The technological applications of YBa₂Cu₃O_{7- δ}(YBCO or Y123) superconducting thin films are envisioned over wide range of temperature and magnetic field [1], [2], [3]. Many applications such as light-weight motors and generators, future electricity grids, high energy accelerators, potential compact fusion systems require high critical current density (J_c) of YBCO thin films. Applications such as transmission cables and fault current limiters (FCLs) are envisioned in the high-temperature, low-field regime where the system is subjected to cable's self-field. There are, however, other applications such as generation of hiigh magnetic fields (as in NMR, MRI), superconducting magnetic storage (SMES), motors, generators which are envisioned in the low-temperature, high-field regime. It is, therefore, highly desired to improve the J_c performance of YBCO thin films over wide range of temperature and applied magnetic field [3].

In order to have high J_c under applied magnetic fields, it is important to contain the driven motion of the quantized magnetic vortices, penetrating the superconducting films, due to Lorentz force [4]. The strategy to contain the vortex motion relies on the creation of non-superconducting regions or defects within superconducting matrix which would generate pinning potentials and make it difficult for the vortices to overcome. The vortices prefer to be located on such microscopic non-superconducting sites to conserve energy and thus these defects provide “pinning” to the quantized vortices [5]. In quest of enhancing in-field J_c of YBCO thin films, many defects with varying geometries have been studied [6], [7], [8]. Some of these defects evolve naturally during the growth of the films and are thus called natural pinning centers. Dislocations, point defects, stacking faults, twin boundaries etc. fall under this category of pinning centers. The J_c resulting from these natural pinning centers, however, is not high as such pinning centers are weak in nature and cannot prevent the driven motion of the vortices due to thermal fluctuations at elevated temperatures [9], [10]. Additional defects are, therefore, intentionally generated inside YBCO film matrix which serve as vortex pin sites and are termed as artificial pinning centers (APCs). These APCs are generated by various methodologies including irradiation by heavy ions or neutrons [11], [12], doping of rare-earth atoms [13], [14], inclusion of nanoscale non-superconducting secondary phases [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29] and decoration of the substrate surface by nanoparticles of non-superconducting materials [30], [31].

The APCs generated through the introduction of nanoscale non-superconducting phases, such as Y₂O₃ [15], [16], Y₂BaCuO₅ [17], [18], YFeO₃ [19], BaZrO₃ [20], [21], [22], BaHfO₃ [23], [24], BaSnO₃ [25], BaTiO₃ [26], YBa₂NbO₆ [27], [28] and YBa₂TaO₆ [29], into YBCO superconducting matrix have been extensively studied and demonstrated to be very effective in improving the vortex pinning properties leading to enhanced in-field J_c, particularly at 77 K. It has been observed that while some of these phases self-assemble as nanocolumnar structures, others grow as nanoparticles within YBCO matrix. According to their morphologies and densities, these secondary phase nanoinclusions are effective in enhancing the in-field J_c and controlling its angular anisotropy.

The inclusion of secondary phase nanoparticles into YBCO films for enhancing the vortex pinning has drawn considerable interest in recent past. These secondary phase nanoparticles are considered to be strong pinning centers and provide rather isotropic pinning in contrast to the nanocolumnar structures which are effective for a narrow angular range of magnetic field orientation when the field is aligned along these nanocolumnar structures. The incorporation of Y₂O₃ nanoparticles as strong pinning centers inside YBCO films has been reported to enhance the in-field J_c and improve its angular anisotropy at 77 K [32]. In a recent report, the inclusion of Y₂O₃ nanoparticles inside the YBCO matrix resulted in extremely high pinning force density of 0.9 TNm⁻³ at 4.2 K with substantially improved J_c anisotropy at 30 K and 20 K [16]. In other reports, Y211 nanoparticles incorporated into YBCO thin films resulted in substantially enhanced in-field J_c [17], [18]. However, the angular anisotropy of J_c was not studied in these reports. In our earlier study, it has been observed that Y211 nanoparticles are remarkably effective in improving the angular anisotropy of the YBCO thin films at 77 K and 65 K [33]. In addition, the vortex pinning strength was observed to be in proportion with the Y211 concentration inside YBCO films at these two temperatures.

