**2. Experimental**

**2. Experimental**  The samples used in our works were mostly *c*-axis oriented YBCO thin films and GdBCO coated conductors. The *c*-axis oriented YBCO thin films were fabricated by a pulsed laser deposition (PLD) technique on (100) surface of SrTiO3 single crystal substrates. The thickness of the films was about 300 nm. The GdBCO coated conductor, on the other hand, was fabricated on an ion-beam-assisted deposition (IBAD) substrate by a PLD method (Fujikura Ltd., Tokyo, Japan). The thickness of GdBCO layer is 2.2 µm and the self-field critical current *I*c of this tape with 5 mm width is about 280 A. The samples were cut from the tape of the GdBCO coated conductor. The Ag stabilizer layer on the superconducting layer was removed by a chemical process. The YBCO thin films and the samples cut from the GdBCO coated conductor were patterned into a shape of about 40 The samples used in our works were mostly *c*-axis oriented YBCO thin films and GdBCO coated conductors. The *c*-axis oriented YBCO thin films were fabricated by a pulsed laser deposition (PLD) technique on (100) surface of SrTiO<sup>3</sup> single crystal substrates. The thickness of the films was about 300 nm. The GdBCO coated conductor, on the other hand, was fabricated on an ion-beam-assisted deposition (IBAD) substrate by a PLD method (Fujikura Ltd., Tokyo, Japan). The thickness of GdBCO layer is 2.2 µm and the self-field critical current *I*<sup>c</sup> of this tape with 5 mm width is about 280 A. The samples were cut from the tape of the GdBCO coated conductor. The Ag stabilizer layer on the superconducting layer was removed by a chemical process. The YBCO thin films and the samples cut from the GdBCO coated conductor were patterned into a shape of about 40 µm wide and 1 mm long micro-bridge before the irradiation.

µm wide and 1 mm long micro-bridge before the irradiation. The heavy-ion irradiations with Xe ions were performed using the tandem accelerator of JAEA in Tokai, Japan. Tuning of the discontinuity of CDs along the *c*-axis can be controlled by the irradiation energy. The values of *S*<sup>e</sup> for the Xe-ion irradiation energies above 200 MeV are above 2.9 keV/Å, which is above the threshold value of *S*<sup>e</sup> = 20 keV/nm to create continuous CDs along the *c*-axis over the whole sample thickness for YBCO [17]. pletely.

Thus, the irradiation with 200 MeV Xe ions was performed to install continuous CDs into YBCO thin films. In addition, the Xe-ion irradiation with 270 MeV was applied in order to create continuous CDs for GdBCO coated conductors, where the projectile length was longer than the thickness of 2.2 µm. Discontinuous CDs, on the other hand, were formed into YBCO thin films and GdBCO coated conductors by the irradiation with 80 MeV Xe ions, where the value of *S*<sup>e</sup> is below 20 keV/nm: the radius of CDs strongly fluctuates along the ion path and CDs are shortly segmented at intervals in their longitudinal direction when the *S*<sup>e</sup> is lower than the threshold value, as shown in Figure 3 [19,20,25]. All of the irradiation energies used in our works are enough for the projectile ranges to exceed the thickness of the samples: the incident ions pass through the superconducting layer completely. irradiation directions. The fluence of the irradiation is often represented as a matching field *B*φ: *B*φ is the magnetic field where the density of flux lines is equal to that of CDs, e.g., the fluence of 4.84 × 1010 ions/cm2 corresponds to *B*φ = 1 T. It should be noted that the introduction of irradiation defects causes a lattice distortion of the host matrix, which affects the superconducting properties such as critical temperature (*T*c). The strain induces the oxygen vacancies [26], resulting in the reduction of *T*c: the value of *T*c decreases when the fluence of the irradiation increases [24]. The strain also affects the *J*c properties through the influence on *T*c: *J*c decreases largely, when the influence of the strain increases excessively. Therefore, the irradiation fluences were adjusted to avoid heavy damage to the crystallinity in our works.

