nanoscale defects. In FST thin films, since large-scale and excessive numbers of defects can degrade the entire superconducting matrix 22 and FST has a short coherence length (~2 nm) 23 , the formation of minimally sized defects is required for inducing nanostrain to prevent Cooper pair breaking while improving J c .
Herein, we report that nanostrain was successfully formed in an epitaxial FST thin film through the formation of minimal nanoscale defects in an FST thin film using sequential pulsed laser deposition (S-PLD), which can artificially insert the desired material while fabricating an epitaxial thin film 4,24,25 . We injected precisely controlled trace amounts of CeO 2 to minimize the residual insertion of materials to form nanoscale defects. CeO 2 was used as an insertion material because CeO 2 exhibits not only good chemical stability but also an in-plane lattice constant compatible with that of FST 14,[26][27][28] , and hence, the degradation of superconductivity can be minimized rather than inserting other oxides, even if residual CeO 2 exists in FST. The crystallinity and structure of the CeO 2 -injected FST (Ce-FST) were confirmed using X-ray diffraction (XRD) measurements. The nanostrain was analyzed using atomic-resolution scanning transmission electron microscopy (STEM) with geometric phase analysis (GPA). The nanostrained Ce-FST thin film exhibits a significantly enhanced J c compared with that of a pristine FST (P-FST) thin film.

Sample preparation
We fabricated both P-FST and Ce-FST thin films on a (001)-oriented CaF 2 substrate by PLD using a KrF (248 nm) excimer laser (Coherent, COMPEX PRO 205F) in a vacuum of 2 × 10 −5 Pa at 400°C. We used an FeSe 0.45 Te 0.55 target made by an induction melting method. The FST thin films were grown using a laser energy density of 3 J/cm 2 , a pulse repetition rate of 3 Hz, and a target-to-substrate distance of 4 cm.
The method for fabricating the Ce-FST thin films is as follows. We first deposited a 20-nm (445 laser pulses) FST layer on the CaF 2 substrate. Then, CeO 2 was deposited on the FST layer.
These processes were repeated four times in total, and finally, an FST layer was deposited on the top surface. The total thickness of all the FST thin films was 100 nm (2225 laser pulses).
CeO 2 was deposited between the FST layers with a dependence on p (2, 5, 10, and 20), where p is the number of laser pulses for the inserted CeO 2 (laser energy density of 1.5 J/cm 2 and a repetition rate of 1 Hz). The target changing time to switch between the FST and CeO 2 targets was 10 s, which was the drive time when the laser was turned off and then on again. The composition of the FST thin film was considered to be approximately FeSe 0.7 Te 0.3 , based on our previous report 11 .

Characterization
To characterize the crystal structure, the θ-2θ, azimuthal phi, and rocking curve were measured using a four-circle XRD (PANalytical, X'Pert pro, λ = 1.5406 Å). We also performed an additional θ-2θ scan in beamline 3 A of the Pohang Accelerator Laboratory with a six circle XRD (λ = 1.148 Å). The STEM images and energy dispersive spectroscopy (EDS) maps were obtained by a C scorrected FEI Titan Themis G2 at an accelerating voltage of 300 kV with a beam current of 70 pA, a convergence semiangle of 15 mrad, and a collection semiangle snap in the range of 80-379 mrad. To obtain GPA maps of the Ce-FST and P-FST thin films, the same parameters were used for all calculations (same Fourier vector, resolution: 5 nm, smoothing: 10 nm, color scale: −0.1-0.12). The resistivity-temperature measurements were performed using a physical property measurement system (Quantum Design). T onset c and T zero c were determined using the 0.9 ρ n criterion and 0.01 ρ n criterion, respectively, where ρ n is the resistivity at 23 K. The magnetization J c was measured using a vibrating sample magnetometer (VSM, Oxford) by applying a magnetic field perpendicular to the film. This parameter was estimated using the Bean model for a thin film: J c = 15ΔM/Vr, where V is the thin film volume in cubic centimeters, r is the equivalent radius of the sample size (πr 2 = a × b; a and b are the width and length of the sample, respectively), and ΔM is the width of the magnetic moment from the M-H loop (for further information, see Supplementary Fig. S1). The transport J c is obtained by direct transport measurement of the patterned FST sample using a standard four-probe method.

