IOP PUBLISHING

SUPERCONDUCTOR SCIENCE AND TECHNOLOGYSupercond. Sci. Technol. 22 (2009) 065014 (8pp)

doi:10.1088/0953-2048/22/6/065014

Thermal and magnetic behaviors of amelt-textured superconducting bulk
magnet in the zero-field-coolingmagnetizing process
T Oka1 , K Yokoyama2, H Fujishiro3 and K Noto3
1

Faculty of Engineering, Niigata University, 8050 Ikarashi-Nino-cho,Nishi-ku, Niigata 950-2181, Japan
2
Ashikaga Department of Electrical and Electronic Engineering, Institute of Technology,268-1 Ohmae-cho, Ashikaga, Tochigi 326-8558, Japan
3
Faculty of Engineering, Iwate University, 3-4-5 Ueda, Morioka, Iwate 020-8551, Japan
E-mail: okat@eng.niigata-u.ac.jp

Received 15 February 2009, in final form 5 April 2009
Published 19 May 2009
Online at stacks.iop.org/SUST/22/065014
Abstract
The heat generation and magnetic field trapping behaviors of the melt-textured single-domain
Sm–Ba–Cu–O bulk superconductor have been precisely investigated in the zero-field-coolingmagnetizing processes (ZFC). The temperature and magnetic flux density were simultaneously
measured in the temperature range of 50–60 K. Since the invasion of magnetic flux issuppressed by the superconducting pinning effect, the applied magnetic field is not supplied to
the whole of the sample. Therefore, the trapped field distributions consequently exhibit
trapezoid shapes. According to the balance of heat generation and draining, the temperature
profiles show us distinctive behaviors of magnetic fluxes. Both the temperature and themagnetic flux density kept increasing even after the external magnetic field has stopped growing
at 5 T. This is attributed to the flux creeping phenomenon which propagates from the peripheryto the center portion of the sample like a snow slide. The highest temperature rise due to theflux motion reached 7.5 K even when the sample was magnetized at a slow sweeping rate of
5.06 mT s−1 . As the temperature profiles were different between the ascending and descending
field processes, it is suggested that the magnetic fluxes invade in and diffuse out in different
heating manners between the processes. This assists the hypothesis that the time while themoving fluxes heat the sample strongly affects the total amount of heat generation, which acts
contrary to the FC case. This behavior implies that the improvements of the heat propagation
property of the HTS bulk material by embedding metallic membranes and more
powerful/efficient cooling systems must suppress the temperature increases and enhance thefield trapping abilities.
(Some figures in this article are in colour only in the electronic version)

fields [1, 2]. As reported by Gruss et al [3], the maximum
trapped field has reached 16 T at 24 K by doping Zn in it. The
highest value of 17.24 T has been reported by Tomita et al[4], where the Y123 bulk sample was reinforced by the resin
impregnation technique. These data of the field trapping abilityof bulk magnets are generally measured by the field-coolingmethod (hereafter abbreviated as FC). Since it is important to

1. Introduction
Melt-textured large grain bulk superconductors composed of
REBa2 Cu3 O7−y compounds (RE = Y, Sm, Gd, abbreviatedas RE123) which include RE2 BaCuO5 (RE211) particles are
known to act as quasi-permanent magnets (hereafter referred
to as bulk magnets) when they trap the applied magnetic
0953-2048/09/065014+08$30.00

1© 2009 IOP Publishing Ltd Printed in the UK

Supercond. Sci. Technol. 22 (2009) 065014

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Figure 1. Experimental set-up, (a) a cross-sectional view of the magnetic pole and (b) a top view showing the positions of thermocouples anda Hall sensor on the sample surface.

