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[Y Takeda](https://orcid.org/0000-0001-7217-9853), [G Nishijima](https://orcid.org/0000-0001-7493-0559), [T Motoki](https://orcid.org/0000-0003-3218-0977), [J Shimoyama](https://orcid.org/0009-0007-1783-676X), [H Kitaguchi](https://orcid.org/0000-0002-5998-2649)

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[Temperature, magnetic field, and field angular dependence of critical current of REBCO intermediate grown superconducting joint](https://mdr.nims.go.jp/datasets/e1f4a32b-b3b4-47e1-a3ed-b439719e8dd3)

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Temperature, magnetic field, and field angular dependence of critical current of REBCO intermediate grown superconducting jointSuperconductorScience andTechnology     PAPER • OPEN ACCESSTemperature, magnetic field, and field angulardependence of critical current of REBCOintermediate grown superconducting jointTo cite this article: Y Takeda et al 2025 Supercond. Sci. Technol. 38 125003 View the article online for updates and enhancements.You may also likeDevelopment of a persistent-mode NMRmagnet with superconducting jointsbetween high-temperaturesuperconductorsY Yanagisawa, R Piao, Y Suetomi et al.-Development of a persistentsuperconducting joint between Bi-2212/Ag-alloy multifilamentary round wiresPeng Chen, Ulf P Trociewitz, Daniel SDavis et al.-Review of the temporal stability of themagnetic field for ultra-high fieldsuperconducting magnets with a particularfocus on superconducting joints betweenHTS conductorsY Takeda, H Maeda, K Ohki et al.-This content was downloaded from IP address 144.213.253.16 on 04/12/2025 at 00:48https://doi.org/10.1088/1361-6668/ae1eaa/article/10.1088/1361-6668/ac2120/article/10.1088/1361-6668/ac2120/article/10.1088/1361-6668/ac2120/article/10.1088/1361-6668/ac2120/article/10.1088/1361-6668/30/2/025020/article/10.1088/1361-6668/30/2/025020/article/10.1088/1361-6668/30/2/025020/article/10.1088/1361-6668/ac5645/article/10.1088/1361-6668/ac5645/article/10.1088/1361-6668/ac5645/article/10.1088/1361-6668/ac5645/article/10.1088/1361-6668/ac5645Superconductor Science and TechnologySupercond. Sci. Technol. 38 (2025) 125003 (10pp) https://doi.org/10.1088/1361-6668/ae1eaaTemperature, magnetic field, and fieldangular dependence of critical currentof REBCO intermediate grownsuperconducting jointY Takeda1,∗, G Nishijima1, T Motoki2, J Shimoyama2 and H Kitaguchi11 National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan2 Department of Physical Sciences, Aoyama Gakuin University, 5-10-1 Fuchinobe, Chuo-ku, Sagamihara,Kanagawa 252-5258, JapanE-mail: TAKEDA.Yasuaki@nims.go.jpReceived 3 July 2025, revised 28 October 2025Accepted for publication 12 November 2025Published 3 December 2025AbstractClarifying the critical current characteristics of high-temperature superconducting joints cancontribute to the development of persistent-mode high-temperature superconducting magnets.We evaluated the temperature, magnetic field, and field angular dependence of the criticalcurrent of intermediate grown superconducting (iGS) joints formed between high-temperaturesuperconducting REBa2Cu3Oy (REBCO, RE = rare earth, y ≈ 7) tapes. The critical currentswere determined by performing current decay measurements on closed-loop samples, eachcontaining an iGS joint. The temperature, magnetic field, and field angular dependence of thecritical current of the iGS joints were found to be similar to that of commercially availableREBCO tapes. The critical current characteristics of iGS joints can be described using modelsdeveloped for the tapes. This similarity in the characteristics can contribute to the design ofpersistent-mode magnets using REBCO tapes.Keywords: superconducting joint, high-temperature superconductor, angular dependence,persistent-mode magnet1. IntroductionREBa2Cu3Oy (REBCO, RE= rare earth, y≈ 7) is a promisinghigh-temperature superconductor (HTS) that can be used todevelop superconducting magnets generating very high mag-netic fields at low temperatures, or magnets operated at highertemperatures. REBCO conductors are commercially availablein the form of coated conductor tapes [1, 2]. These tapes have∗Author to whom any correspondence should be addressed.Original content from this work may be used under theterms of the Creative CommonsAttribution 4.0 licence. Anyfurther distribution of this work must maintain attribution to the author(s) andthe title of the work, journal citation and DOI.been used in the development of REBCOmagnets