Angular dependence of Jc in YBCO films with c-axis correlated nano-rods and in-plane-distributed nano-particles

The quasi-multilayered films consisting of YBa2Cu3Oy layers with BaSnO3 nano-rods and the pseudo layers of in-plane-distributed BaSnO3 nano-particles were fabricated using a PLD method, in order to clarify the pinning landscape simultaneously improving the critical current densities, Jcs, both at B || c and at B || ab. The insertion of the pseudo layers into YBa2Cu3Oy films contributes to the enhancement of Jc at B || ab but it is a tendency to reduce the Jc at B || c. When the density of the nano-particles per layer is decreased, by contrast, the Jc at B || ab can be enlarged without the reduction of the c-axis peak. This is attributed to the fragmentation of the channel for flux creep motion through the pseudo layers. Furthermore, the Jc in tilted magnetic fields off the c-axis enhances as well as c-axis peak in a high magnetic field, when BaSnO3 nano-particles are increased.


Introduction
To improve a critical current density Jc in magnetic field for REBa2Cu3Oy (REBCO, RE: rare earth elements) based coated conductors, an introduction of additional crystalline defects and impurities into REBCO films is a promising way, where nano-sized defects work as pinning centers (PCs) and effectively arrest flux lines penetrating in superconducting materials [1]. Nano-rods, which are formed through self-assembled stacks of BaMO3 (M = Zr, Sn, Hf, etc.) along the c-axis into REBCO films, belongs to one-dimensional (1D) PCs and effectively interrupt the motion of flux lines when the magnetic field is applied parallel to the c-axis [2,3]. Planar defects consisting of continuous impurity layers along the ab-plane are two-dimensional (2D) PCs and act as ab-correlated PCs, leading to a weak field dependence of Jc at B || ab [4]. Nano-particles classified as three-dimensional (3D) PCs, on the other hand, have the morphology with no correlated orientation for flux pinning, leading to the isotropic pinning force against any orientations of magnetic field [5].
In recent years, further improvement of flux pinning including a reduction of the anisotropy of Jc has been attempted by using a combination of different types of PCs, which is referred to as hybrid flux pinning [6,7]. The hybrid flux pinning by using nano-rods and nano-particles enhances not only the Jc peak centered at B || c but also the Jc in a wide angular range of magnetic field [7], where nano-particles play an important role in the prevention of the sliding motion of flux lines for magnetic fields tilted off the direction of nano-rods and in the suppression of the motion of double kinks of flux lines due to thermal fluctuation [8]. The combination of 1D and 3D PCs, however, does not sufficiently reduce the anisotropy of Jc, where the caxis Jc-peak is larger than the Jc peak at B || ab in most cases. The combination of 1D and 2D PCs consisting of c-axis-aligned nano-rods and ab-plane-aligned planar nanostructures, on the other hand, can contribute to the improvement of Jc both at B || c and at B || ab [6,9]. The insertion of planar defects along the ab-plane, however, tends to reduce the c-axis peak in the Jc anisotropy caused by nano-rods, since flux lines along the c-axis easily move along the ab-aligned nanostructure layers for B || c [4] or the structure of flux lines changes from conventional Abrikosov vortices to pan-cake vortices [10].
In this work, we investigated the hybrid flux pinning structure which improves the Jc in all magnetic field orientations, i.e. at B || c, at B || ab, and in the intermediate-angle region, by preparing the quasimultilayered films consisting of YBCO layers with BaSnO3 nano-rods and the pseudo layers of in-planedistributed BaSnO3 nano-particles using a pulsed laser deposition (PLD) method. Figure 1 schematically illustrates distribution of the nano-rods and nano-particles in the multilayered films. The nano-rods consisting of BaSnO3 contribute to the enhancement of Jc at B || c, while the in-plane-distributed BaSnO3 nano-particles act as PCs with features of both 2D and 3D PCs: the nano-particles aligned along the abplane can be expected to enhance the Jc at B || ab and in the intermediate-angle region, but without reducing the c-axis peak.

Experimental details
The quasi-multilayered films consisting of YBCO layers with BaSnO3 nano-rods and the pseudo layers of in-plane-distributed BaSnO3 nano-particles were fabricated on (100) SrTiO3 substrates by a PLD technique alternating a 2.0 vol.% BaSnO3 doped YBCO target and a BaSnO3 target. The repetition rate of the laser was 2 Hz for the deposition of YBCO layers with BaSnO3, while the pseudo layers of BaSnO3 were deposited at 1 Hz. The growth of BaSnO3 nano-rods in the YBCO layer would be continuous along the film-thickness direction even in the multilayering process [11]. The deposition of BaSnO3 by several laser pulses, on the other hand, provides not a BaSnO3 layer but in-plane-aligned BaSnO3 nano-particles [12]. During the deposition, the substrate was heated at 760 °C and the oxygen partial pressure was 300 mTorr. After the deposition, the films were cooled down naturally from 760 °C to 500 °C and from 200 °C to room temperature in 600 Torr oxygen, whereas the cooling rate was controlled at 10 °C/min from 500 °C to 200 °C. A series of the quasi-multilayered films in this work is listed in Table 1. We refer to a sample as B(m, n), where m and n denote the number of laser pulses on the BaSnO3 target and the total number of BaSnO3 / YBCO+BaSnO3 bilayers, respectively. A layer of YBCO+BaSnO3 was always deposited on the top of the multilayered films and the total number of laser pulses on the BaSnO3 doped YBCO target was kept constant at 3600 pulses, resulting in the film thickness of about 300 nm. Simultaneously, a 2.0 Vol.% BaSnO3 doped YBCO film was prepared as a reference sample, which are referred to as BSO2.
Transport properties were measured using a four-probe method, where the films were patterned into bridge geometry with about 40 m width and 1 mm length using a standard photolithography. The value of Jc was defined by electric field criterion of 1 V/cm. The angular dependence of Jc was evaluated as a function of the angle  between the magnetic field and the c-axis, where the magnetic field was always applied perpendicular to the direction of the current (the maximum Lorentz force configuration).

