*3.2. Modification of J<sup>c</sup> Anisotropy by Controlling Number of Heavy-Ion Irradiation Directions*

*3.2. Modification of Jc Anisotropy by Controlling Number of Heavy-Ion Irradiation Directions*  We further increased the number of the directions of CDs by controlling the irradiation directions (see Figure 9), in order to spread the strong pinning effect of CDs over a wider magnetic field angular range. Figure 10 shows the magnetic field angular depend-We further increased the number of the directions of CDs by controlling the irradiation directions (see Figure 9), in order to spread the strong pinning effect of CDs over a wider magnetic field angular range. Figure 10 shows the magnetic field angular dependence of *J*<sup>c</sup> and *n*-values for YBCO thin films with direction-dispersed CDs, where the number of directions of CDs was applied from one to five every 30 degrees [36]. The *n*-value is estimated from a linear fit to empirical formula of electric field (*E*) versus current density (*J*), *E* ~ *J n* in the range of 1 to 10 µV/cm. The *n*-value is equivalent to *U*<sup>0</sup> / *k*B*T* (*U*0: pinning potential energy) [37,38], representing thermal activation for flux motion. When the number of CD directions is increased, the angular region with high *J*<sup>c</sup> is more expanded. Note that the height of the *J*<sup>c</sup> peak at *B* || *c* declines, since the density of CDs decreases with increasing number of irradiation directions in this work. Thus, the large directiondispersion of CDs is effective for the enhancement of *J*<sup>c</sup> over a wider magnetic field angular region centered at *B* || *c*.

The *J*<sup>c</sup> around *B* || *ab*, on the other hand, does not seems to be affected by flux pinning of the direction-dispersed CDs: both *J*<sup>c</sup> and *n*-value at *θ* = 90◦ rather tend to decrease with increasing the degree of the direction-dispersion of CDs. One of the reasons for the reduction of *J*<sup>c</sup> at *B* || *ab* by the introduction of CDs is the damage on the superconductivity and/or the *ab*-plane-correlated PCs [16]. It should be noted that the sample of Quintmodal contains CDs crossing at ±30◦ relative to the *ab*-plane (i.e., *θ*<sup>i</sup> = ±60◦ ); nevertheless, the crossed CDs do not seem to contribute to the pinning interaction around *B* || *ab*. Figure 11 represents the magnetic field angular dependence of *J*<sup>c</sup> for YBCO thin films including bimodal angular configurations of CDs with *θ*<sup>i</sup> = ±30◦ and ±60◦ relative to the *c*-axis, respectively [39]. The crossing angle of ±30◦ relative to the *c*-axis induces the enhancement

of *J*<sup>c</sup> over a wide angular region centered at *B* || *c*. The crossing of CDs at ±30◦ relative to the *ab* plane, i.e., *θ*<sup>i</sup> = ±60◦ , by contrast, is ineffective in pushing up the *J*<sup>c</sup> at the middirection of the crossing angle, i.e., at *B* || *ab*, whereas the peak of J<sup>c</sup> emerges at θ = ±60◦ . These results indicate that the flux pinning around *B* || *ab* is hardly affected even by CDs tilted toward the ab-plane, which significantly differs from the flux pinning of CDs at *B* || *c*. Thus, the flux pinning of CDs around *B* || *ab* is a new issue for the complete reduction of the *J*<sup>c</sup> anisotropy. of *J*c over a wide angular region centered at *B* || *c*. The crossing of CDs at ±30° relative to the *ab* plane, i.e., *θ*i = ±60°, by contrast, is ineffective in pushing up the *J*c at the mid-direction of the crossing angle, i.e., at *B* || *ab*, whereas the peak of Jc emerges at θ = ±60°. These results indicate that the flux pinning around *B* || *ab* is hardly affected even by CDs tilted toward the ab-plane, which significantly differs from the flux pinning of CDs at *B* || *c*. Thus, the flux pinning of CDs around *B* || *ab* is a new issue for the complete reduction of the *J*c anisotropy.

ence of *J*c and *n*-values for YBCO thin films with direction-dispersed CDs, where the number of directions of CDs was applied from one to five every 30 degrees [36]. The *n*-value is estimated from a linear fit to empirical formula of electric field (*E*) versus current density (*J*), *E* ~ *J <sup>n</sup>* in the range of 1 to 10 µV/cm. The *n*-value is equivalent to *U*0 / *k*B*T* (*U*0: pinning potential energy) [37,38], representing thermal activation for flux motion. When the number of CD directions is increased, the angular region with high *J*c is more expanded. Note that the height of the *J*c peak at *B* || *c* declines, since the density of CDs decreases with increasing number of irradiation directions in this work. Thus, the large direction-dispersion of CDs is effective for the enhancement of *J*c over a wider magnetic