intended forvarious applications, including magnetic resonance imaging[3], nuclear magnetic resonance (NMR) [4], maglev systems[5], generators [6], and fusion energy systems [7].An HTS exhibits anisotropic electromagnetic properties.The critical current (Ic) of a REBCO tape depends on the dir-ection of the applied magnetic field. Superconducting mag-nets made of REBCO tapes have been designed consideringthis anisotropy, that is, the field angular dependence of Ic[8–11]. To accommodate such designs, REBCO tapes havebeen characterized considering the dependence of Ic not onlyon the temperature and magnetic field strength but also on thefield angle [1, 8, 12].Despite the challenges in achieving superconducting jointsbetween HTS conductors, Park et al successfully fabricateda superconducting joint between REBCO tapes [13]. Since1 © 2025 The Author(s). Published by IOP Publishing Ltdhttps://doi.org/10.1088/1361-6668/ae1eaahttps://orcid.org/0000-0001-7217-9853https://orcid.org/0000-0001-7493-0559https://orcid.org/0000-0003-3218-0977https://orcid.org/0009-0007-1783-676Xmailto:TAKEDA.Yasuaki@nims.go.jphttp://crossmark.crossref.org/dialog/?doi=10.1088/1361-6668/ae1eaa&domain=pdf&date_stamp=2025-12-3https://creativecommons.org/licenses/by/4.0/Supercond. Sci. Technol. 38 (2025) 125003 Y Takeda et althis pioneering work, various research groups have developedREBCO superconducting joints [14–19]. One of the mostpromising methods for fabricating such joints is the inter-mediate grown superconducting (iGS) joint technique, whichadopts a joining strap [16]. The REBCO layers of the tapesare connected to the joining strap via an epitaxially grownREBCO intermediate layer. Existing papers report a high Icof the joint (Icj) and a low joint resistance of less than 10−13 Ω[16, 20, 21]. A REBCO coil connected at both ends with iGSjoints was fabricated and combined as an insert in a 400 MHzNMRmagnet. This demonstrates that iGS joints are applicableto persistent-mode NMR magnets [20].The in-field Icj characteristics of several types of REBCOsuperconducting joints have been reported at varioustemperatures [20, 22, 23]. In these studies, the magneticfield was either perpendicular or parallel to the surface of thejoined tape. However, in practice, the direction of the mag-netic field applied to the superconducting joints in a magnetis not necessarily perpendicular or parallel. Since the currentin the iGS joint must flow along the c-axis of REBCO, theangular dependence of Icj may not be as simple as that of Ic ofthe tape.In addition, the reported Icj values of various REBCOsuperconducting joints were evaluated through transportmeasurements, similar to the Ic measurement of a supercon-ducting tape/wire, with a voltage criterion on the order of10−6 V. The voltage of 10−6 V corresponds to the joint res-istance of 10−8 Ω at 100 A. This resistance is too high for apersistent current to flow.We developed (Bi,Pb)2Sr2Ca2Cu3Oy (Bi-2223) HTS jointsand investigated the Icj characteristics of Bi-2223 closed-loopsamples using current decay measurements [24]. This meas-urement method enabled the evaluation of Icj with a low-voltage criterion (Vc) of 10−8 V. This Icj value is comparableto the maximum current at which an iGS joint can exhibit alow resistance. Our previous study suggested that a joint res-istance of 10−12 Ω could be achieved at a current of about 0.8times Icj (Vc = 10−8 V) [25]. In addition, by applying a mag-netic field to the joint in various directions, we evaluated thefield angular dependence of Icj [24].To appropriately design REBCO persistent-mode magnets,the Icj characteristics of the iGS joints with a low-voltage cri-terion should be investigated in detail. In this study, we eval-uated Icj of REBCO closed-loop samples with an iGS joint.The temperature, magnetic field, and field angular dependenceof Icj in the iGS joints are discussed. This study contributesto a better understanding of the underlying materials scienceinvolving REBCO superconducting joints.2. MethodTwo one-turn closed-loop samples, designated as #A and #B,were prepared, each containing an iGS joint. Figures 1(a) and(b) show a schematic of the sample and a schematic of themagnified view of the iGS joint, respectively. The loop dia-meter was 100 mm. The self-inductance (L) of the sampleswas 0.47 µH.Figure 1. (a) Schematic of a one-turn closed-loop sample, alongwith the definition of the magnetic field angle (θ). The magneticfield (B) is applied only to the iGS joint. (b) Schematic of amagnified view of the iGS