The vortex phase in the mixed state of YBCO is known to be determined by the interaction among the vortices, the interaction between vortices and defects and depends on the thermal energy [34]. Vortices are elastic in nature and their arrangement within a superconducting matrix is determined by the pinning landscape present in the superconducting matrix. It is very important to understand the underlying vortex pinning mechanism to improve the vortex pinning properties of YBCO thin films over wide range of temperature and applied magnetic field.

In this paper, we report the effect of Y211 nanoparticles in influencing the vortex pinning properties of YBCO thin films over wide temperature range of 4-77 K. At lower temperatures, moderate concentration of Y211 nanoparticles is observed to be most efficient in contrast to higher temperatures (65 K and 77 K) where higher concentration exhibited optimum in-field J_c performance [33]. Microstructures of the YBCO+Y211 nanocomposite films were examined in detail and it was observed that the larger concentration of Y211 phase inside YBCO films leads to agglomeration of secondary phase nanoparticles which are not as efficient at lower temperatures as they are at higher temperatures due to the reduced coherence length of the YBCO films at lower temperatures.

It has been mentioned earlier that the understanding of the temperature and magnetic field dependence of J_c of YBCO films consisting of APCs are crucial for the development of many technologies which require YBCO based coated conductors. In this paper, the temperature dependence of J_c for YBCO films with different concentrations of Y211 nanoparticles have been studied for the identification of possible vortex pinning mechanism in these nanocomposite films. The role of strong pinning centers such as secondary phase nanoparticles, weak pinning centers such as vacancies and lattice distortions and various other defects in influencing the vortex pinning properties of the YBCO nanocomposite films are also discussed.

YBCO thin film without Y211 nanoinclusions and with varying concentrations of Y211 nanoinclusions were deposited onto single crystal SrTiO₃ (STO) substrates using PLD technique (KrF excimer laser, λ = 248 nm) and employing the surface modified target method [33]. Three different concentrations of Y211 nanoinclusions were incorporated into YBCO films by modifying the YBCO target surface with three different sizes of Y211 rectangular pieces: 1.8 area%, 3.6 area% and 5.4 area% which are referred to as Y211A, Y211B and Y211C. Accordingly, the nanocomposite films are termed as YBCO+Y211A, YBCO+Y211B and YBCO+Y211C respectively. The thickness of the thin film samples were measured by a stylus profilometer (DEKTAK, Bruker). The thickness of these thin films was found to vary between 200 and 300 nm.

A transmission electron microscope (TEM) (JEOL JEM-2100F) was employed to observe the planar and cross-sectional views of the microstructure of the thin film samples. Elemental STEM-EDX color mapping was also conducted to identify the phases observed in the TEM images.

All the thin film samples were subjected to UV photolithography and wet-chemical etching technique to fabricate microbridges for the measurement of electrical transport properties. Gold contact pads were deposited onto patterned samples using sputtering technique. The patterned samples have microbridges 50–60 μm wide and 1 mm long. Among the as deposited Au contact pads, the current source contact points are 8 mm apart and the voltage contact points are 2 mm apart. A Physical Property Measurement System (PPMS, Quantum Design) was used to measure the electrical transport properties of the thin film samples by employing standard four-probe method. T_c was determined by measuring the temperature dependence of the resistivity and employing the 10⁻³ $ρ_n$ criterion, where $ρ_n$ is the normal-state resistivity at T_c. J_c values of all the thin films are obtained at different temperatures and applied magnetic fields using a voltage criterion of 1 μVcm⁻¹.