Results and discussion
Crystalline phases Figure 1 shows a schematic diagram of two different Ce-FST thin films. First, if the amount of inserted CeO 2 is very small (2 p, smaller than 0.5 unit cell), nanoscale defects can be formed inside the FST thin film, not the CeO 2 layer, given that the inserted 2 p CeO 2 is an infinitesimal amount that is insufficient to form nucleation clusters or layers inside an FST. These nanoscale defects can generate nanostrain inside an FST thin film (left side of Fig. 1). The mechanism is discussed later in detail. If the inserted CeO 2 (20 p, 2.5 unit cell) is sufficient to form a CeO 2 layer in an FST thin film, a CeO 2 layer is formed between the FST layers without nanostrain (right side of Fig. 1). Thus, a 20 p Ce-FST thin film forms a superlattice FST thin film with CeO 2 .
We performed a θ-2θ scan using XRD to identify the out-of-plane crystalline qualities of the Ce-FST thin films. Figure 2a shows the out-of-plane θ-2θ XRD spectra of the P-FST and Ce-FST thin films dependent on p (2, 5, 10, and 20). The θ-2θ scans clearly show only (00l) peaks for Ce-FST thin films with CaF 2 (00l) peaks. However, there are no other phase peaks present despite the periodically injected CeO 2 because the amount of CeO 2 inserted is too small to be measured by XRD. Figure 2b shows an enlarged section of Fig. 2a close to the (001) peak of the Ce-FST thin films. The (001) peak of 2 p Ce-FST is noticeably shifted more to the left than that of P-FST, indicating that 2 p Ce-FST experiences tensile strain along the c-axis. Intriguingly, the degree of shift of the (001) peak returns to zero with increasing p. This result indicates that the strain relaxes in Ce-FST thin films with increasing p. Additionally, the same shift tendency is observed in other 00l peaks in Ce-FST thin films (for further information, see Supplementary Fig. S2).
We additionally measured the θ-2θ of the 2 p Ce-FST and 20 p Ce-FST thin films using a synchrotron-based XRD to further verify the crystalline structure (for further information, see Supplementary Fig. S3). As shown in Fig.  S3, only (00l) peaks are observed in both the 2 p Ce-FST and 20 p Ce-FST thin films, and the (001) peaks display satellite peaks, which have been generally observed in superlattice thin films 4 . Since 20 p Ce-FST thin films can have a superlattice structure with CeO 2 , satellite peaks can be observed. However, in the 2 p Ce-FST thin film, it is difficult to form a superlattice structure with the formation of an intact CeO 2 layer in the FST matrix because a trace amount of CeO 2 is injected into the FST matrix. Thus, we speculate that the satellite peaks of the 2 p Ce-FST thin film are due to small changes, such as nanostrain at the interfaces between the FST layers.
Additionally, we measured the rocking curve of the (001) reflection of both the P-FST and 2 p Ce-FST thin films using four circles of XRD to compare the out-ofplane crystalline qualities and the mosaicity (Fig. 2c). The calculated full-width at half-maximum (FWHM) of the (001) reflection is 0.67°for the 2 p Ce-FST and 0.55°for the P-FST. The difference between the FWHMs of the P-FST and 2 p Ce-FST thin films is minimal, and the FWHM of 2 p Ce-FST is similar to those of other reported FeSe x Te 1−x thin films 5,9,11 . This result indicates that the 2 p Ce-FST thin film grew well along the c-axis despite the insertion of oxide materials into the FST matrix.
To confirm the in-plane texture and epitaxial quality, we performed an azimuthal phi scan using four circles of XRD. Figure 2d indicates the azimuthal ɸ scan of the (113) peak from the CaF 2 substrate and the (112) peak from the 2 p Ce-FST thin film.

Strain analysis
To determine the nanoscale strain caused by the infinitesimal CeO 2 injection at the interface of each FST layer, we analyzed atomic-resolution-STEM images of the 2 p Ce-FST thin film. Figure 3a shows a cross-sectional atomic-resolution-STEM image of the 2 p Ce-FST thin film. As shown in Fig. 3a, no other dominant phases, such as CeO 2 particles, are observed except for the FST phase. Although we double checked for the presence of CeO 2 particles in the 2 p Ce-FST thin film, there are no CeO 2 layers, CeO 2 particles, or large-scale defects present (for further information, see Supplementary Fig. S4). However, fine bright lines are observed at 20-nm vertical intervals in the 2 p Ce-FST thin film. To analyze the fine bright lines in the 2 p Ce-FST thin films, we performed GPA based on the atomic-resolution-STEM image in Fig. 3a. GPA is generally used to show strain distributions and to determine the deformation of the lattice constant in crystalline structures 29 . Figure 3b shows an extracted strain map of the out-of-plane strain (ε zz ) of the identical region in Fig.  3a. The GPA map undoubtedly displays a strained region with 20-nm vertical intervals; the thickness of the nanostrained region is approximately 5-10 nm. To further analyze the strain, we plotted the line profile of the strain of the 2 p Ce-FST thin film based on the GPA results. As shown in Fig. 3c, nanostrains are observed with 20-nm vertical intervals. This nanostrain is tensile strain (ε zz ≅ 0.02) along the c-axis, and the position of the nanostrain agrees well with the location of the site where we intentionally inserted CeO 2 .