joint. (c) Cross-sectional view (not toscale) of the joint structure. The position is shown in (b).To prepare the sample, a 1 m-long and 4 mm-wide REBCOtape was used. Ic of the tape at 77 K in the self-field was 280 A,as evaluated by transport measurements under an electric fieldcriterion of 10−6 V cm−1. Both ends of the tape were con-nected via an iGS joint. Figure 1(c) shows a cross-sectionalview (not to scale) of the joint structure. The copper stabiliz-ing layer and silver protection layer at both ends were removedby chemical etching. The intermediate layer was epitaxiallygrown using the joining strap with a microcrystalline REBCOfilm. After a heat treatment with pressure and oxygen anneal-ing, the iGS joint was formed [14, 16]. This joining processdoes not cause severe degradation of the tape. A persistent cur-rent with a low resistance was observed in closed-loop samples[21, 25]. For the iGS joints, every effort was made to ensurethat the area of the REBCO layer exposed to the environmentwas as small as possible.The sample was placed in a previously developed joint res-istance evaluation system [26]. We carefully fixed the samplesto avoid degradation, using the handling method established2Supercond. Sci. Technol. 38 (2025) 125003 Y Takeda et alin our previous study [21]. The angle of the magnetic field (θ)was defined as shown in figure 1(a). The magnetic field dir-ection at θ = 0 was perpendicular to the surface of the join-ing strap, that is, parallel to the c-axis of REBCO. We appliedthe magnetic field only to the joint and rotated the samplearound the central axis, as indicated by the gray dashed linein the figure. This enables the control of the magnetic fieldangle [24].The Icj values were evaluated in the temperature (T) andmagnetic field (B) ranges of 4–77 K and 0.1–2.0 T, respect-ively, under various field angles. Using the evaluation sys-tem, we introduced a current into the closed-loop sample. Thedecay of the introduced loop current (Iloop), that is, the time (t)dependence of Iloop, was measured at a sampling rate of 1 Hz.From the obtained Iloop–t curve, the Iloop dependence of thevoltage (V) was calculated using V=−L∆Iloop/∆t. The V–Iloop was smoothed using a 25-point moving average. The Icjvalue was determined at a voltage criterion (Vc) of 10−8 Vusing the smoothed V–Iloop curve at voltages ranging from4 × 10−9–2 × 10−8 V. To estimate the Icj values by extrapol-ation, some of the smoothed V–Iloop curves were fitted to anempirical power law model (V∝ Iloopn, where n is a constant)using the least-squares method. The details of the evaluationsystem, including the Iloop measurements, and the Icj evalu-ation method are described in [21, 24], respectively.Table 1 shows the Icj and n values of the samples #A and#B at 77 K in the self-field, as evaluated using the methoddescribed in the previous paragraph. The n valuewas evaluatedin the voltage range of 0.5–2× 10−8 V. Sample #A exhibited ahigher self-field Icj than sample #B. In contrast, the n values forthe samples were comparable. Note that the same fabricationprocess for the iGS joint, as described in [16], was applied toboth #A and #B. No artificial pinning centers were introducedinto the REBCO of the iGS joints.3. Results and discussion3.1. Temperature dependenceFigure 2 shows the temperature dependence of Icj in samples#A and #B at θ = 0 (B // c), 45◦, and 75◦ in the magneticfield range of 0.5–1.5 T.We did not evaluate the high Icj valuesfor #A at low temperatures or high fields. There are two mainreasons for this. First, there is an upper limit of the initial Iloopvalue that can be introduced into the sample using our eval-uation system [24]. Another reason is that introducing a highIloop may mechanically degrade the superconducting joint loc-ated in the magnetic field due to the electromagnetic force.Similar to the self-field Icj shown in table 1, a higher Icj wasobserved in #A than in #B at 0.5 T and in the 0–75◦ range.Icj for both #A and #B increased with decreasing temperat-ure under the same magnetic field and angle. Regardless ofthe strength and angle of the magnetic field, the increase in Icjappears to be exponential at temperatures below 50 K in both#A and #B. Such an exponential increase is generally observedin the temperature dependence of the critical current density(Jc) for REBCO tapes below 50 K [27–29]. Considering thenear-single-crystal texture of REBCO in an iGS joint similarto that in a tape [16, 30], the exponential temperature depend-ence of Jc for the tapes can be applied to