Fig. 1 shows the TEM images of the planar view of YBCO+Y211 nanocomposite films. Secondary phase nanoparticles can easily be observed in all the TEM images, which are predominantly Y211 phase. The nanoparticle density can be observed to increase in YBCO+Y211B and YBCO+Y211C films as compared to YBCO+Y211A film. Some larger nanoparticles are also observed in the TEM image of YBCO+Y211C film which are marked by dotted white arrows. In order to confirm the composition of the larger particles, EDX elemental color mapping was conducted. In Fig. 2, (a) shows the planar view of the YBCO+Y211C film whereas (b) and (c) show the corresponding EDX color mapping for Y and Ba elements respectively. While most of the nanoparticles are of Y211 phase, the formation of a relatively larger Y₂O₃ nanoparticle can also be seen in these figures. The presence of Y and absence of Ba elements confirm it to be Y₂O₃ which also act as a promising APC. In order to further examine the size distribution of Y211 nanoparticles within YBCO+Y211 films, the cross-sectional TEM image needs to be observed. Fig. 3 shows the cross-sectional TEM image of (a) YBCO+Y211B and (b) YBCO+Y211C nanocomposite films. Although, the distribution of the Y211 nanoparticles inside YBCO matrix seems to be random in the thin films, their average diameter seems to increase in the YBCO+Y211C film. As estimated from these images, the average diameter of Y211 nanoparticles in YBCO+Y211B film is 5.3 nm with largest Y211 particle size being 7.3 nm. For YBCO+Y211C film, the average diameter of the Y211 nanoparticles is 7 nm with largest Y211 particle having diameter of 13 nm. The size variation of the Y211 secondary phase nanoinclusions in YBCO+Y211 films are presumably determined by the supersaturation of the secondary phase, the kinetic aspects of the nucleation rate and the diffusion length of the adatoms. As per the plan of the ablation of the surface modified target, both YBCO and Y211 phases are ablated alternatively leading to the nucleation of the precipitates beginning at the initial stage of film growth. The concentration of the adatoms (Y, B, Cu) determines the final composition (i.e., primary and secondary phases) of the nanocomposite thin films. The adatoms forming the Y211 phase are supposed to act as impurity gettering centers and the nuclei once formed can prevent the local supersaturation of the secondary phase and further nucleation of the precipitates might be suppressed [35]. There appears to be a certain limit of the nucleation sites being formed depending on the supply of the adatoms corresponding to the Y211 phase. As further nucleation is suppressed, the adatoms are bound to be diffused into already formed nanoparticles leading to increased size of the Y211 nanoparticles in the Y123 films with larger Y211 concentration. The dimension of these Y211 nanoinclusions plays a critical role in influencing the vortex pinning properties especially at lower temperatures when the coherence length of YBCO reduces substantially as compared to that at 77 K. In addition to the Y211 nanoparticles, the presence of some planar defects (parallel to the ab-plane) can also be confirmed in these nanocomposite films. The planar defects are supposed to be stacking faults which are generated during the growth of the film.

Fig. 4 shows the magnetic field (H // c-axis) dependence of J_c for YBCO+Y211 nanocomposite films in comparison to that of pristine YBCO film measured at different temperatures between 4.2 K to 50 K. The in-field J_c performance of YBCO+Y211 nanocomposite films is significantly enhanced at all the temperatures and is more prominently observed at higher applied magnetic fields, although the measurement is limited to 9 T (the upper limit in our PPMS). The measurement of J_c at lower applied magnetic fields could not be carried out at lower temperatures due to heat generation at the electrodes caused by large electric currents (I_c being much higher). Although, the in-field J_c values for YBCO+Y211B film are very close to that for YBCO+Y211C film at 50 K, these exceed substantially as the measurement temperature is lowered further. At lower temperatures, the YBCO+Y211B film exhibit highest in-field J_c values among the studied samples: ∼10 MAcm⁻² at 10 K, 2 T and ∼5 MAcm⁻² at 10 K, 9 T. These are very high values of J_c for YBCO thin films having nanoparticles as APCs. Even at 30 and 40 K, the enhancement in J_c values for YBCO+Y211B film as compared to pristine YBCO film is about 4-fold which is consistent with the lift-factor discussion proposed recently by Xu et al. [36], although, their study deals with BZO nanocolumn incorporation in GdBCO matrix. Such manifold enhancement in the in-field J_c values of YBCO+Y211 nanocomposite films is attributed to the strong pinning of vortices induced by Y211 nanoinclusions.