For a more accurate comparison, we performed STEM analysis of the P-FST and 20 p Ce-FST thin films. The P-FST thin film exhibits a relatively clear phase, as shown in Fig. 3d; there is no particular strain field in the out-ofplane GPA strain map from the atomic-resolution-STEM image of the P-FST film (Fig. 3e). Figure 3f shows the line profile of the out-of-plane strain of the P-FST thin film. As shown in Fig. 3f, the strain in the P-FST thin film fluctuates around zero.
The 20 p Ce-FST thin film exhibits a clear CeO 2 layer between the 20-nm intervals of FST layers (Fig. 3g). Figure  3h shows an out-of-plane GPA image of the 20 p Ce-FST thin film. Figure 3i shows a line profile of the out-of-plane strain in the 20 p Ce-FST thin film. The large strain contrast at the CeO 2 layer in Fig. 3h, i is an artifact that is caused by the structural difference between FST and CeO 2 . Relatively small strain fields (<0.02) are irregularly observed near the CeO 2 layer in the GPA map of the 20 p Ce-FST thin film. Interestingly, nanostrain is observed in the STEM image of the 2 p Ce-FST thin film, although there are no CeO 2 layers or particles visible. Thus, it is important to demonstrate why the injected trace amount of CeO 2 forms nanostrain in the FST matrix and why there are no CeO 2 particles in the 2 p CeO 2 FST thin film.
In general, nanostrain is induced at various types of defect perimeters 16,[18][19][20][21] . Interestingly, lattice distortion points (dashed circle in GPA maps of Fig. 3) such as dislocation cores and damaged FST layers are prominently observed in the nanostrain region in the GPA image of the 2 p Ce-FST thin film. Additionally, there are a few nanoscale defects that are formed irrespective of CeO 2 insertion in the FST thin films, as shown in Fig. 3d. These nanoscale defects can cause nanostrain in FST thin films. However, it is difficult to form nanostrain over a broad region by means of only these nanoscale defects because these defects form a localized strain field 18 .
To further understand the origin of the nanostrained region, we analyzed an enlarged STEM image of the nanostrained region with no lattice distortion points using EDS mapping. Figure 4a-c shows different STEM images  (Fig. 4a-c).
One interesting discovery is that not only fine decreases in both the Se and Fe ratios but also a fine increase in the Te ratio are observed in the nanostrained region in the EDS maps of the 2 p Ce-FST thin film when these EDS maps are analyzed using plot profiles (for further information, see Supplementary Fig. S5). The decrease in the Se ratio can cause an increase in the lattice constant 11 . This result indicates that nanostrain can be induced near the Se-deficient region that is generated by infinitesimal CeO 2 insertion.
Thus, it is important to demonstrate why Se deficiency is observed in nanostrained regions without residual CeO 2 particles. In the PLD system, the laser ablation of the target forms a plume that contains ionized species with high kinetic energy. These ionized energetic species cause resputtering and the formation of fine defects on the surface in the initial stage before these species form clusters or layers 30 . In this resputtering stage, it is impossible for the inserted CeO 2 to form an intact CeO 2 layer; instead, resputtering forms nanoscale defects and damaged FST layers (or a transition layer). These phenomena are observed in not only our 20 p Ce-FST thin film, as shown in Fig. 4d, but also in other studies when a CeO 2 layer is deposited into or onto an FST thin film 26,27,31 . Furthermore, Se deficiency can be generated in the resputtering stage, provided that the atomic ratio of FST abnormally changes during thin film growth because of instability in the Fe-Se bonding 11 . Collectively, nanostrain can be induced by nanoscale defects, such as lattice distortion points, a damaged FST layer, and Se deficiency, that are formed by inserting an infinitesimal amount of CeO 2 .
Furthermore, we examined whether the formation of nanostrain is affected by pausing (10 s) for an exchange of the FST and CeO 2 targets because Se and Te are sensitive and volatile in FST thin films 11 . The paused FST thin film was fabricated following the same fabrication process as that of the 2 p Ce-FST thin film except for CeO 2 injection; the CeO 2 plume was screened during the laser ablation of the CeO 2 target. The θ-2θ scan of the paused FST thin film using synchrotron-based XRD shows well-oriented (001) peaks without satellite peaks, indicating that the pausing time has a negligible effect on the formation of nanostrain in the FST matrix (for further information, see Supplementary Fig. S3).