suppress the heat generation during the activation process, as
discussed in this paper, the sweep rates of applied fields must
be carefully chosen even in the FC processes using quasi-static
fields [5, 6].
In the magnetizing processes using pulsed magnetic fields(PFM), it is known that the flux motion in the sample causes a
considerable heating, raises its temperature, lowers the criticalcurrent density Jc and subsequently degrades the trapped fieldability [7]. Fujishiro et al [8, 9] have recently achieved the best
performance of a trapped magnetic field of 5.2 T for the firsttime in the world by a smart process called MMPSC, which isa kind of PFM process. The experiment has been conductedin a manner that suppresses the heat generation by applying
iterative pulsed fields at two temperatures. The behavior ofinvading fluxes is strongly affected by the residual trapped field
activated by the former magnetic pulses. They reported that
it is important for high field trapping to form an M-shaped
magnetic flux distribution before applying intense fields [9].
Zero-field cooling (ZFC) is a kind of magnetizing method
to activate the bulk magnets. An intense magnetic field isapplied to the sample with low sweep rates in a quasi-static
manner after cooling it to the superconducting state. As theflux lines invade the sample through the sample surface, theZFC technique is regarded as the ultimate model of the PFM
methods with extremely slow flux invasion speeds. In a sense,
it must be important to know the flux behavior in the ZFC
processes so as to obtain excellent trapped field performancesin the PFM operations.
In this study, we precisely trace the temperature evolution
from the aspect of the phenomena and evaluate the temperaturerises due to the heat generation caused by the flux motion in
the bulk superconducting magnet during the ZFC processes
operated at two initial temperatures of 50 and 60 K.

Sm123 bulk magnet was manufactured by Dowa Mining Co.,Ltd and adapted to ZFC operations as well as FC [5, 6].
The dimensions of the sample were 45 mm in diameter and
15 mm in thickness. The sample was reinforced by putting a
stainless steel ring on it with epoxy resin to prevent fracture dueto the magnetic and thermal stresses during the magnetizing
procedures. The trapped field distributions without any strains
in FC imply that the material magnetically exhibits a perfect
single-domain structure and makes it possible for us to performthe high field trapping ability.
The sample was fixed on the copper stage through analumina crystal to improve the thermal contact between thecopper stage and the bulk sample. The copper stage wasconnected to the cold head of a compact Gifford–McMahon
refrigerator (manufactured by AISIN SEIKI, model GR-103)
by a copper heat conduction rod. The nominal output andinput powers at 77 K were reported as 15 W and 1000 W,
respectively, and the refrigerator enables us to obtain theultimate temperature of 50 K. The temperature was controlled
by a heater which was attached beneath the copper stage.
Five pairs of chromel–constantan thermocouples (T1–T5) wereseparately glued at both positions of a grain sector region(GSR) and a grain sector boundary (GSB) of the polishedbulk sample surface, as shown in figure 1(b). The initial
temperatures are defined as the averaged data of T1–T5. A
Hall sensor (F W Bell, type BHT 921) was attached near thecenter of the bulk surface to trace the flux behavior during
the magnetizing processes and the resultant trapped fields. It
must be added that the trapped field data thus obtained do notprecisely indicate the maximum trapped fields on the sample
surface.
2.2. Procedure
We use a superconducting solenoid magnet with a room
temperature bore of 100 mm in diameter, which was
manufactured by Japan Superconductor Technology Inc. (typeJMTD-5T100). The vacuum chamber containing an HTS
bulk sample was inserted into the bore and then the sample
was cooled by the GM refrigerator. A static field of 5 T

2. Experimental procedure
2.1. HTS bulk sample and experimental equipment
Illustrations of the experimental set-up are shown in figure 1.
A melt-processed high temperature superconducting (HTS)2Supercond. Sci. Technol. 22 (2009) 065014

T Oka et al

(a)

(b)

Figure 2. Trapped field distributions of an Sm123 HTS bulk magnet magnetized by a 5 T ZFC process at 60 K at a couple of sweep rates(a) 5.06 and (b) 11.3 mT s−1 . Data were measured at 0.5 mm above the magnetic pole surface.

Figure 4. Temperature and trapped field evolution in ZFC at a sweep
rate 5.06 mT s−1 at 50 K.