The direction of CDs was adjusted by controlling the incident ion beam direction tilted off the *c*-axis by *θ*i, which was always directed perpendicular to the bridge direction of the sample (see Figure 4). When the irradiation directions are dispersed, the fluence in each irradiation direction is calculated by dividing the total fluence by the number of the

The heavy-ion irradiations with Xe ions were performed using the tandem accelerator of JAEA in Tokai, Japan. Tuning of the discontinuity of CDs along the *c*-axis can be controlled by the irradiation energy. The values of *S*e for the Xe-ion irradiation energies above 200 MeV are above 2.9 keV/Å, which is above the threshold value of *S*e = 20 keV/nm to create continuous CDs along the *c*-axis over the whole sample thickness for YBCO [17]. Thus, the irradiation with 200 MeV Xe ions was performed to install continuous CDs into YBCO thin films. In addition, the Xe-ion irradiation with 270 MeV was applied in order to create continuous CDs for GdBCO coated conductors, where the projectile length was longer than the thickness of 2.2 µm. Discontinuous CDs, on the other hand, were formed into YBCO thin films and GdBCO coated conductors by the irradiation with 80 MeV Xe ions, where the value of *S*e is below 20 keV/nm: the radius of CDs strongly fluctuates along the ion path and CDs are shortly segmented at intervals in their longitudinal direction when the *S*e is lower than the threshold value, as shown in Figure 3 [19,20,25]. All of the irradiation energies used in our works are enough for the projectile ranges to exceed the thickness of the samples: the incident ions pass through the superconducting layer com-

*Quantum Beam Sci.* **2021**, *5*, x FOR PEER REVIEW 4 of 22

**Figure 3.** Cross-sectional TEM images of GdBCO coated conductors irradiated with (**a**) 270 MeV and (**b**) 80 MeV Xe ions, respectively. The irradiation dose is 1.94 × 1011 ions/cm2. The arrows indicate several ion tracks. Reprinted with permission from [25], copyright 2015 by IEEE. **Figure 3.** Cross-sectional TEM images of GdBCO coated conductors irradiated with (**a**) 270 MeV and (**b**) 80 MeV Xe ions, respectively. The irradiation dose is 1.94 <sup>×</sup> <sup>10</sup><sup>11</sup> ions/cm<sup>2</sup> . The arrows indicate several ion tracks. Reprinted with permission from [25], copyright 2015 by IEEE.

The direction of CDs was adjusted by controlling the incident ion beam direction tilted off the *c*-axis by *θ*<sup>i</sup> , which was always directed perpendicular to the bridge direction of the sample (see Figure 4). When the irradiation directions are dispersed, the fluence in each irradiation direction is calculated by dividing the total fluence by the number of the irradiation directions. The fluence of the irradiation is often represented as a matching field *B*ϕ: *B*<sup>ϕ</sup> is the magnetic field where the density of flux lines is equal to that of CDs, e.g., the fluence of 4.84 <sup>×</sup> <sup>10</sup><sup>10</sup> ions/cm<sup>2</sup> corresponds to *B*<sup>ϕ</sup> = 1 T. *Quantum Beam Sci.* **2021**, *5*, x FOR PEER REVIEW 5 of 22

**Figure 4.** Sketch of the experimental arrangement in this work. **Figure 4.** Sketch of the experimental arrangement in this work.

The cross sections of the irradiated samples were observed by conventional transmission electron microscopy (TEM) with a JEM-2000 EX instrument (JEOL, Tokyo, Japan) operating at 200 kV. The thin TEM specimens were prepared by a focused ion beam method using an Quanta 3D system (FEI, Hillsboro, Oregon, USA). The *J*c properties were meas-It should be noted that the introduction of irradiation defects causes a lattice distortion of the host matrix, which affects the superconducting properties such as critical temperature (*T*c). The strain induces the oxygen vacancies [26], resulting in the reduction of *T*c: the value of *T*<sup>c</sup> decreases when the fluence of the irradiation increases [24]. The strain also affects the *J*<sup>c</sup> properties through the influence on *T*c: *J*<sup>c</sup> decreases largely, when the influence

ured through the transport properties by using a four-probe method. The *J*c was defined

field angular dependences of *J*c were evaluated as a function of the angle *θ* between the

Heavy-ion irradiation can introduce CDs in any direction in a controlled manner, so we can install CDs at the magnetic field angles where the *J*c shows a minimum, one by one: the material processing with heavy-ions is one of effective ways to modify the *J*c anisotropy in high-*T*c superconductors, which enables us to push up overall *J*c, as shown in

**Figure 5.** Schematic image of modification of the *J*c anisotropy by controlling the irradiation directions ((**a**) typical *J*c anisotropy of unirradiated high-*T*c superconductors, (**b**) modified *J*c anisotropy

We first examined the influence of bimodal angular distribution of CDs consisting of CDs crossing at ±*θ*i relative to the *c*-axis on the *J*c properties in a wide magnetic field

with CDs along the *c*-axis, (**c**) modified *J*c anisotropy with direction-dispersed CDs).

