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Direct Jc measurements and trapped field profiles using an identical superconducting bulk

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2011 Supercond. Sci. Technol. 24 105003(http://iopscience.iop.org/0953-2048/24/10/105003)
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IOP PUBLISHING

SUPERCONDUCTOR SCIENCE AND TECHNOLOGYSupercond. Sci. Technol. 24 (2011) 105003 (6pp)

doi:10.1088/0953-2048/24/10/105003

Direct Jc measurements and trapped field
profiles using an identical superconducting
bulk
Hiroyuki Fujishiro1 , Tomoyuki Naito1 , Daiki Furuta1 ,Takahiro Arayashiki1 , Yousuke Yanagi2 and Yoshitaka Itoh2
1
2

Faculty of Engineering, Iwate University, 4-3-5 Ueda, Morioka 020-8551, JapanIMRA Material R&D Co. Ltd, 2-1 Asahi-cho, Kariya 448-0032, Japan

E-mail: fujishiro@iwate-u.ac.jp

Received 20 February 2011, in final form 22 July 2011
Published 12 August 2011
Online at stacks.iop.org/SUST/24/105003
Abstract
We measured the trapped field profiles on a 45 mm GdBCO superconducting bulk plate of
2 mm thickness magnetised using pulsed field magnetisation (PFM), zero-field-cooledmagnetisation (ZFC) and field-cooled magnetisation (FCM). The profiles were compared withthe distribution of the absolute value of the critical current density ( Jc ) estimated by themagnetisation measurements using small pieces cut from the bulk plate. The Jc value wasenhanced about 20% below the seed crystal compared with that in the growth sector regions(GSRs). The Jc value was also slightly enhanced on the growth sector boundaries (GSBs). For alower applied pulsed field than that for full magnetisation for PFM, a small amount of themagnetic flux was preferentially trapped at the lower Jc region around the bulk periphery, which
was not necessarily similar to that by ZFC. For a higher applied pulsed field, the magnetic flux
was finally trapped below the seed crystal and at the GSBs.

profile depends qualitatively on the Jc distribution and thestrength of the applied pulsed field; Jc in the GSB is larger
than that in the GSR. The Jc and the transition temperature
Tc distributions using the magnetisation measurement werereported by Dewhurst et al for the YBCO bulk of 20 mm indiameter [3]. These values depended on the distance from theseed crystal along the radius and c-axis directions. However,the difference in the absolute value of Jc between GSB and
GSR has not been reported. Eisterer et al measured the‘magnetoscan’ profile at 77 K on the bulk, which was thought
to represent the relative Jc distribution and investigated therelation between the magnetoscan profile and the trapped field
one magnetised by FCM [4]. However, they did not report theabsolute value of Jc on GSB and GSR, and there were no dataon the position dependence of the absolute value of Jc .
Zero-field-cooled magnetisation (ZFC) is a magnetisingtechnique using a superconducting coil, just as FCM does.
Actually, ZFC can be regarded as a kind of PFM techniquein which the duration of the applied magnetic pulse is aslong as 100–1000 s. Consequently, the temperature rise for
ZFC is fairly small because of the much lower velocity for

1. Introduction
Recently, pulsed field magnetisation (PFM) has been studied
intensively as a convenient magnetising technique forsuperconducting bulk materials. The trapped field BTP by PFM
was, however, small compared with the trapped field BTFCM byconventional field-cooled magnetisation (FCM) because of alarge increase in temperature caused by the dynamical motionof the magnetic flux. The trapped field profile by FCM showsa symmetrical cone shape, even though a small fluctuation of
the critical current density Jc exists in the bulk. However,
the trapped field profile by PFM is very inhomogeneous ingeneral [1] because the magnetic flux motion is as fast as
1–100 ms with a local and large temperature rise, whichis thought to be highly sensitive to the inhomogeneous Jc
distribution in the bulk. Yanagi et al reported that themagnetic flux was trapped in SmBCO bulk mainly aroundthe growth sector region (GSR) for the lower magnetic pulse
application; then the trapped flux region was inclined at
45◦ to the growth sector boundary (GSB) for the higher
magnetic field [2]. These results suggest that the trapped field
0953-2048/11/105003+06$33.00