Icj as follows:Icj (T,B,θ) = Icj (T= 0,B,θ)exp(−T/T∗) , (1)where T∗ is a parameter related to the number of defects thatact as effective pinning centers. From the Icj–T curves in thetemperature range of 20–50 K, we evaluated T∗ for samples#A and #B using (1). Figure 3 shows the angular dependenceof T∗ for #A and #B. Sample #A showed a lower T∗ thansample #B. This implies that there were more pinning defectsin #A than in #B. The T∗ values were in the temperature rangeof 19.7–35.9 K, which were comparable to those reported forvarious REBCO tapes (14–36 K) in the magnetic field rangeof 0–2 T [27–29].We compared the field dependence of T∗ for the iGS jointwith that for REBCO tapes. Figure 4 shows the field depend-ence of T∗ in the angle range of 0–80◦ for #A. The fielddependence can be divided into three angular regions. Inthe low-angle region of 0–45◦, T∗ was independent of thefield, although a slight decrease in T∗ was observed with theincreasing angle. In contrast, at high angles of 75◦ and 80◦,T∗ decreased with increasing field strength. An intermediatebehavior was observed at 60◦, which corresponds to the inter-mediate region.The field dependence of T∗ for the iGS joint is similar tothat reported for various REBCO tapes [27, 29]. In the fieldrange of 0–2 T, the T∗ value for REBCO tapes is independentof the field at θ values of 0 and 45◦, whereas it decreases withincreasing field at 90◦. It is suggested that the Icj for the iGSjoint depends exponentially on the temperature below 50 K,similar to Jc for REBCO tapes.3.2. Magnetic field dependenceFigure 5 shows the magnetic field dependence of Icj at 77 Kand 0–90◦ for #A and #B. In both the samples, Icj at θ= 0 (B //c) was lower than that at 90◦ (B // ab). This is consistent withthe anisotropy of Icj for iGS joints reported previously [20].Icj for both #A and #B decreased with the increasing field.Generally, the field dependence of Jc for REBCO tapes canbe divided into three regimes: a low-field regime where Jc isnearly independent of the field; an intermediate-field regimewith a power-law decrease in Jc; and a high-field regimewhere Jc drops sharply [27, 31]. REBCO superconductingjoint samples, which are not the iGS joints, are known toexhibit a field dependence for Icj in the three regimes [23].As shown in figure 5, the field dependence of Icj in #A and#B at 77 K can be classified into the low- or intermediate-fieldregimes.In the intermediate-field regime at about 1 T, the power lawJc ∝ B−α, where α is a fitting parameter, is generally used forREBCO tapes [27, 32–34]. In the magnetic field range of 0.5–1.5 T, the power law can be applied to Icj–B. We calculated αfor #A in the temperature range of 35–77 K and for #B at 77 Kusing Icj ∝ B−α in the field range of 0.5–1.5 T.Figure 6 shows the angular dependence of α for #A and#B. Random pinning is effective in REBCO tapes with α of3Supercond. Sci. Technol. 38 (2025) 125003 Y Takeda et alFigure 2. Temperature dependence of Icj in samples #A and #B at θ = 0, 45◦, and 75◦ and in the magnetic field range of 0.5–1.5 T. Icjexponentially increases with decreasing temperature below 50 K. At temperatures ranging from 20 to 50 K, the exponential temperaturedependence of Icj described in equation (1) is applicable.Table 1. Self-field Icj (Vc = 10−8 V) and n values (obtained at0.5–2× 10−8 V) of the tested REBCO closed-loop samples at 77 K.Sample Icj (A) n (–)#A 108 36#B 47.5 35Figure 3. Angular dependence of T∗ in samples #A and #B in themagnetic field range of 0.5–1.5 T. Sample #A shows a lower T∗ thansample #B, implying that it contains more pinning defects than #B.about 0.5 [32, 33]. In the temperature and angle ranges of 35–50 K and 0–75◦, respectively, the α value for #A was about0.5, where random pinning is probably the dominant pinningmechanism. The decrease in α close to 90◦ is due to the ab-plane correlated pinning centers [32]. In contrast, α for #Aand #Bwas higher at 77 K. It is reported that α increases as theeffectiveness of the c-axis correlated pinning centers weakens,particularly at high temperatures [34]. This explains the higherFigure 4. Field dependence of T∗ in sample #A in the angle rangeof 0–80◦, which can be divided into three angular regions:low-angle region (0–45◦), intermediate-angle region (60◦), andhigh-angle region (75–90◦). The similar field dependence has beenreported for various REBCO tapes.