*3.1. Modification of Jc Around B || c by Controlling Heavy-Ion Irradiation Angles* 

magnetic field and the *c*-axis of the samples (see Figure 4).

**3. Results and Discussion** 

Figure 5.

of the strain increases excessively. Therefore, the irradiation fluences were adjusted to avoid heavy damage to the crystallinity in our works. The cross sections of the irradiated samples were observed by conventional transmission electron microscopy (TEM) with a JEM-2000 EX instrument (JEOL, Tokyo, Japan) op-

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

**Figure 4.** Sketch of the experimental arrangement in this work.

The cross sections of the irradiated samples were observed by conventional transmission electron microscopy (TEM) with a JEM-2000 EX instrument (JEOL, Tokyo, Japan) operating at 200 kV. The thin TEM specimens were prepared by a focused ion beam method using an Quanta 3D system (FEI, Hillsboro, Oregon, USA). The *J*<sup>c</sup> properties were measured through the transport properties by using a four-probe method. The *J*<sup>c</sup> was defined by a criterion of electric field, 1 µV/cm. The transport current was always perpendicular to the magnetic field and the *c*-axis (maximum Lorentz force configuration). The magnetic field angular dependences of *J*<sup>c</sup> were evaluated as a function of the angle *θ* between the magnetic field and the *c*-axis of the samples (see Figure 4). erating at 200 kV. The thin TEM specimens were prepared by a focused ion beam method using an Quanta 3D system (FEI, Hillsboro, Oregon, USA). The *J*c properties were measured through the transport properties by using a four-probe method. The *J*c was defined by a criterion of electric field, 1 µV/cm. The transport current was always perpendicular to the magnetic field and the *c*-axis (maximum Lorentz force configuration). The magnetic field angular dependences of *J*c were evaluated as a function of the angle *θ* between the magnetic field and the *c*-axis of the samples (see Figure 4). **3. Results and Discussion** 

#### **3. Results and Discussion** *3.1. Modification of Jc Around B || c by Controlling Heavy-Ion Irradiation Angles*

#### *3.1. Modification of J<sup>c</sup> Around B || c by Controlling Heavy-Ion Irradiation Angles* Heavy-ion irradiation can introduce CDs in any direction in a controlled manner, so

Heavy-ion irradiation can introduce CDs in any direction in a controlled manner, so we can install CDs at the magnetic field angles where the *J*<sup>c</sup> shows a minimum, one by one: the material processing with heavy-ions is one of effective ways to modify the *J*<sup>c</sup> anisotropy in high-*T*<sup>c</sup> superconductors, which enables us to push up overall *J*c, as shown in Figure 5. we can install CDs at the magnetic field angles where the *J*c shows a minimum, one by one: the material processing with heavy-ions is one of effective ways to modify the *J*c anisotropy in high-*T*c superconductors, which enables us to push up overall *J*c, as shown in Figure 5.

**Figure 5.** Schematic image of modification of the *J*c anisotropy by controlling the irradiation directions ((**a**) typical *J*c anisotropy of unirradiated high-*T*c superconductors, (**b**) modified *J*c anisotropy with CDs along the *c*-axis, (**c**) modified *J*c anisotropy with direction-dispersed CDs). **Figure 5.** Schematic image of modification of the *J*c anisotropy by controlling the irradiation directions ((**a**) typical *J*c anisotropy of unirradiated high-*T*c superconductors, (**b**) modified *J*c anisotropy with CDs along the *c*-axis, (**c**) modified *J*c anisotropy with direction-dispersed CDs).