1© 2011 IOP Publishing Ltd Printed in the UK & the USA

Supercond. Sci. Technol. 24 (2011) 105003

H Fujishiro et al

the magnetic flux propagation than that for PFM [5]. The
temperature rise for PFM also decreases concomitantly withdecreasing strength of the pulsed field [6]. We can presume
that the trapped field profile and the temperature rise for PFM
with a lower pulse application than that for full magnetisation
somewhat resembles those for ZFC. That is, the magnetic flux
might be trapped around the lower Jc region for a lower pulsed
field.
The superconducting bulk is commercially available as
30–60 mm in diameter, with 10–20 mm thickness. The
inhomogeneity of the Jc might exist both in the ab plane
and along the c axis in the bulk because of the characteristic
mechanism of the crystal growth of bulk superconductors [7].
It is unsuitable to use the thick bulk to clarify the relation
between the trapped field profile and the Jc distribution becauseof the inhomogeneity of Jc along the c axis. The penetration of
the flux for the thin bulk occurs both from the side surface andfrom the top and bottom surfaces. The full penetration field forthe thin bulk is much lower than that for the thick bulk and theflux dynamics may be different.
As described in this paper, we sliced the 45 mm
superconducting thick bulk to a thin plate of 2 mm thickness.
We investigated the trapped field profiles on the thin bulk platemagnetised by PFM, ZFC and FCM under the lower appliedfield. The bulk plate was later cut into small pieces and the
Jc distribution was estimated using the small pieces. The
relation between the trapped field profiles and the distributionof the absolute value of Jc was investigated. The mechanismof the flux penetration and trap was also discussed during
magnetising processes.

Figure 1. Experimental set-up for (a) PFM and (b) ZFC and FCM.
(c) Position of the small pieces cut from the bulk plate. Using thepieces, the magnetisations, M(H ) and M(T ), were measured for theestimation of the critical current density Jc and the transition
temperature Tc .

2. Experimental details
A 45 mm GdBaCuO superconducting thin disc of 2 mm
thickness (SRL/ISTEC, Japan) was sliced from the top surfaceof the 15 mm thick bulk disc [8], for which NdBaCuO single
crystal was used as a seed crystal. Figure 1(a) presents theexperimental set-up for PFM. The thin bulk disc was mounted
tightly on the cold stage of a Gifford–McMahon (GM) cycle
helium refrigerator with a 1 mm thick stainless steel cap. The
magnetising solenoid copper coil, which was cooled using
liquid nitrogen, was placed outside the vacuum chamber. The
temperature Ts of the bulk was controlled to 40 or 60 K. A
magnetic pulse Bex with a rise time of 12 ms and durationof 100 ms was applied to the bulk plate. Two-dimensional
trapped field profiles of BTP (1 mm) were mapped at a distanceof z = 1 mm above the bulk surface, stepwise with a pitchof 1 mm by scanning an axial-type Hall sensor (BHA 921;
F W Bell) inside the vacuum chamber using an x – y stage
controller.
Figure 1(b) shows the experimental set-up for ZFC and
FCM. The bulk plate was tightly anchored similarly on the
refrigerator. The ZFC was performed at Ts = 40 K
using a cryo-cooled superconducting solenoid magnet (JMTD10T100, JASTEC. Inc.). During ZFC, the magnetic field
was increased with 3 mT s−1 . Thereafter, it was kept at the
maximum field for 10 min and then reduced to 0 T with
−3 mT s−1 . For FCM, the magnetic field of 1.5 T was reduced

to zero with −3 mT s−1 at 40 K. Contrary to the trapped field
profile for PFM measured at z = 1 mm, the trapped field
profiles, BTZFC (4 mm) and BTFCM (4 mm), were measured on
the vacuum sheath surface at a distance of z = 4 mm from thebulk surface. We cannot measure the trapped field profiles for
PFM and ZFC/FCM under an identical distance, z , from the top
surface of the bulk because of the limitation of the experimental
apparatus.
After measurements of the trapped field profiles magnetised by PFM, ZFC and FCM, the thin bulk was cut into
small pieces. Figure 1(c) shows the positions of these small
pieces. The 27, 30 and 33 small pieces were, respectively,
cut along the A, B and C lines. The C line is just on
the GSB. The position of X = −7 mm is the position atwhich the seed crystal was put during the crystal growth.
The size of the small pieces was about 1 × 1 × 2 mm3 .
The magnetisation M was measured at 50 and 77 K underthe magnetic field parallel to the c axis of the pieces up
to μ0 H = 5 T using a commercial SQUID magnetometer(MPMS-5T; Quantum Design). The critical current density
Jc was estimated from the M(H ) hysteresis loop using theextended Bean model, Jc = 20M/a(1 − a/3b), where a2Supercond. Sci. Technol. 24 (2011) 105003

H Fujishiro et al

Figure 2. (a) Trapped field BT (z = 1 mm) at the centre of the bulk magnetised by PFM ( Ts = 40 and 60 K) as a function of the applied field
Bex . The trapped field profiles for (b) Bex = 1.35 T and (c) Bex = 1.67 T. The positions of the GSB and the seed are referred to in figure 1(c).