Pinning force density (F_p) is another related parameter which provides more precise understanding of how efficiently the vortices are pinned in a superconducting sample. F_p is the vector product of the J_c and the applied magnetic field at which it is measured. The variation of F_p with applied magnetic field for all the thin film samples, calculated for different temperatures between 4.2 and 50 K, are shown in Fig. 5. At 50 K, the F_p values of YBCO+Y211A are enhanced compared to that of pristine YBCO film. However, for YBCO+Y211B and YBCO+Y211C films, this enhancement is much more pronounced. As the temperature goes down to 40, 30, 20, 10 and 4.2 K, the F_p values for YBCO+Y211B film surpasses that for YBCO+Y211A and YBCO+Y211C films substantially for the entire investigated applied magnetic field regime. F_pmax is the maximum F_p observed for the investigated applied magnetic field range and for YBCO+Y211B film, it is close to 0.5 TNm⁻³ at 4.2 K, 9 T which is very high for an YBCO film with nanoparticle APCs.

A pinned vortex line is known to have lower energy than a free vortex in a superconductor. The energy gained by the unit length of a vortex line, in the case of a non-superconducting region or nanoinclusion, refers to the condensation energy in the core region. Considering the core pinning interactions resulting from local variation of condensation energy at a pinning site, the energy changes as a vortex line crosses through a pinning center. The vortex core represents a volume of $\pi \xi^{2}$ per unit length and energy of $\left(\mu_{0} / 2\right) H_{c}^{2}$ per unit volume where ξ and $H_c$ represent the coherence length and thermodynamic critical field respectively. If the non-superconducting pinning center in consideration has diameter a < 2 ξ with its volume being V, the interaction of the vortex line with the pinning center can lower its energy by $\left(\mu_{0} / 2\right) H_{c}^{2}V$. Therefore, the pinning force required to dislodge the flux line from its core would be $\left(\mu_{0} / 2\right) H_{c}^{2}V$. However, if the diameter of the pinning center is larger than 2 ξ, the energy gain would be $\left(\mu_{0} / 2\right) H_{c}^{2} \pi \xi^{2} a$ [37]. As the vortex line moves away from the pinning center, the intersection length would decrease continuously. Considering the appropriate intersection length to be a, the pinning force, in this case, can be expressed as $\mu_{0} H_{c}^{2} \pi \xi^{2}$. If the elastic energies of the vortices are considered small in comparison to the pinning energies, each of the vortices would be individually pinned and the global pinning force per unit volume (F_p) would be represented by a direct summation over all the interacting pinning centers [38].

where N represents the number of pinning centers per unit volume, d_p the average spacing between two pinning centers and $a_0$ the average distance between adjacent vortices. According to this equation, the global pinning force is proportional to the density of the pinning centers which is reflected in the enhanced in-field J_c and F_p values of YBCO+Y211 nanocomposite films at 77 and 65 K. In contrast to the results obtained at 77 and 65 K, the enhancement in the in-field J_c and the corresponding F_p values for YBCO+Y211 nanocomposite films at lower temperatures is not monotonic with respect to the density of Y211 nanoinclusions.

Fig. 6 summarizes the F_pmax values for all the thin film samples and presents their variation with respect to measurement temperature. It is, however, to be noted that the F_pmax at 4.2 K, 10 K and 20 K are actually the F_p values obtained at 9 T. It seems that there is a cross-over temperature, below which, YBCO+Y211B films exhibits higher F_pmax values and above which, YBCO+Y211C film does so. Table 1 summarizes the F_p values of these samples obtained for a magnetic field of 9 T at 4.2 K, 10 K and 20 K. These are some of the highest F_p values obtained for PLD grown YBCO film consisting of nanoparticles as APCs. Table 2 provides a glimpse of some of the highest F_p values obtained in YBCO and other REBCO nanocomposite films. Unfortunately, there are not many reports on temperature dependent critical current properties of YBCO thin films prepared by PLD technique with nanoparticles as APCs. Therefore, in this table, the best existing pinning force density values at lower temperatures as reported for various REBCO thin films prepared by different techniques such as metal organic chemical vapor deposition (MOCVD) and chemical solution deposition (CSD) with varying pinning centers are listed for comparison [16], [39], [40], [41], [42], [43].