α value observed at 77 K. At low angles, #B showed higher αthan #A at 77 K. This implies that #B contained fewer c-axiscorrelated pinning centers than #A.We compared the temperature dependence of α for #Awith that for REBCO tapes. Figure 7 shows the temperaturedependence of α for #A in the angle range of 0–90◦. Similarto the field dependence of T∗ shown in figure 4, the temperat-ure dependence of α can be divided into three angular regions.In the low-angle range of 0–45◦, α was largely independentof the temperature in the range of 35–50 K, though it slightlyincreased from 0.47 to 0.56with increasing angle. In the 0–45◦and 50–77 K ranges, α increased with increasing temperature.In contrast, in the 60–80◦ range, α increased linearly with theincreasing temperature from 35 K to 77 K. The temperaturedependence at 80◦ was stronger than that at 60◦ and 75◦. At4Supercond. Sci. Technol. 38 (2025) 125003 Y Takeda et alFigure 5. Field dependence of Icj in samples #A and #B at 77 K and0–90◦. This can be classified into low- or intermediate-field regime,which is used in the division of the field dependence of Jc forREBCO tapes. In the intermediate-field regime of 0.5–1.5 T, thepower law Icj ∝ B−α can be applied.Figure 6. Angular dependence of α in the temperature range of35–77 K for #A and #B. The decrease in α close to 90◦ is due to theab-plane correlated pinning centers. The higher α values at 77 Kcan be attributed to the weakening of the effectiveness of c-axiscorrelated pinning centers.50 K, the lowerα values of 0.33 and 0.37 were observed at 85◦and 90◦, respectively, than those in the 0–80◦ range (0.48–0.58). These results imply that α exhibits a strong temperat-ure dependence in the high-angle range of 80–90◦ from low tohigh temperatures. This corresponds to a decrease inα close to90◦ shown in figure 6, which is due to the ab-plane correlatedFigure 7. Temperature dependence of α in the angle range of 0–90◦in sample #A, which can be divided into three angular regions,similar to the field dependence of T∗ shown in figure 4. The similartemperature dependence of α for various REBCO tapes is reported.pinning centers. The temperature dependence in the 60–75◦range can be classified into the intermediate-angle region.The temperature dependence of α for the iGS joint is sim-ilar to that reported for various REBCO tapes [27, 33]. ForREBCO tapes, α is largely independent of the temperaturebelow 50 K at θ values of 0 and 45◦, while it increases withincreasing temperature above 20 K at 90◦. It is suggested thatthe Icj for the iGS joint depends on the field with a power law inthe intermediate-field regime, similar to Jc for REBCO tapes.3.3. Field angular dependenceFigure 8 shows the field angular dependence of Icj in samples#A and #B in the temperature range of 4–77 K and in the fieldstrength range of 0.1–2.0 T, where the symbols indicate theexperimentally obtained values. At 4, 20, and 35 K, the Icj val-ues close to 90◦ are missing due to the upper limit of the initialIloop value and avoiding a large electromagnetic force. Figure 8shows all the evaluated Icj data points for #B. Regardless of thefield and temperature, Icj for both #A and #B exhibited a peakat 90◦ (B // ab). This peak is generally observed in the angulardependence of Jc for REBCO tapes without artificial pinningcenters [12, 35].In the 1.0–2.0 T range and at θ = 0, a small peak for Icj wasobserved in #A. This peak is typically observed in the angu-lar dependence of Jc for an undoped REBCO film [36]. Thisis due to c-axis correlated defects, such as twin boundaries orstacking faults. Considering the near-single-crystal texture inan iGS joint [16, 30], the same pinning mechanism is applic-able. It is suggested that the c-axis correlated defects acted aseffective pinning centers in #A. This is consistent with the dis-cussion in section 3.2: There are fewer c-axis correlated pin-ning centers in #B. This is because no Icj peak was observedat θ = 0 in #B.5Supercond. Sci. Technol. 38 (2025) 125003 Y Takeda et alFigure 8. Angular dependence of Icj in samples #A and #B in the temperature range of 4–77 K and the magnetic field strength range of0.1–2.0 T. Symbols indicate the experimentally obtained values. Black solid curves are the fitted curves at 50 and 77 K obtained usingequations (2) and (3). Regardless of the field and temperature, Icj for both #A and #B shows a peak at 90◦. Although equations (2) and (3)are proposed for a REBCO tape, the Icj–θ fitted curves are in good agreement with the experimentally obtained values.Given that the angular dependence of Icj for both #A and #Bwas similar to that of Jc for REBCO tapes, the Icj–θ data werefitted using the Ic model for the tapes. We fitted the Icj–θ dataat 50 and 77 K, where the Icj (θ = 90◦) values were obtained.The black solid curves in figure 8 are the fitted curves obtainedusing equations (2) and (3), as follows [37]:Icj (T,B,θ) = a1f1 (ω1 (T,B) ,θ)+ a2f2 (ω2 (T,B) ,θ) ,{f1 (ω1,θ) =1ω12cos2θ+sin2θf2 (ω2,θ) =1√cos2θ+ω22sin2θ(2)(a1a2)=ω12ω21−ω12ω2[ω2−1 −1−1 ω1−2](Icj (θ = 0)Icj (θ = 90◦)).