and b are the dimensions of the ab plane of the sample andM is the width of the M(H ) loop. The superconducting
transition temperature Tc of the samples was determined fromthe midpoint of the characteristically sharp transition using thetemperature dependence of the magnetisation M(T ) under themagnetic field of μ0 H = 0.4 mT during ZFC.

increased concomitantly with increasing Bex . It should benoticed that BTZFC (4 mm) was larger than BTP (1 mm) as shownin figure 2(a) for Bex  1.5 T, even though the measuring
distance of the trapped field by ZFC is further than that by PFM
from the bulk surface. Because the magnetic flux penetrated
gradually for ZFC it was trapped during the slow ascent anddescent periods, with the long hold time. Using the analytical
calculation presented by Chen et al [9], we calculated the
BT (z) along the central axis. The BT (z) for z = 4 mm wasabout 57% as small as that for z = 1 mm for the bulk diameterof 45 mm and the thickness of 2 mm under an identical
Jc . Figures 3(b) and (c) present the trapped field profiles at
z = 4 mm magnetised by ZFC for Bex = 0.5 T and 1.5 T.
A small amount of magnetic flux was trapped mainly at theupper region of the figures and also at the right and lower
regions of the bulk periphery. For lower Bex , the region inwhich the magnetic flux was mainly trapped is presumed to
be a low Jc region. The rise time of the applied field for ZFC
at Bex = 1.5 T was about 900 s, which was four orders ofmagnitude longer than that of the present PFM. The differenceof the velocity of the magnetic flux results in the temperaturerise in the bulk. Using our previous results [6], the temperaturerise for PFM was estimated as 5 K for Bex = 1.5 T at 40 K.
The temperature rise for ZFC was reportedly as small as 1 K
for Bex = 1.5 T [5].
These results suggest a lack of interrelation between thetrapped field profiles for ZFC and PFM. The mechanism of themagnetic flux penetration and trap for PFM was not necessarily
the same as that for ZFC, even though the applied field Bex was
identical. In figure 3(a), BTFCM (4 mm) = 0.76 T magnetised
by FCM (Ts = 40 K) was also shown. The trapped field
profile BTFCM (4 mm) was shown in figure 3(d), which showed
the concentric circular shape. The measurement of the trapped

3. Results and discussion
3.1. Trapped field profiles by PFM, ZFC and FCM
Figure 2(a) shows the trapped field BTP (1 mm) magnetised by
PFM (Ts = 40 and 60 K) at the centre of the bulk as a functionof the applied pulsed field Bex . Figures 2(b) and (c) show
the trapped field profiles at z = 1 mm for Bex = 1.35 and1.67 T. BTP (1 mm) was nearly zero for lower Bex than 1.5 T at
Ts = 40 K and a small amount of the magnetic flux was trapped
only around the bulk periphery. For Bex = 1.35 T shownin figure 2(b), the magnetic flux can be trapped mainly at thelower right and the upper left regions. However, the magnetic
flux penetrated suddenly; it was trapped at the bulk centre for∗Bex  Bex(=1.5 T). For Bex = 1.67 T shown in figure 2(c), themagnetic flux penetrated in the centre of the bulk and a large
amount of magnetic flux was trapped mainly around the seed∗region and along the GSBs. The critical field Bex
decreasedconcomitantly with increasing Ts because of the decrease in thecritical current density of the bulk. The BTP versus Bex curves∗
are popular for the ordinary bulk [6]. However, Bex
for a thinbulk plate is lower than that for ordinary bulks as thick as 10–
15 mm in thickness.
Figure 3(a) shows the trapped field BTZFC (4 mm)
magnetised by ZFC at 40 K at the centre of the bulk asa function of the applied field Bex . BTZFC (4 mm) slowly
3Supercond. Sci. Technol. 24 (2011) 105003

H Fujishiro et al

Figure 3. (a) Trapped field BT (z = 4 mm) magnetised by ZFC and BT (z = 4 mm) magnetised by FCM at the centre of the bulk ( Ts = 40 K)
as a function of the applied field Bex . The trapped field profiles for (b) Bex = 0.5 T by ZFC, (c) Bex = 1.5 T by ZFC and (d) Bex = 1.5 T by
FCM. The positions of the GSB and the seed are referred in figure 1(c).