The *J*c around *B* || *ab*, on the other hand, does not seems to be affected by flux pinning of the direction-dispersed CDs: both *J*c and *n*-value at *θ* = 90° rather tend to decrease with increasing the degree of the direction-dispersion of CDs. One of the reasons for the reduction of *J*c at *B* || *ab* by the introduction of CDs is the damage on the superconductivity and/or the *ab*-plane-correlated PCs [16]. It should be noted that the sample of Quintmodal contains CDs crossing at ±30° relative to the *ab*-plane (i.e., *θ*i = ±60°); nevertheless, the crossed CDs do not seem to contribute to the pinning interaction around *B* || *ab*. Figure 11 represents the magnetic field angular dependence of *J*c for YBCO thin films including bimodal angular configurations of CDs with *θ*i = ±30° and ±60° relative to the *c*-axis, respectively [39]. The crossing angle of ±30° relative to the *c*-axis induces the enhancement

*Quantum Beam Sci.* **2021**, *5*, x FOR PEER REVIEW 9 of 22

field angular region centered at *B* || *c*.

**Figure 9.** Bright field TEM image showing CDs tilted at *θ*i = 0°, ±30° and ±60° relative to the *c*-axis of the YBCO film, which are installed by 200 MeV Xe ion irradiation. The arrows indicate several ion tracks. Reprinted with permission from [36], copyright 2018 by IOP. **Figure 9.** Bright field TEM image showing CDs tilted at *θ*<sup>i</sup> = 0◦ , ±30◦ and ±60◦ relative to the *c*-axis of the YBCO film, which are installed by 200 MeV Xe ion irradiation. The arrows indicate several ion tracks. Reprinted with permission from [36], copyright 2018 by IOP. *Quantum Beam Sci.* **2021**, *5*, x FOR PEER REVIEW 10 of 22

**Figure 10.** Magnetic-field angular dependence of *J*c (upper, (**a**)) and *n*-value (lower, (**b**)) for YBCO thin films with various CD configurations (Unimodal: parallel CD configuration with *θ*i = 0°, Trimodal: trimodal-configuration with *θ*i = 0° and ±30°, and Quintmodal: quintmodal-configuration with *θ*i = 0°, ±30° and ±60°). The arrows indicate the peaks or the shoulder on the *n*(*θ*) curve for Quintmodal. Reprinted with permission from [37], copyright 2013 by IEEE. **Figure 10.** Magnetic-field angular dependence of *J*c (upper, (**a**)) and *n*-value (lower, (**b**)) for YBCO thin films with various CD configurations (Unimodal: parallel CD configuration with *θ*<sup>i</sup> = 0◦ , Trimodal: trimodal-configuration with *θ*<sup>i</sup> = 0◦ and ±30◦ , and Quintmodal: quintmodal-configuration with *θ*<sup>i</sup> = 0 ◦ , ±30◦ and ±60◦ ). The arrows indicate the peaks or the shoulder on the *n*(*θ*) curve for Quintmodal. Reprinted with permission from [37], copyright 2013 by IEEE.

**Figure 11.** Magnetic-field angular dependence of *J*c at temperature of 60 K and magnetic field of 3 T to 7 T for YBCO thin films with CDs crossing at (**a**) *θ*i = ±30° and (**b**) ±60° relative to the *c*-axis,

A significant enhancement of *J*c at *B* || *c* has been caused by the introduction of artificially PCs, which is much higher than *J*c at *B* || *ab* now [40]. Thus, the improvement of *J*<sup>c</sup> at *B* || *ab* has been required at the next step, in order to increase overall *J*c. The influence of CDs on the flux pinning at *B* || *ab*, however, has not been well studied so far, because the *J*c at *B* || *ab* is the highest innately due to the electronic mass anisotropy in high-*T*<sup>c</sup> superconductors [4] and the introduction of CDs is generally difficult in the direction close

*3.3. Modification of Jc Around B || ab by Controlling Heavy-Ion Irradiation Directions* 

respectively. Reprinted with permission from [36], copyright 2018 by IOP.