(3)The fitting parameters ω1 and ω2 are the peak sharpnessparameters. Equations (2) and (3) describe the angular depend-ence of Ic for a commercially available REBCO tape [37].The excellent fit shown in figure 8 indicates that the angulardependence of Icj for the iGS joints can be described using themodel for the REBCO tape.Figure 9 shows the magnetic field dependence of the fittingparametersω1 andω2 for #A and #B at 50 and 77 K. The figuresuggests that ω1 for both #A and #B depends on the magneticfield and probably converges to about 5 with increasing fieldstrength. In contrast, ω2 is largely independent of the magneticfield. The variation in ω2 (0.67–1.21) was lower than that in ω1(2.30–8.30). The lower variation in ω2 has also been reportedfor the fitted Icj–θ curves of a REBCO tape [38].Equation (2) shows that f 2 is concave upward with ω2 > 1.The term a2f 2 in (2) has little effect on the sharpness of the Icjpeak at 90◦ with ω2 ≳ 1. The peak sharpness is in turn mainlydetermined by the term a1f 1. Equation (2) also shows that withFigure 9. Field dependence of the fitting parameters ω1 and ω2 inequations (2) and (3) for samples #A and #B at 50 and 77 K. It issuggested that ω1 depends on the field and probably converges toabout 5 with increasing field strength. In contrast, ω2 is largelyindependent of the field and its variation is lower than that of ω1.ω1 > 1, the greater the ω1 value, the sharper the peak of f 1 at90◦. An increase in ω1 with increasing field was observed in#A at 50 K with ω2 in the range of 1.12–1.21. This increase inω1 corresponds to the peak sharpening of Icj.To evaluate the sharpness of the Icj peak at 90◦, we cal-culated the full width at half maximum (FWHM) of the peakusing the fitted Icj–θ curves shown in figure 8. Figure 10 showsthe magnetic field dependence of the FWHM for #A and #B6Supercond. Sci. Technol. 38 (2025) 125003 Y Takeda et alFigure 10. Field dependence of FWHM in samples #A and #B at 50and 77 K. FWHM decreases with the applied field and converges toa range of 20–25◦ above 1 T. Inset shows the relationship betweenFWHM and ∆θ defined by equation (4). The gray dashed linecorresponds to FWHM = ∆θ. Most of the data points are in thevicinity of this line, suggesting that the Icj peak at 90◦ can beinterpreted by Long’s model.at 50 and 77 K. The FWHM decreases with increasing fieldand converges to a range of 20–25◦ above 1 T. Long repor-ted that the effectiveness of c-axis correlated pinning centersincreases at low fields in a REBCO tape, resulting in peakbroadening [35]. This is consistent with the field dependenceof the FWHM, as shown in figure 10. A decrease in the FWHMwith increasing field was observed for #A at 50 K. This cor-responds to the peak sharpening of Icj with an increase in ω1described above.We physically interpret the relationship between ω1 andthe FWHM. Long proposed a physical model to explain theangular dependence of Jc in a REBCO tape [35]. The modelassumes that the pinned vortex path can be described as adirected random walk along defects. The relationship Jc ∝(cos2θ+Γ22sin2θ)−1is proposed, whereΓ2 is the peak sharp-ness parameter. The parameter Γ2 has a physical meaningassociated with the random walk and is inversely proportionalto the average spacing of c-axis correlated defects.As described above, from equation (2), the peak sharpnessis mainly determined by the term a1f 1 withω2 ≳ 1. In this case,Icj ∝(cos2θ+ω1−2sin2θ)−1is applicable to describe the peakat 90◦. This means that ω1−1 is probably consistent with Γ2 inLong’s model. Here, we assume Icj ∝(cos2θ+ω1−2sin2θ)−1to describe the peak at 90◦. The FWHM for the peak (∆θ) iscalculated as follows:∆θ = 2arcsin1√ω12 + 1. (4)The inset in figure 10 shows the relationship between ∆θand FWHM for #A and #B at 50 and 77 K and in the fieldstrength range of 0.1–2.0 T. The gray dashed line correspondsto FWHM = ∆θ.Most of the data points are near the dashed line. This sug-gests that the above assumption is correct for these data points,meaning that ω1−1 is consistent with Γ2 in Long’s model. At77 K and in the 0.5–2 T range, Γ2 is reported to range from0.09 to 0.22 [35], which is comparable