field profile magnetised by FCM was performed after the PFM
and ZFC. No plausible crystal damage, introduced by thethermal and mechanical stresses, was observed by the BTFCM(4 mm) profile, as Tomita pointed out [10], which may result
from the Ag addition in the bulk.
3.2. Tc and Jc distributions estimated by the magnetisation
measurements
To estimate the Tc and Jc distributions in the bulk directly,
the bulk disc was cut into small pieces along the threelines. Then the temperature and applied field dependences ofmagnetisation, M(T ) and M(H ), were measured. Figure 4
depicts the position dependences of Tc along three lines. Along
A and B lines, Tc is nearly 93 K and the change of Tc is within
0.5 K, which is independent of the position X . However, it
should be noticed that, along the C line, Tc around the seed
position was relatively low, which may result from the Ndcontamination from the seed crystal, as was seen in the YBCO
bulk [3].
Figures 5(a) and (b) respectively depict the estimated Jc asa function of the applied field μ0 H at 50 K for the small pieces
along the B line and the C line. The Jc –μ0 H curves do notshow the monotonic decrease concomitantly with increasing
the applied field, but show the so-called ‘peak effect’, which
results from the existence of the field-induced pinning centre.
The position, at which the peak effect took place, and themagnitude of the peak effect depended clearly on the positionof the small pieces.
Figures 6(a) and (b) respectively show the position
dependence of the Jc at 50 K and 77 K along the three lines.

Figure 4. Position dependence of the Tc (mid) along the three lines,
which was defined as half the value of the normalised magnetisation.

Jc was estimated at μ0 H = 1.6 T using the Jc –μ0 H curves as
depicted in figure 5. Because the maximum applied field was as
low as 2 T for the present magnetisation procedures, it should
be noted that the Jc values increase for the A, B and C lines
in this order at each position because the C line is on the GSB
and the pinning strength is greater than that on the GSR. The
position dependence of Jc is not necessarily consistent with thetrapped field profiles by ZFC and PFM for lower applied field.
In the C line, it is noteworthy that the Jc value wasabout 20% enhanced broadly at around the seed position( X = −7 mm), compared with other positions. Aroundthe seed position, Tc decreased slightly as shown in figure 4.
The enhancement of Jc comes from the increase in the4Supercond. Sci. Technol. 24 (2011) 105003

H Fujishiro et al

Figure 5. Estimated Jc as a function of the applied field μ0 H at 50 K
for small pieces along (a) the B line and (b) the C line.

Figure 6. Position dependence of the Jc at (a) 50 K and (b) 77 K
along the three lines.

field-induced pinning centres of the weak superconducting
region such as the Nd-substitution region for the Ba site [8].
The Jc value was also enhanced slightly around the GSB
in the B line. The enhancement of the Jc was confirmed
experimentally around the GSB, which resulted from theincrease of the crystal defect around the GSB and the seed
position, and acted as strong pinning centres.
Similarposition dependences were confirmed at other magnetic fields.
However, the inhomogeneity of the measured Jc was rather
small. The inhomogeneity in the trapped field profile by
PFM was rather large as shown, for example, in figure 2(c)for higher applied pulsed field. Because the magnetic flux
penetrates in the bulk from the bulk periphery during PFM,
the inhomogeneity of the trapped field profile results from thevery small fluctuation of the Jc value around the outermost
peripheral region. The trapped field of the bulk materials wasreported to be much lower than that expected from the Jc values
measured using small samples. It is difficult to correlate local
Jc properties with trapped field behaviour on the bulk.

of important results and conclusions obtained from this study
is presented below.
(1) For a lower applied pulsed field than that for fullmagnetisation for PFM, a small amount of the magnetic
flux was preferentially trapped at the lower Jc region
around the bulk periphery, which was not necessarily
similar to that by ZFC.
(2) For a higher applied pulsed field, the magnetic flux
penetrated in the centre of the bulk and was mainly trapped
below the seed crystal and at the growth sector boundaries(GSBs). The results were qualitatively consistent withthose reported by Yanagi et al.
(3) The Jc value, as estimated using the magnetisation
curves, was enhanced about 20% below the seed crystal,compared with that on the GSRs. The Jc value was alsoslightly enhanced on the GSBs.
(4) The trapped field profile for PFM depends mainly on the
Jc distribution. The profile also depends on the appliedfield Bex and the local temperature rise. The magnetic flux
necessarily penetrates the bulk from the lower Jc region
around the outermost periphery of the bulk. However,
it is difficult to determine the intrusion position of themagnetic flux for a high-quality superconducting bulk
and to correlate the local Jc properties with trapped field
behaviour of the bulk.

4. Summary
We have measured the trapped field profiles on a 45 mm
GdBCO superconducting bulk disc of 2 mm thickness
magnetised using PFM, ZFC and FCM, and comparedthose with the transition temperature Tc and Jc distributions
estimated using the magnetisation measurements. A summary5Supercond. Sci. Technol. 24 (2011) 105003

H Fujishiro et al

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