We first examined the influence of bimodal angular distribution of CDs consisting of CDs crossing at ±*θ*i relative to the *c*-axis on the *J*c properties in a wide magnetic field We first examined the influence of bimodal angular distribution of CDs consisting of CDs crossing at ±*θ*<sup>i</sup> relative to the *c*-axis on the *J*<sup>c</sup> properties in a wide magnetic field angular range [27,28]. Figure 6 shows the magnetic-field angular dependence of *J*<sup>c</sup> normalized by the self-magnetic-field critical current density *J*c0 for YBCO thin films with the crossed CDs, which were installed by 200 MeV Xe ion irradiation with *B*<sup>ϕ</sup> = 2 T (c10-2: *θ*<sup>i</sup> = ±10◦ , c25-2: *θ*<sup>i</sup> = ±25◦ , c45-2: *θ*<sup>i</sup> = ±45◦ , p06-2: parallel CD configuration of *θ*<sup>i</sup> = 6◦ , and Pure: unirradiated samples). The magnetic field was rotated in the splay plane where the two parallel CD families are crossing each other, as shown in Figure 4. All the irradiated samples show an additional peak of the normalized *J*<sup>c</sup> around *B* || *c* (*θ* = 0◦ ) for lower magnetic fields: the values of the normalized *J*<sup>c</sup> are enhanced around *B* || *c* compared to the unirradiated one. This indicates that CDs with any crossing angle work as effective PCs, pushing up the *J*<sup>c</sup> around *B* || *c*. The influence of the crossing angle of CDs is evident in the shape of the additional peak around *B* || *c*: the width of the normalized *J*<sup>c</sup> peak becomes broader when the crossing angle is larger. Therefore, the bimodal angular distribution of CDs can expand the magnetic field angular range where the normalized *J*<sup>c</sup> increases, by controlling the crossing angle.

the crossing angle.

**Figure 6.** Magnetic field angular dependence of *J*c normalized by the self-magnetic-field critical current density *J*c0 for YBCO thin films with the crossed CDs (c10-2: *θ*i = ±10°, c25-2: *θ*i = ±25°, c45-2: *θ*i = ±45°, p06-2: parallel CD configuration of *θ*i = 6°, and Pure: unirradiated samples). Reprinted with permission from [28], copyright 2016 by IOP. **Figure 6.** Magnetic field angular dependence of *J*<sup>c</sup> normalized by the self-magnetic-field critical current density *J*c0 for YBCO thin films with the crossed CDs (c10-2: *θ*<sup>i</sup> = ±10◦ , c25-2: *θ*<sup>i</sup> = ±25◦ , c45-2: *θ*<sup>i</sup> = ±45◦ , p06-2: parallel CD configuration of *θ*<sup>i</sup> = 6◦ , and Pure: unirradiated samples). Reprinted with permission from [28], copyright 2016 by IOP.

angular range [27,28]. Figure 6 shows the magnetic-field angular dependence of *J*c normalized by the self-magnetic-field critical current density *J*c0 for YBCO thin films with the crossed CDs, which were installed by 200 MeV Xe ion irradiation with *B*φ = 2 T (c10-2: *θ*i = ±10°, c25-2: *θ*i = ±25°, c45-2: *θ*i = ±45°, p06-2: parallel CD configuration of *θ*i = 6°, and Pure: unirradiated samples). The magnetic field was rotated in the splay plane where the two parallel CD families are crossing each other, as shown in Figure 4. All the irradiated samples show an additional peak of the normalized *J*c around *B* || *c* (*θ* = 0°) for lower magnetic fields: the values of the normalized *J*c are enhanced around *B* || *c* compared to the unirradiated one. This indicates that CDs with any crossing angle work as effective PCs, pushing up the *J*c around *B* || *c*. The influence of the crossing angle of CDs is evident in the shape of the additional peak around *B* || *c*: the width of the normalized *J*c peak becomes broader when the crossing angle is larger. Therefore, the bimodal angular distribution of CDs can expand the magnetic field angular range where the normalized *J*c increases, by controlling