**Figure 11.** Magnetic-field angular dependence of *J*c at temperature of 60 K and magnetic field of 3 T to 7 T for YBCO thin films with CDs crossing at (**a**) *θ*i = ±30° and (**b**) ±60° relative to the *c*-axis, respectively. Reprinted with permission from [36], copyright 2018 by IOP. **Figure 11.** Magnetic-field angular dependence of *J*<sup>c</sup> at temperature of 60 K and magnetic field of 3 T to 7 T for YBCO thin films with CDs crossing at (**a**) *θ*<sup>i</sup> = ±30◦ and (**b**) ±60◦ relative to the *c*-axis, respectively. Reprinted with permission from [36], copyright 2018 by IOP.

**Figure 10.** Magnetic-field angular dependence of *J*c (upper, (**a**)) and *n*-value (lower, (**b**)) for YBCO thin films with various CD configurations (Unimodal: parallel CD configuration with *θ*i = 0°, Trimodal: trimodal-configuration with *θ*i = 0° and ±30°, and Quintmodal: quintmodal-configuration with *θ*i = 0°, ±30° and ±60°). The arrows indicate the peaks or the shoulder on the *n*(*θ*) curve for

Quintmodal. Reprinted with permission from [37], copyright 2013 by IEEE.

#### *3.3. Modification of Jc Around B || ab by Controlling Heavy-Ion Irradiation Directions 3.3. Modification of J<sup>c</sup> Around B || ab by Controlling Heavy-Ion Irradiation Directions*

A significant enhancement of *J*c at *B* || *c* has been caused by the introduction of artificially PCs, which is much higher than *J*c at *B* || *ab* now [40]. Thus, the improvement of *J*<sup>c</sup> at *B* || *ab* has been required at the next step, in order to increase overall *J*c. The influence of CDs on the flux pinning at *B* || *ab*, however, has not been well studied so far, because the *J*c at *B* || *ab* is the highest innately due to the electronic mass anisotropy in high-*T*<sup>c</sup> superconductors [4] and the introduction of CDs is generally difficult in the direction close A significant enhancement of *J*<sup>c</sup> at *B* || *c* has been caused by the introduction of artificially PCs, which is much higher than *J*<sup>c</sup> at *B* || *ab* now [40]. Thus, the improvement of *J*<sup>c</sup> at *B* || *ab* has been required at the next step, in order to increase overall *J*c. The influence of CDs on the flux pinning at *B* || *ab*, however, has not been well studied so far, because the *J*<sup>c</sup> at *B* || *ab* is the highest innately due to the electronic mass anisotropy in high-*T*<sup>c</sup> superconductors [4] and the introduction of CDs is generally difficult in the direction close to the *ab*-plane. In contrast, heavy-ion irradiation can be an effective tool even for exploring the flux pinning effect of CDs at *B* || *ab*, because CDs can be installed in any direction by adjusting the irradiation direction.

GdBCO-coated conductors were irradiated with 270 MeV Xe-ions, where the irradiation angle Θ<sup>i</sup> relative to the *ab*-plane was controlled in the range from ±5 ◦ to ±15◦ relative to the *ab*-plane in order to install crossed CDs around the *ab*-plane [41]. The cross-sectional TEM image of the GdBCO-coated conductor irradiated at Θ<sup>i</sup> = ±10◦ , Figure 12, shows the formation of continuous CDs along the irradiation directions. At the bottom part of the GdBCO layer, by contrast, some CDs become thinner and indicate angular dispersion in the irradiation directions. This is due to smaller value of *S*<sup>e</sup> than the threshold value of 20 keV/nm for the formation of continuous CDs [17,42], because the *S*<sup>e</sup> changes from 29.1 to 7.40 keV/nm through the GdBCO layer for the oblique irradiation at Θ<sup>i</sup> = 10◦ .

Figure 13 shows the magnetic field angular dependence of *J*<sup>c</sup> for the irradiated samples with Θ<sup>i</sup> = ±5 ◦ , ±10◦ , and ±15◦ , respectively. The CD crossing-angles of Θ<sup>i</sup> ≤ ±15◦ significantly affect the magnetic field angular variation of *J*<sup>c</sup> around *B* || *ab*. The introduction of crossed CD at Θ<sup>i</sup> = ±15◦ provides a triple peak of *J*<sup>c</sup> centered at *B* || *ab*, where a large *J*<sup>c</sup> peak exists at *B* || *ab* and the other two *J*<sup>c</sup> peaks emerge around *θ* = 75◦ and 105◦ , independently each other. This behavior is in contrast to the case of CDs crossing at *θ*<sup>i</sup> ≤ ±30◦ relative to the *c*-axis, which shows a single peak of *J*<sup>c</sup> centered at *B* || *c*, as represented in Figures 6 and 11. As the crossing-angle of Θ<sup>i</sup> decreases, the two divided peaks of *J*<sup>c</sup> at ±Θ<sup>i</sup> overlap with the central *J*<sup>c</sup> peak at *B* || *ab*: a single peak centered at *θ* = 90◦ occurs for the crossing angles of Θ<sup>i</sup> ≤ ±10◦ . In particular, the crossing angle of Θ<sup>i</sup> = ±5 ◦ provides the large and sharp *J*<sup>c</sup> peak at *B* || *ab*, showing the highest value of all the samples at *B* || *ab*. To our knowledge, it is the first confirmation that CDs contribute to the improvement of *J*<sup>c</sup> at *B* || *ab*.