to the ω1−1 range of0.18–0.21. Thus, at most temperatures andmagnetic fields, thepeak of Icj at 90◦ can be interpreted using Long’s model. Thisimplies that ω1−1 has the same physical meaning as Γ2. Theω1 value of about 5 at 77 K and field strength range of 0.5–2 Tfor both #A and #Bmay suggest that the average spacing of theeffective c-axis correlated defects is similar in both the joints,which were fabricated using the same fabrication process.The data points at 77 K under 0.1 T (#A) and 0.1–0.2 T(#B) are far from the dashed line. Under these conditions, theIcj peak at 90◦ was relatively heavy-tailed. This makes it diffi-cult to describe the peak using f 1. From equation (2), f 2 withω2 < 1 is concave downward and influences the peak shape.Considering the heavy-tailed peaks with ω2 < 1 in these datapoints, the FWHM was determined by both f 1 and f 2. Thisresulted in data points that were far from the dashed line. Notethat f 2 is also used to express the Jc peak at 90◦ for REBCOtapes, particularly when random pinning is effective [39–41].This probably corresponds to the fact that heavy-tailed peaksare observed at low fields in the field strength range of 0.1–0.2 T.Icj of the iGS joints depends on the magnetic field angle,similar to Jc of REBCO tapes. The Icj peak at 90◦ can be phys-ically interpreted at most temperatures and magnetic fieldsusing Long’s model to explain the Jc peak for the tape [35].3.4. DiscussionAs discussed in sections 3.1–3.3, our results suggest that theIcj(T, B, θ) characteristics of the iGS joint are similar to theJc(T, B, θ) characteristics of the REBCO tapes. This findingcan contribute to the design of persistent-mode REBCO mag-nets using iGS joints. Because Icj is noticeably lower than Icfor REBCO tapes, the iGS joints should be placed in a low-field area and the surface of the joining strap should be nearlyparallel to the magnetic field, that is, B // ab.The critical current ratio (CCR: Icj divided by wire Ic) isoccasionally used to compare the performance of a supercon-ducting joint with that of the virgin wire [42]. We attempted toestimate the rough CCR at 77 K in the self-field using the Icj(Vc = 10−8 V) values. Ic of the tape (Ictape) at 10−8 Vcm−1 canbe extrapolated to be 220 A from that at 10−6 V cm−1 (280 A),assuming that a typical n value of 20 [2] is constant at electricfields lower than 10−6 V cm−1. The rough CCR values wereestimated to be 49% for #A and 21% for #B. These CCR val-ues appear to indicate the joint performance comparedwith thevirgin tape. However, Ictape at 10−8 V cm−1 would be under-estimated due to higher n values at lower electric fields [43].In addition, for the proper calculation of CCR, Icj and Ictapemust be determined using the same criterion of the voltageor electric field. The estimated rough CCR values have littlequantitative meaning. They are merely a qualitative indicatorshowing that the performance of the iGS joint is still lowerthan that of the virgin tape.7Supercond. Sci. Technol. 38 (2025) 125003 Y Takeda et alThe similarity in the characteristics of the iGS joint to thoseof the REBCO tapes is contrary to our initial expectation.Although the entire assembly of the iGS joint is REBCO, thecurrent in the joint must flow along the c-axis. This is a consid-erable difference compared with a tape, in which the ab-planetransport should determine Ic. The c-axis transport propertiesin HTS materials have been an interesting topic of discussion[44]. The clarification of the Icj characteristics of the iGS jointwill contribute to this discussion of the c-axis transport.From this study, however, it is difficult to clarify whetherIcj is determined by Jc parallel to the ab-plane (Jc//ab) or c-axis (Jc//c) at the joint. Considering the similarity in the char-acteristics of the iGS joint to those of the REBCO tapes, it ispossible that Jc//ab at the joint contributes significantly to Icj.However, previous studies have suggested that Icj is determ-ined by Jc//c at the joint [16, 20]. Jia et al reported that Jc//c at90◦ (B // ab) is higher than that at θ = 0 (B // c) for a REBCOtape [45]. This implies that the angular dependence of Jc//c issimilar to that of Jc//ab for the REBCO tape. Considering thisangular dependence, it is possible that Jc//c at the joint contrib-utes significantly to Icj. Further studies are needed to clarifythe contribution of Jc//ab and Jc//c to Icj.Sample #B exhibits a lower Icj value than sample #A.This difference in Icj cannot be attributed to the effectivejoint area but to the effective