It would be interesting to understand the temperature dependence of F_p at constant applied magnetic fields where the average spacing among the vortices remains the same but λ and ξ change with temperature. As the temperature decreases, these two parameters become shorter. Although, the average vortex spacing remains the same, its cross-sectional area decreases and therefore, its interaction volume with a pinning center decreases as well. Although, the interaction volume ‘V’ decreases, the pinning energy $\left(\mu_{0} / 2\right) H_{c}^{2} V$ increases as the thermodynamic critical field increases rapidly at the same time [44]. The rise in the pinning energy at the lower temperatures gives rise to increase in the elemental pinning force ‘$f_p$’ at lower temperatures. So the variation of the global pinning force ‘F_p’ in Fig. 6 directly corresponds to the variation of ‘$f_p$’ resulting from the variation of λ, ξ and H_c with respect to the temperature.

Looking at Fig. 6, the cross-over temperature, where YBCO+Y211B film outperforms YBCO+Y211C films in terms of F_p values is somewhere near to 50 K. We attempt to discuss this result on the basis of the variation of coherence length ξ with temperature for these two thin films. The calculation of ξ_ab(T) for YBCO+Y211B (T_c = 89.6 K) and YBCO+Y211C (T_c = 88.8 K) films was made using the relation $B_{c 2}(0)=\varphi_{0} / 2 \pi \xi_{a b}^{2}$ and the Werthamer-Helfand-Hohenberg formula $B_{c 2}(0)=0.691 T_{c}\left|d B_{c 2} / d T\right|$ [45]. Using two different values of $d B_{c 2} / d T$= -1.01 T/K and $d B_{c 2} / d T$= -1.27 T/K as reported earlier for YBCO thin films, obtained from the resistivity measurements in high magnetic fields [46], [47], and employing the GL equation ξT∝[1-T/Tc]-1/2, the variation of ξ_ab with temperature could be plotted as shown in Fig. 7. It can be observed that the ξ_ab(T) values for YBCO+Y211B and YBCO+Y211C films are almost similar for most of the temperatures and vary only at higher temperatures due to their different T_cs. At higher temperatures (65 and 77 K), ξ_ab is sufficiently large and the interaction volume between a vortex and the pinning center (Y211 nanoparticle in this case) is expected to make use of most of the volume of the pinning center and therefore, the elementary pinning force ‘f_p’ is proportional to Y211 concentration. However, as ξab decreases substantially at lower temperatures, the interaction volume decreases and only a part of the pinning center is useful and therefore, the larger nanoparticles as in YBCO+Y211C film are not as efficient as the smaller ones as in YBCO+Y211B film [48].