Superconductivity measurements
We measured the temperature dependence of the resistivity to obtain the T c to compare the superconducting properties of the P-FST and Ce-FST thin films (Fig. 5a). The measured T onset c values are 21.3, 20.4, 19.0, 16.9, and 16.7 K for the P-FST, 2 p Ce-FST, 5 p Ce-FST, 10 p Ce-FST, and 20 p Ce-FST thin films, respectively. In particular, the T c values of the FST thin films decrease with increasing p of CeO 2 . The primary reason for the T c degradation in the Ce-FST thin films is the degradation of the crystalline quality with increasing amounts of inserted CeO 2 (for further information, see Supplementary Fig.  S6). Figure 5b, c, and S7 (for further information, see Supplementary S7) show the resistivity as a function of temperature up to 9 T with H//c for the 2 p Ce-FST, P-FST, and other Ce-FST thin films, respectively. Interestingly, the suppression of the T c of the 2 p Ce-FST thin film (ΔT zero c; field = 2.6 K), which is dependent on the magnetic field (ΔT zero c; field = T zero c; 9T −T zero c; 0T ), is lower than that of the P-FST thin film (ΔT zero c; field = 3.2 K); the measured T zero c; 0T and T zero c; 9T are 19.8 and 16.6 K, respectively, for the P-FST thin film and 18.9 and 16.3 K, respectively, for the 2 p Ce-FST thin film. This result indicates that the 2 p Ce-FST thin film has a lower magnetic field dependence than the P-FST thin film, although the T c of 2 p Ce-FST is lower than that of the P-FST thin film.
We estimated the H irr and H c2 of the Ce-FST and P-FST thin films using the 0.01 ρ n criterion and the 0.9 ρ n criterion with ρ n = ρ(23 K) as a function of the normalized temperature (t = T/T onset c ) to characterize the temperature dependence of the characteristic fields. (Fig. 5d). The improved H irr of 2 p Ce-FST is indicative of the beneficial effect of the periodic nanostrained region with nanoscale defects as pinning centers under high magnetic fields. In contrast, the H c2 and H irr of other Ce-FST (5, 10, and 20 p) are degraded after CeO 2 insertion, indicating that CeO 2 particles and layers can degrade H irr and H c2 in an FST thin film.
The J c of both the 2 p Ce-FST and the P-FST thin films was measured to verify the effect of the nanostrain as a pinning center on the supercurrents in the FST thin films (Fig. 6). Figure 6a, b shows the magnetic field dependence magnetization J c of the 2 p Ce-FST and the P-FST thin films at various temperatures (4.2, 7, 10, and 12 K) up to 13 T (H//c). The magnetization J c of the 2 p Ce-FST thin film has a value of 3.2 MA/cm 2 in a self-field and 0.44 MA/cm 2 under 13 T at 4.2 K. The self-field J c of the 2 p Ce-FST thin film is the highest value for an ironchalcogenide superconductor to the best of our knowledge 15,32 . The magnetization J c of the P-FST thin film has a value of 2.3 MA/cm 2 in a self-field and 0.23 MA/cm 2 under 13 T at 4.2 K. The magnetization J c of the P-FST thin film is similar to and higher than other reported values 15,16,27 . The transport J c of both the P-FST and Ce-FST thin films was measured at 6 and 10 K to verify the magnetization J c derived using the Bean model (Fig. 6c). The 2 p Ce-FST shows a transport J c of 3.5 MA/cm 2 in a self-field and of 0.44 MA/cm 2 under 13 T at 6 K, which is reasonably similar to the magnetization J c of the Ce-FST thin film at 4.2 K. The P-FST shows a transport J c of 0.91 MA/cm 2 in a self-field and of 0.10 MA/cm 2 under 13 T at 6 K, which is similar to the magnetization J c of the P-FST thin film at 7 K.
Additionally, the J c enhancement was calculated to confirm the effect of nanostrain in detail based on the magnetization J c (for further information, see Supplementary Fig. S8). The J c enhancement of 2 p Ce-FST compared with that of P-FST increases from 40% to 120% up to 5 T and gradually decreases under a high magnetic field. These results clearly demonstrate that 2 p Ce-FST maintains a high J c under a high magnetic field and a low magnetic field. Furthermore, we measured the angular dependence of the transport J c of the 2 p Ce-FST and P-FST at a constant reduced temperature T/T c~0 .6 to understand the pinning effects of nanostrain with nanoscale defects. As shown in Fig. 6d, the in-plane J c is 48% higher than the perpendicular J c in the P-FST thin films. The 2 p Ce-FST film shows an enhanced in-plane J c of 1.6 MA/cm 2 , which is 60% higher than the perpendicular J c of 1.0 MA/cm 2 due to the in-plane pinning effect by the lateral nanostrain. Above all, nanostrain with other nanoscale defects improves the J c of the 2 p Ce-FST film under all directions of magnetic field.