pinning centers. This is because#B has fewer c-axis correlated pinning centers, such as twinboundaries [36]. It is possible that the insufficient oxygen sup-ply in #B, which is due to the formation of an intermedi-ate grown layer that requires longer time for oxygen diffu-sion, resulted in fewer twin boundaries and a lower Icj. Theintermediate grown layer in #B may contain a small num-ber of grain boundaries, which act as oxygen diffusion paths[16]. Microstructural analyses, including lattice constant eval-uations and microstructural observations, will help verify thisassumption. The lattice constants evaluated by x-ray diffrac-tion measurements will determine the average oxygen con-tent of the joints. The distribution of oxygen content maybe clarified by measuring local critical temperatures usingmagneto-optical imaging or magnetic microscopy. The micro-structural observations will reveal the presence of c-axis cor-related defects in the joints, such as twin boundaries or stack-ing faults.In a preliminary experiment, we observed the variation inIcj in four closed-loop samples, including #A and #B, althoughthe same fabrication process for the iGS joint [16] was applied.The four samples showed the Icj (Vc = 10−8 V) values of 40.6,47.5, 88.5, and 108 A at 77 K in the self-field, respectively.There is room for improving the reproducibility of fabricatingan iGS joint. This may be due to the mechanical pressure dur-ing heat treatment, the quality of the REBCO layer of tapes,and the tape thickness are not uniform. Also, the oxygen con-tent is one of the dominant factors affecting Icj, as describedin the previous paragraph. It is necessary to clarify the effectof various factors on Icj. This will contribute to improving thefabrication reproducibility.One of the promising methods to increase Icj reproduciblyis the introduction of effective pinning centers into an iGSjoint. This may also lead to achieving a flatter angular depend-ence of Icj. We studied the introduction of BaMO3 (M = Sn,Zr, Hf) nanoparticles and Ba2Cu3O4X2 (X = Cl, Br) precipit-ates as pinning centers into REBCO films fabricated using themetal-organic deposition (MOD) process [46–48]. Our previ-ous studies have reported that the Ba2Cu3O4X2 precipitates notonly promote epitaxial growth of the REBCO layer at lowertemperatures but also act as c-axis correlated pinning centers.Given that an iGS joint is fabricated using a similar MODprocess [14, 16], these secondary phases may serve as effect-ive pinning centers. We plan to fabricate iGS joints with thesesecondary phases introduced.To contribute to the discussion of the c-axis transport prop-erties in HTS materials and improve the reproducibility of thefabrication, the bottleneck in the iGS joint where Icj is dom-inant should be clarified. The iGS joint contains three layersof REBCO: REBCO in the joined tapes, REBCO in the join-ing strap, and an intermediate grown layer [16]. The currentflowing through the iGS joint passes through three REBCOlayers and four joining interfaces. We plan to analyze eachREBCO film in the joined tapes, joining strap, and interme-diate grown layer. Further studies can consider the dominantfactors affecting Icj for the iGS joint. This can help to morecomprehensively understand the materials science involved inHTS joints.4. ConclusionIn this study, the temperature, magnetic field, and field angulardependence of Icj (Vc = 10−8 V) in iGS joints was discussed.The Icj characteristics of these joints were found to be sim-ilar to the Jc characteristics of commercially available REBCOtapes. The temperature, field, and angular dependence of Icjcan be described using models developed for REBCO tapes.Icj depends exponentially on the temperature, on the magneticfield strength with a power law in the intermediate-field regimeand on the angle, which shows a peak in the field parallel tothe ab-plane. The similarity between the characteristics of theiGS joint and REBCO tapes can contribute to the design ofpersistent-mode magnets using REBCO tapes.Data availability statementAll data that support the findings of this study are includedwithin the article (and any supplementary files).AcknowledgmentThis work was supported by JST Mirai-Program GrantNumbers JPMJMI17A2 and JSPS KAKENHI Grant NumberJP22K14482, Japan. 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Introduction 2. Method 3. Results and discussion 3.1. Temperature dependence 3.2. Magnetic field dependence 3.3. Field angular dependence 3.4. Discussion 4. Conclusion References