to the *ab*-plane. In contrast, heavy-ion irradiation can be an effective tool even for exploring the flux pinning effect of CDs at *B* || *ab*, because CDs can be installed in any direction

7.40 keV/nm through the GdBCO layer for the oblique irradiation at *Θ*i = 10°.

GdBCO-coated conductors were irradiated with 270 MeV Xe-ions, where the irradiation angle *Θ*i relative to the *ab*-plane was controlled in the range from ±5° to ±15° relative to the *ab*-plane in order to install crossed CDs around the *ab*-plane [41]. The cross-sectional TEM image of the GdBCO-coated conductor irradiated at *Θ*i = ±10°, Figure 12, shows the formation of continuous CDs along the irradiation directions. At the bottom part of the GdBCO layer, by contrast, some CDs become thinner and indicate angular dispersion in the irradiation directions. This is due to smaller value of *S*e than the threshold value of 20 keV/nm for the formation of continuous CDs [17,42], because the *S*e changes from 29.1 to

Figure 13 shows the magnetic field angular dependence of *J*c for the irradiated samples with *Θ*i = ±5°, ±10°, and ±15°, respectively. The CD crossing-angles of *Θ*<sup>i</sup> ≤ ±15° significantly affect the magnetic field angular variation of *J*c around *B* || *ab*. The introduction of crossed CD at *Θ*i = ±15° provides a triple peak of *J*c centered at *B* || *ab*, where a large *J*<sup>c</sup> peak exists at *B* || *ab* and the other two *J*c peaks emerge around *θ* = 75° and 105°, independently each other. This behavior is in contrast to the case of CDs crossing at *θ*<sup>i</sup> ≤ ±30° relative to the *c*-axis, which shows a single peak of *J*c centered at *B* || *c*, as represented in Figures 6 and 11. As the crossing-angle of *Θ*i decreases, the two divided peaks of *J*c at ±*Θ*<sup>i</sup> overlap with the central *J*c peak at *B* || *ab*: a single peak centered at *θ* = 90° occurs for the crossing angles of *Θ*<sup>i</sup> ≤ ±10°. In particular, the crossing angle of *Θ*i = ±5° provides the large and sharp *J*c peak at *B* || *ab*, showing the highest value of all the samples at *B* || *ab*. To our knowledge, it is the first confirmation that CDs contribute to the improvement of *J*c at *B*

by adjusting the irradiation direction.

**Figure 12.** Cross-sectional TEM images of a GdBCO coated conductor irradiated with 270 MeV Xe ions at *Θ*i = ±10° relative to the *ab*-plane (**a**) near the surface and (**b**) at the bottom part of GdBCO layer, respectively. The arrows show several ion tracks. Reprinted with permission from [41], copyright 2017 by IEEE. **Figure 12.** Cross-sectional TEM images of a GdBCO coated conductor irradiated with 270 MeV Xe ions at Θ<sup>i</sup> = ±10◦ relative to the *ab*-plane (**a**) near the surface and (**b**) at the bottom part of GdBCO layer, respectively. The arrows show several ion tracks. Reprinted with permission from [41], copyright 2017 by IEEE. *Quantum Beam Sci.* **2021**, *5*, x FOR PEER REVIEW 12 of 22

**Figure 13.** Magnetic-field angular dependence of *J*c at 77.3 K, 1.5 T in GdBCO coated conductors with crossed CDs at ±*Θ*i relative to the *ab*-plane ((**a**) *Θ*i = ±15°, (**b**) *Θ*i = ±10°, and (**c**) *Θ*i = ±5°). The broken lines are drawn at the positions of the irradiation angles. Reprinted with permission from [41], copyright 2017 by IEEE. **Figure 13.** Magnetic-field angular dependence of *J*<sup>c</sup> at 77.3 K, 1.5 T in GdBCO coated conductors with crossed CDs at ±Θ<sup>i</sup> relative to the *ab*-plane ((**a**) Θ<sup>i</sup> = ±15◦ , (**b**) Θ<sup>i</sup> = ±10◦ , and (**c**) Θ<sup>i</sup> = ±5 ◦ ). The broken lines are drawn at the positions of the irradiation angles. Reprinted with permission from [41], copyright 2017 by IEEE.