It is noteworthy that the crossover phenomenon from the broad-plateau-like behavior to the double peak emerges on the normalized *J*c around *B* || *c* for c45-2 when the magnetic field increases across the matching field of *B*φ = 2 T: the normalized *J*c more rapidly reduces at *B* || *c* with increasing magnetic field, which results in a dip structure at *B* || *c* for c45-2 at 2 T, as shown in Figure 6. In general, the *J*c peak in the magnetic field angular dependence of *J*c is a sign of long-axis correlated flux pinning of CDs. Their-longaxis correlated flux pinning is maintained up to higher magnetic fields [29,30]. For the crossing angle of *θ*i = ±45°, by contrast, the influence of the long-axis correlated flux pinning is weakened at *B* || *c*, since the directions of CDs are far from the *c*-axis direction. It is noteworthy that the crossover phenomenon from the broad-plateau-like behavior to the double peak emerges on the normalized *J*<sup>c</sup> around *B* || *c* for c45-2 when the magnetic field increases across the matching field of *B*<sup>ϕ</sup> = 2 T: the normalized *J*<sup>c</sup> more rapidly reduces at *B* || *c* with increasing magnetic field, which results in a dip structure at *B* || *c* for c45-2 at 2 T, as shown in Figure 6. In general, the *J*<sup>c</sup> peak in the magnetic field angular dependence of *J*<sup>c</sup> is a sign of long-axis correlated flux pinning of CDs. Their-long-axis correlated flux pinning is maintained up to higher magnetic fields [29,30]. For the crossing angle of *θ*<sup>i</sup> = ±45◦ , by contrast, the influence of the long-axis correlated flux pinning is weakened at *B* || *c*, since the directions of CDs are far from the *c*-axis direction. Thus, the dip behavior at *B* || *c* is a sign of disappearance of their-long axis correlated flux pinning at *B* || *c*.

The effective magnetic field angular region for flux pinning of CDs is described by a trapping angle *ϕ<sup>t</sup>* , at which flux lines begin to be partially trapped by CDs [4]. The general formula of *ϕ<sup>t</sup>* is expressed as:

$$
\varphi\_l = \sqrt{2\,\varepsilon\_p/\varepsilon\_l} \tag{1}
$$

where *ε<sup>p</sup>* is the pinning energy of CDs and *ε<sup>l</sup>* is the line tension of flux lines. The line tension energy of flux lines in anisotropic superconductors is given by the following equation:

$$
\varepsilon\_l(\Theta) \propto \varepsilon\_0 / \gamma^2 \varepsilon(\Theta)^3 \tag{2}
$$

where Θ is the angle between the magnetic field and the *ab*-plane, *ε*<sup>0</sup> is a basic energy scale, *γ* is the mass anisotropy, and *ε*(Θ) = (sin2Θ + *γ* −2 cos2Θ) 1/2 [4]. The trapping angle *ϕ<sup>t</sup>* is experimentally estimated as the difference in the angle between the peak value and the minimum one on the magnetic field angular dependence of *J*<sup>c</sup> [31]. For p06-2, the

value of *ϕ<sup>t</sup>* is ~55◦ at *B* < *B*ϕ, which is estimated from Figure 6a. Using this value of *ϕ<sup>t</sup>* as the trapping angle of CDs parallel to the *c*-axis approximately and *γ* = 5 together with equations (1) and (2), the value of *ϕ<sup>t</sup>* for CDs tilted at *θ*<sup>i</sup> = 45◦ is about 37◦ . Therefore, CDs tilted at *θ*<sup>i</sup> = 45◦ hardly contribute to trapping flux lines at *B* || *c*: CDs tilted at *θ*<sup>i</sup> = 45◦ does not work as their-long-axis correlated PCs for *B* || *c*.

The bimodal angular distribution of CDs for *θ*<sup>i</sup> ±45◦ gives rise to the drop in *J*<sup>c</sup> at the mid-direction of the crossing angle. Secondly, we investigated the flux pinning properties for a trimodal angular distribution of CDs consisting of CDs crossing at *θ*<sup>i</sup> = 0◦ and ±45◦ (referred to as the "standard" trimodal-configuration), in order to obtain high *J*<sup>c</sup> with no drop over a wide magnetic field angular region [32]. In addition, another geometry for the trimodal configuration was prepared, where a splay plane defined by the three irradiation angles is parallel to the transport current direction (referred to as "another" trimodalconfiguration), as shown in Figure 7: the two trimodal configurations enable us to elucidate the influence of the splay plane direction on the *J*<sup>c</sup> properties directly. Figure 8 shows the magnetic field angular dependence of normalized *J*<sup>c</sup> by *J*c0 (= *j*c) at several magnetic fields from 1 T up to 5 T for YBCO thin films with the trimodal angular configurations of CDs. A large enhancement of *j*<sup>c</sup> centered at *B* || *c* can be seen for all the irradiated samples. In particular, both the trimodal angular configurations show a much broader peak with larger *j*<sup>c</sup> than that of the parallel CD configuration. It should be noted that there is no drop of *j*<sup>c</sup> at *B* || *c* for both the trimodal configurations. This result indicates that the three parallel CD families tilted at *θ*<sup>i</sup> = 0◦ and ±45◦ effectively work as strong PCs in each irradiation direction: flux pinning at *B* || *c* where CDs tilted at *θ*<sup>i</sup> = ±45◦ slightly contribute to trapping flux lines, is reinforced by CDs along the *c*-axis. *Quantum Beam Sci.* **2021**, *5*, x FOR PEER REVIEW 8 of 22 direction of the splay plane is one of key factors for flux pinning of direction-dispersed CDs, as well as the degree of the direction-dispersion [32,35].