Vortices interact with a pinning center either through the spatial variation in Tc (between superconducting matrix and non-superconducting/insulating pinning center) or the spatial variations in the charge carriers’ mean free path, l near the lattice defects. Both these interactions result in the spatial variation of the GL order parameter and the pinning resulting from these interactions are termed as "$\delta T_{c}$" and "δl" pinning respectively. Following Blatter et al. [5] and Griessen et al. [49], $J_c$ is a function of reduced temperature t (=T/T_c) and in the single vortex pinning regime, it follows the relation $J_{c}(t) \propto\left[1-\left(T / T_{c}\right)^{2}\right]^{n}$[50]. The value of the characteristic exponent ‘n’ determines the dominant vortex pinning mechanism in the superconducting sample. n = 1.2 is ascribed to $\delta T_{c}$ pinning while n = 2.5 refers to δl pinning. As mentioned before, $\delta T_{c}$ pinning is expected for nanoparticle dominated pinning landscape and δl pinning is expected for a pinning landscape completely dominated by point defects. Fig. 8 shows the log–log plot of $J_c$ vs. $1-\left(T / T_{c}\right)^{2}$ for YBCO+Y211 nanocomposite films at an applied magnetic field of 1 T. The values of n, as extracted from these plots, are 1.99, 1.72, 2.41 and 2.05 for YBCO, YBCO+Y211A, YBCO+Y211B and YBCO+Y211C films respectively. In one of the earlier reports on YGdBCO films consisting of BZO nanoparticles, the value of the exponent n (=1.24) was found to be closer to the theoretical value of 1.2 indicative of δTc pinning [51]. This value is much different than that for YBCO+Y211 films being investigated in this paper. There are two principal differences that can be considered for such a variation in the n value in these two studies: (i) The median size of the BZO nanoparticles in the YGdBCO films is much larger (∼23 nm) than that for Y211 nanoparticles (∼5–7 nm) in YBCO+Y211 films being studied in this paper. In the previous report, a fair amount of Y225 nanoparticles were also observed which were even larger in size (∼80 nm). (ii) The growth process of PLD and MOD are very different which result in very different interfaces between the host matrix and the secondary phases. In a recent report, high resolution plan-view TEM images and geometrical phase analysis were employed to reveal the strain induced by secondary phase nanoinclusions in the PLD and MOD grown films [52]. The strain component maps reveal that in PLD grown films, the compressive and tensile stains are localized near the matrix/APC coherent interfaces and spread over a distance of ∼10 nm whereas, for MOD grown thin films, the strain is localized over far shorter distance (∼2 nm) around the incoherent matrix/APC interfaces. The range of lattice deformation, therefore, is much different in films grown by PLD and MOD techniques. Since, these local lattice deformations are the main sources of δl pinning, the PLD and MOD grown films are expected to exhibit different values of the characteristic exponent ‘n’ indicative of the type of pinning prevalent in the films. As the pinning landscape in YBCO+Y211 thin films being investigated in this paper is complex consisting of the Y211 nanoinclusions, dislocations along the ab-plane, and weak point pinning centers as well, the precise n values as predicted for $\delta T_{c}$ or δl pinning are not expected [53]. It is, however, noteworthy that in YBCO+Y211B film, the n value is much higher than the rest of the samples and is close to 2.5, indicating that the contribution due to point pinning centers is substantial in this film. This observation seems rational as the high in-field $J_c$ in YBCO+Y211 film at lower temperatures requires these weak point pinning centers act efficiently.

The size of the pinning center influences the temperature dependent critical current properties not only when the magnetic field is parallel to the c-axis but also for other orientations with respect to the c-axis. When the magnetic field is oriented at an angle θ with respect to the c-axis, the vortex cross-section changes from circular to elliptical as per the relation $\xi(\theta)=\xi_{a b} \varepsilon(\theta)$ where $\varepsilon(\theta)=\sqrt{\left(\cos ^{2} \theta+\gamma^{-2} \sin ^{2} \theta\right)}$ and γ(=5–7) is the electronic mass anisotropy parameter. Atθ = 90°, $\xi_{a b}(\theta)$ becomes equal to ξ_c. Using two different reported values of $d B_{c 2} / d T$ for YBCO thin films and γ = 7, the variation of $2 \xi_{a b}$ with respect to the magnetic field orientation is plotted for different temperatures between 40–77 K which is represented in Fig. 9. The solid symbols represent the values obtained using $d B_{c 2} / d T$= -1.01 T/K while the open symbols represent the values obtained using $d B_{c 2} / d T$ = -1.21 T/K. The shaded region in green represents the length scale over which the Y211 nanoparticles have been observed in YBCO+Y211B film. At 40 and 50 K, the Y211 nanoparticles seem to be covering the angular region between 0 to 60°. However, if the size of the Y211 nanoparticles increases, as in the case of YBCO+Y211C film, its efficiency for vortex pinning is expected to be limited to narrower angular range and higher temperatures.

Fig. 10 [(a)-(f)] show the angular variation of J_c measured at 2, 4 and 6 T at 40 and 50 K. In these figures $\theta=0^{\circ}$ and $\theta=180^{\circ}$ correspond to the direction parallel to the c-axis while $\theta=90^{\circ}$ corresponds to the ab-plane of the films. In all of the samples, J_c peak parallel to the ab-plane is visible which is ascribed to the intrinsic-pinning resulting from non-conducting BaO/YO layers between the superconducting CuO₂ planes [34]. There is no other J_c peak observed in any of the thin films. The J_cs of the YBCO+Y211 nanocomposite films seem to be uniformly enhanced as compared to that of YBCO film over the angular region 0°≤ θ ≤ 75°particularly for YBCO+Y211B and YBCO+Y211C films. Between 75°and 90°, J_c decreases before again increasing and exhibiting a peak for H // ab-plane. Such a decrease in J_c near the ab-plane has been discussed in our earlier work and ascribed to the competition between pinning due to Y211 nanoparticles and pinning due to planar defects along the ab-plane [33].