Results and discussion
Firstly, we compare the angular behaviour of Jc between the multi-layered films with different m, in order to clarify the thinning-out effect of the in-plane-distributed nano-particles on the c-axis peak formed by the nano-rods. Figure 2(a) shows the Jc as a function of magnetic field orientation at 77 K and 1 T for the 5-bilayer films with different m, compared with BSO2. Two peaks can be observed in the angular dependences of Jc for all the samples. One of the peaks emerges at  = 0, which arises from the c-axis correlated pinning due to the nano-rods. Another is the steep peak at  = 90, which is generally attributed to the stacking faults or to the intrinsic pinning due to the CuO2 planes. The Jc peak at  = 90 is also affected by the structure of multilayered films [5] and is more evolved with increasing m, as shown in Figure 2(a). This is because the BaSnO3 nano-particles aligned along the in-plane direction of the film effectively work as correlated PCs along the ab-plane. It is noteworthy that the multilayared films with larger m more enlarge the Jc in the intermediate angle region between B || c and B || ab. This suggests that the in-plane-distributed BaSnO3 do not grow into layers but into particles: each nano-particles is isolated enough to work as 3D-PCs.
The insertion of the impurity layers aligned along the ab-plane, on the other hand, tends to weaken the c-axis peak [10,13]. For B(6, 5), the Jc peak at  = 0 is lower than that for BSO2. This is because the in-plane-distributed BaSnO3 nano-particles for B(6, 5) easily induce the flux creep motion of the interstitial flux lines between nano-particles [4], resulting in the negative effect for the flux pinning at B || c (see figure 3). Note that the dimensionality of the YBCO system, which significantly affects the flux pinning by linear defects [10], would not be modified by the insertion of the impurity layers in this work, since the thickness of the bilayer is about 30-60 nm and the impurity deposition did not form complete non-superconducting-layers. When m is decreased, by contrast, no deterioration in the c-axis peak is identified for B (3,5), resulting in the upward shift in the Jc over the entire magnetic field directions compared to BSO2. The influence of m on the Jc becomes more evident when the number of bilayers is increased to n = 10, as shown in Figure 4. These results suggest that the thinning of in-plane-distributed nano-particles effectively suppresses the flux creep motion between the nano-particles, resulting in the improvement of the Jc at   B || ab without a reduction of the c-axis peak. In increasing the magnetic field, the influence of the nanoparticle pinning becomes apparent even on the Jc at B || c: the Jc around  = 0 for the multilayered film with m = 3 exceeds that for BSO2. When flux lines outnumber the nano-rods in high magnetic field, interstitial flux lines existing between the nano-rods are effectively trapped by the in-plane-distributed BaSnO3 nano-rods [13].
To explore further optimization for the flux pinning effect of the multilayered films, we investigated the influence of the bilayer number n on the angular behaviour of Jc for the multilayered films with m = 3, as shown in figure 5. The multilayered films with m = 3 show upward shift in Jc compared to BSO2 in overall orientations of magnetic field, although the c-axis peak for the multilayered films is equal to or slightly higher than that of BSO2 for 1 T. When the number of bilayer n increases, the upward shift in Jc becomes more remarkable at B || ab and in the intermediate angle region. The increase in Jc at B || ab is due to a large number of the bilayers which work as pseudo planar PCs. In the intermediate angle region, on the other hand, the nano-particles play a role in 3D PCs [7,13], which can pin the segments of flux lines released from the nano-rods along the c-axis. Therefore, a large number of bilayers is effective for the improvement of Jc both in high magnetic field and in the intermediate angle region.
In Figure 6, we compare the angular dependence of Jc between the multilayered films with m  n = 30, which means the same amount of nano-particles regardless of the different multilayer structures. The Jc in a wide range of magnetic field orientations can be improved by thinning out the nano-particles on each layer and by increasing the number of bilayers, even if the amount of nano-particles is the same. In other words, tuning of spatial distribution of nano-particles would be one of the keys to further enhance the overall Jc for the hybrid flux pinning. Note that the Jc peaks at B || ab for B(3, 10) and  B(6, 5) nearly overlap each other for both 1 T and 3 T. The in-plane-distributed nano-particles contribute to effective flux pinning at B || ab. The same peak behaviour of Jc, however, is not always provided for B || ab by the different multi-layered structures even if the amount of nano-particles is the same [13].

Conclusions
In order to clarify the pinning structure simultaneously attaining high Jc both at B || c and at B || ab, we investigated the influence of the structure of the multilayered YBCO films with BaSnO3 nano-rods and in-plane-distributed BaSnO3 nano-particles on the angular behaviour of Jc, where the number of nanoparticles per layer and the number of bilayers were controlled. The in-plane-distributed nano-particles can contribute not only to improving the Jc at B || ab but also to keeping the c-axis peak due to the nanorods by thinning out the nano-particles per layer. In addition, the Jc can be further evolved in high magnetic field and in a wide range of magnetic field orientation by increasing the number of bilayers consisting of YBCO layer and the nano-particles. The formation of the in-plane-distributed nanoparticles for the hybrid flux pinning structure is one of the important factors for the improvement of Jc in all magnetic field orientations

Acknowledgement
This work was supported by KAKENHI (16K06269) from the Japan Society for the Promotion of Science.