**Figure 7.** Sketch of CDs dispersed in geometry of "another" trimodal-configuration, where a splay plane defined by the three irradiation angles is parallel to the transport current direction. Reprinted with permission from [32], copyright 2016 by IOP. **Figure 7.** Sketch of CDs dispersed in geometry of "another" trimodal-configuration, where a splay plane defined by the three irradiation angles is parallel to the transport current direction. Reprinted with permission from [32], copyright 2016 by IOP.

Interestingly, the behaviour of *j*<sup>c</sup> around *B* || *c* strongly depends on the direction of the splay plane for the trimodal configuration of CDs: the *j*<sup>c</sup> of another trimodal-configuration shows a peak at *B* || *c*, whereas standard one exhibits not so much a peak as a plateaushaped curve. In addition, the height of *j*<sup>c</sup> peak for another tirmodal-configuration is higher than the value of *j*<sup>c</sup> at *B* || *c* for standard one. For standard trimodal-configuration, sliding motion of flux lines occurs along the tilted CDs at *B* || *c* because of the splay plane parallel to the Lorentz force, resulting in the reduction of the pinning efficiency [33]. The crossed CDs for another trimodal-configuration, by contrast, suppress the motion of flux lines efficiently, since flux lines move across the crossed CDs by the Lorentz force. Thus, the splay plane parallel to the transport current direction provides stronger flux pinning at *B* || *c*, like planar PCs. Furthermore, the *j<sup>c</sup>* of another trimodal-configuration is the highest even when the magnetic field is tilted from the c-axis. This is probably due to the entanglement of flux lines induced in a mesh of the splay plane tilted from the magnetic field, where the motion of flux lines is suppressed [34]. These results suggest that the direction of the splay plane is one of key factors for flux pinning of direction-dispersed CDs, as well as the degree of the direction-dispersion [32,35].

**Figure 8.** Magnetic-field angular dependence of *J*c normalized by the self-magnetic-field critical current density *J*c0 for YBCO thin films with various CD configurations (Pure: unirradiated samples, Para: parallel CD configuration of *θ*i = 0°, Standard: standard trimodal-configuration, and Another: another trimodal-configuration). Reprinted with permission from [32], copyright 2016 by

*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-

IOP.

IOP.

printed with permission from [32], copyright 2016 by IOP.

**Figure 8.** Magnetic-field angular dependence of *J*c normalized by the self-magnetic-field critical current density *J*c0 for YBCO thin films with various CD configurations (Pure: unirradiated samples, Para: parallel CD configuration of *θ*i = 0°, Standard: standard trimodal-configuration, and Another: another trimodal-configuration). Reprinted with permission from [32], copyright 2016 by **Figure 8.** Magnetic-field angular dependence of *J*<sup>c</sup> normalized by the self-magnetic-field critical current density *J*c0 for YBCO thin films with various CD configurations (Pure: unirradiated samples, Para: parallel CD configuration of *θ*<sup>i</sup> = 0◦ , Standard: standard trimodal-configuration, and Another: another trimodal-configuration). Reprinted with permission from [32], copyright 2016 by IOP.

direction of the splay plane is one of key factors for flux pinning of direction-dispersed

**Figure 7.** Sketch of CDs dispersed in geometry of "another" trimodal-configuration, where a splay plane defined by the three irradiation angles is parallel to the transport current direction. Re-

CDs, as well as the degree of the direction-dispersion [32,35].