As observed in the TEM images, the distribution of the Y211 nanoinclusions is random and they are expected to provide isotropic pinning to the vortices. In addition, some point pinning centers are also expected in the microstructure, although they are not clearly visible in the TEM images. There are some ab-plane aligned dislocations and the distorted lattice planes around the Y211 nanoparticles, which are visible in TEM images, and these stacking faults and lattice distortions are surrounded by partial dislocations and consist of point defects (cation and oxygen vacancies) which contribute to vortex pinning as weak pinning centers [54]. So, the matrix of YBCO+Y211 superconducting thin films consist of various defects as represented in the schematic diagram of Fig. 11. When the magnetic field is parallel to the c-axis of the films as shown in (a), the Y211 nanoparticles are expected to pin portions of the vortices strongly, leaving some other portions weakly pinned by the point pins. When current passes through the sample, the Lorentz force generated would drag these weakly pinned portions along its direction. At low temperatures, however, the pinning contribution due to point pinning centers become substantial. In the case of the magnetic field being oriented at an angle with respect to the c-axis of the film, as shown in (b), the pinning by Y211 nanoparticles would not change much, except for the fact that the interaction volume of the vortices with the nanoparticles would be reduced and the corresponding pinning energy would also decrease. Such a situation results in isotropic J_c for YBCO+Y211 films for wide range of applied magnetic field orientation. As the current flowing across the superconducting films increases, the Lorentz force (f_L) on the vortices is balanced by the pinning force by the nanoparticles (f_p,str) and weak pinning centers (f_p,wk) [44], as represented in (c), as per the following relation:

where $f_{p, \text { result }}$ is the resultant pinning force due to strong pinning centers (nanoparticles) and weak pinning centers (lattice defects) and ψ is the angle between the direction of $f_{p, s t r}$ and $f_{p, w k}$. If $f_{p, s t r}$ and $f_{p, w k}$ are normal to each other, the above equation will be identical to the mean-square pinning formula as suggested earlier [38], [55]. Although, nanoparticles are expected to strongly pin the vortices, it is possible for the vortices to shift their location from one nanoparticle to another under the influence of Lorentz force. In such circumstances, pinning of vortex segments by random pinning centers becomes very important.

Temperature dependent J_c measurements of superconducting YBCO+Y211 nanocomposite films have been conducted and their vortex pinning properties are investigated. The efficiency of Y211 nanoparticles in enhancing the J_c of YBCO thin films over a wide range of temperature and applied magnetic field has been established. Moderate concentration of Y211 nanoinclusions resulted in F_pmax values as high as 0.5 TNm⁻³ at 4.2 K, 9 T. In addition, uniform enhancement in the J_c of the YBCO+Y211 nanocomposite films was observed at 50 K and 40 K, which is attributed to the isotropic pinning provided by the Y211 nanoparticles. The enhanced vortex pinning in the YBCO+Y211 films, at lower temperatures, results from contributions from both Y211 nanoinclusions as well as point pinning centers. Due to reduced coherence length, these weak point pinning centers, resulting from lattice distortions around Y211 nanoinclusions and other lattice imperfections, act efficiently resulting in very-high in-field J_c in YBCO+Y211 nanocomposite films. The analysis of the variation of J_c with reduced temperature also indicates δl pinning being dominant in YBCO+Y211 nanocomposite films resulting from pinning due to lattice distortions and imperfections around Y211 nanoinclusions. If somehow, the agglomeration of Y211 nanoparticles is controlled (by means of deposition parameters e.g., growth rate, deposition temperature etc.), it is still possible that the larger concentration of Y211 nanoinclusions would result in even higher in-field J_c values.

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

This work is supported by the ALCA project of Japan Science and Technology Agency.