Relationship between nanostrain and J c
Additionally, we plotted the lattice constant, c, and magnetization, J c , at 4.2 K as a function of the p of inserted CeO 2 to further understand the relationship between nanostrain and J c (Fig. 7). The lattice constants were obtained by the Nelson Riley method based on the XRD results and by fast Fourier transform analysis based on the STEM images (for further information, see Supplementary Figs. S9 and S10). The magnetization J c of the Ce-FST thin films (2, 5, 10, and 20 p) was measured at 4.2 K (for further information, see Supplementary Fig.  S11). As shown in Fig. 7, the change in J c follows the same tendency as the change in the lattice constant, c, which represents the change in strain. This tendency demonstrates that nanostrain is responsible for the enhanced J c in the 2 p Ce-FST thin film.
To understand the pinning mechanism of the 2 p Ce-FST thin film, we plotted J c (t)/J c (0) versus t for both the 2 p Ce-FST and P-FST thin films based on the magnetization J c of both the 2 p Ce-FST and P-FST thin films (for further information, see Supplementary S12). Both the 2 p Ce-FST and P-FST thin films show the δl-pinning type, which is caused by fluctuations in the charge-carrier mean free path. We also calculated the scaled-volume pinning force (f p ) as a function of the normalized field (h); f p is F p / F p_max , and h is H/H irr (for further information, see Supplementary Fig. S12). In general, h values of 0.2 and 0.33 indicate a surface pinning geometry and point pinning geometry, respectively 33 . If the J c of the 2 p Ce-FST thin film is improved by CeO 2 particles or other defects that cause point and volume pinning, the h value is shifted to 0.33. However, the h of f p is approximately 0.2 in both the P-FST and 2 p Ce-FST thin films, indicating that the main pinning type in both the P-FST and 2 p Ce-FST thin films is surface pinning.
In a P-FST thin film that has a pure FST phase without defects, the interlayer spacing between Fe-Se(Te) planes can be an intrinsic pinning center due to the short coherence length of FST 34 . Since this interlayer spacing has a two-dimensional lateral geometry, the pinning type of the interlayer spacing in the P-FST thin film is surface pinning geometry. Interestingly, the 2 p Ce-FST thin film also has a surface pinning geometry even though its J c is relatively improved compared with that of the P-FST thin film. This result means that the 2 p Ce-FST thin film has a pinning type similar to that of the P-FST thin film. The difference between the P-FST thin film and the 2 p Ce-FST thin film is that the c-lattice of the 2 p Ce-FST thin film is expanded by the nanostrain compared with that of the P-FST thin film, indicating that the interlayer spacing of the 2 p Ce-FST thin film at the nanostrained region is larger than that of the P-FST thin film. Thus, the interlayer spacing of 2 p Ce-FST can be a more effective pinning center than that of P-FST.
To evaluate the efficiency of our method, we compared the pinning characteristics with those of previous papers [14][15][16][35][36][37][38] . Figure 8a shows the transport J c of 2 p Ce-FST and P-FST at 6 K for H//c together with the J c of other reported superconductors. The 2 p Ce-FST thin film exhibits a J c higher than the other reported J c of FST thin films [14][15][16][35][36][37][38] . We also estimated the pinning force (F p ) to characterize the effect of nanostrain with nanoscale defects. Figure 8b shows the magnetic field dependences of the vortex pinning force (F p = J c × B) of both the 2 p Ce-FST and the P-FST thin films up to 13 T (H//c) at 6 K together with the reported F p of other superconductors [14][15][16][35][36][37][38] . The 2 p Ce-FST and P-FST thin films show maximum pinning forces (F p,max ) of 57.8 GN/ m 3 under 11.5 T and 14.2 GN/m 3 under 11 T at 6 K, respectively. In particular, the 2 p Ce-FST thin film shows an F p,max~4 00% higher than that of the P-FST thin film at 13 T (H//c). In addition, the 2 p Ce-FST thin film exhibits a higher F p than the other reported FST, even though our samples were measured at a relatively higher temperature of 6 K. Fig. 7 Relationship between J c and nanostrain. As a function of p in the FST thin films, c-lattice constants were calculated from STEM and XRD results, magnetization J c under self-field, and magnetization J c under 13 T.