These behaviors are closely associated with the elastic properties of flux lines around *B* || *ab*. The line tension energy of flux lines becomes very strong at *B* || *ab*, where the core of flux lines shows the elliptical nature in anisotropic superconductors. The strong line tension of flux lines significantly affects the trapping angle *φ*t of CDs tilted toward the These behaviors are closely associated with the elastic properties of flux lines around *B* || *ab*. The line tension energy of flux lines becomes very strong at *B* || *ab*, where the core of flux lines shows the elliptical nature in anisotropic superconductors. The strong line tension of flux lines significantly affects the trapping angle *ϕ<sup>t</sup>* of CDs tilted toward the

hand, can be evaluated by substituting the value of *φ*t ~ 65° for *Θ*<sup>i</sup> = 90° and *γ* = 5 together with equations (1) and (2): *φ*t ~ 6.6° for *Θ*<sup>i</sup> = 5°, *φ*t ~ 8.7° for *Θ*<sup>i</sup> = 10°, and *φ*t ~ 11.9° for *Θ*<sup>i</sup> = 15°. Thus, the trapping angles of CDs tilted toward the *ab*-plane becomes very small: flux lines are hardly trapped along CDs when the magnetic field direction is displaced from the direction of CDs even slightly. In particular, the trapping angle for CDs tilted at *Θ*<sup>i</sup> ≥ 10° is smaller than the CD tilt-angle *Θ*i, suggesting that the tilted CDs hardly affect the flux pinning at *B* || *ab*. Therefore, CDs tilted at *Θ*<sup>i</sup> ≥ 10° and the *ab*-plane correlated PCs provide flux pinning independently. The CDs tilted at *Θ*<sup>i</sup> = 5°, on the other hand, can fully contribute to the improvement of *J*c at *B* || *ab*, because the trapping angle exceeds the

An in-plane aligned *a*-axis-oriented YBCO film offers an excellent opportunity for further exploration into the influence of CDs on the flux pinning at *B* || *ab*, since we can easily install CDs along the *ab*-plane with the ion-beam normal to the film [43]. We prepared the in-plane aligned *a*-axis-oriented YBCO film by a PLD technique with an ArF excimer laser, where a (100) SrLaGaO4 substrate with Gd2CuO4 buffer layer was used to

*3.4. Modification of Jc at B || ab by Heavy-Ion Irradiation along the a-Axis* 

value of *Θ*i.

*ab*-plane. In general, the value of *ϕ<sup>t</sup>* for CDs along the *c*-axis (i.e., at Θ<sup>i</sup> = 90◦ ) is about 65◦ in GdBCO coated conductors [25]. The *ϕ<sup>t</sup>* for CDs tilted at small angle of Θ<sup>i</sup> , on the other hand, can be evaluated by substituting the value of *ϕ<sup>t</sup>* ~ 65◦ for Θ<sup>i</sup> = 90◦ and *γ* = 5 together with equations (1) and (2): *ϕ<sup>t</sup>* ~ 6.6◦ for Θ<sup>i</sup> = 5◦ , *ϕ<sup>t</sup>* ~ 8.7◦ for Θ<sup>i</sup> = 10◦ , and *ϕ<sup>t</sup>* ~ 11.9◦ for Θ<sup>i</sup> = 15◦ . Thus, the trapping angles of CDs tilted toward the *ab*-plane becomes very small: flux lines are hardly trapped along CDs when the magnetic field direction is displaced from the direction of CDs even slightly. In particular, the trapping angle for CDs tilted at Θ<sup>i</sup> ≥ 10◦ is smaller than the CD tilt-angle Θ<sup>i</sup> , suggesting that the tilted CDs hardly affect the flux pinning at *B* || *ab*. Therefore, CDs tilted at Θ<sup>i</sup> ≥ 10◦ and the *ab*-plane correlated PCs provide flux pinning independently. The CDs tilted at Θ<sup>i</sup> = 5◦ , on the other hand, can fully contribute to the improvement of *J*<sup>c</sup> at *B* || *ab*, because the trapping angle exceeds the value of Θ<sup>i</sup> .