Figure 3. Trapped field distributions after FC and ZFC magnetizing
processes at various sweep rates of applied magnetic fields at 60 K.

trapped field of 2.42 T was attained in the FC activation by
the same applied field of 5 T. As the magnetic field was notsatisfactorily given to the whole sample, the magnetic flux
could not penetrate into the central portion of it due to thestrong pinning effect at around 60 K.

was gradually applied and subsequently removed with sweep
rates of 5.06 and 11.3 mT s−1 . The behaviors of temperatureand magnetic flux density were precisely measured at thesame time throughout the procedure. The magnetic field
distributions outside the magnetic pole were measured byscanning a Hall sensor with 0.5 mm gap from the pole surface.

3.2. Time evolution of temperature and trapped magnetic flux
Figure 4 shows the evolution of temperature during the ZFC
process in which the sample temperature was controlled to
be 50 K. The external field was gradually applied to thesample at a sweep rate of 5.06 mT s−1 . The profiles of fivethermocouples on the sample surface indicated that all thetemperatures simultaneously and uniformly began to rise when
the applied magnetic field started rising. This behavior is
attributed to the heat generation due to the flux motion in thebulk magnet. As a matter of fact, the temperature data thus
measured varied to some extent because of the anticipatedcalibration errors. All the temperature data soon saturated at
the same time when the external field reached 5 T and stopped
growing. This saturation implies that the heat generation anddraining are almost balanced in the cooling condition given by
the GM cryocooler. However, the temperatures have gradually

3. Results and discussions
3.1. Distribution of trapped magnetic flux density by ZFC
Figure 2 shows the field distribution maps after ZFC which
was operated at 60 K with sweep rates of (a) 5.06 and (b)11.3 mT s−1 [10]. One can obviously see that the distributions
indicate the concentric contour lines. More precisely, thesecircles slightly deviate towards the outside of the lines whichcorrespond to GSB. This implies that the Jc values at GSB aresuperior to those in other regions (GSR). The trapped field
distributions along the dashed line in figure 2 are shown infigure 3. The profiles obtained by FC are added to themin comparison with ZFC for the same sample. The highest
values obtained by ZFC were suppressed to be 1 T, while the3Supercond. Sci. Technol. 22 (2009) 065014

T Oka et al

Figure 5. Detailed profiles of figure 4 in (a) ascending and (b) descending field processes at 50 K at a sweep rate of 5.06 mT s−1 .

including the bulk magnet, the copper cold stage, etc. Whenthe temperature of the whole system becomes stable, it starts
rising again, showing the flux creep which propagates fromthe periphery to the central portion of the bulk magnet. In
figure 5(b), the surface temperatures are shown to behave ina fairly balanced way while the external field is decreasing.
When the external field reaches zero T, as referred to in
the previous paragraph, the temperatures fall steeply at every
measuring point. According to the balance between the heating
and draining, all the temperature profiles show us a distinctive
behavior of the invading fluxes and diffusing heat.
Figure 6 shows the temperature evolution measured at a
sweep rate of 11.3 mT s−1 . After the drastic temperature rise,
the steep peaks appeared at 500 s as well as in the former casein figure 5. This is attributed to the fact that the generated
heat propagates through the cooling system at extremely slow
speeds for several hundred seconds. This strongly suggeststhat the heat generation uniformly occurs in every part of thebulk sample surface as long as the applied field is growing at
a certain speed and it begins to diffuse into the whole portionof the cooling system when the external field stops rising. As
shown in figure 6(b), one can see the steep temperature riseeven in the descending field process from 5 to 0 T. This isapparently attributed to the fact that the amount of generated
heat is greater than the draining one when the sweep rate isfast.
As the steep temperature rises were observed even on
the descending periods in figure 6(b), detailed data forthe beginning part is redrawn in figure 7. Among thethermocouples, T5 alone has exhibited a unique temperature
gradient. This implies that the heat generation does not equally
happen at every point of the sample surface, especially at leastin the descending process. It is suggested that the paths ofthe magnetic fluxes do not uniformly distribute on the sample
surface. As far as looking at figure 7, the magnetic fluxes might
have avoided position T5 on their way to get out of the sample.
T5 corresponds to one of the higher Jc areas on GRB, where theSm211 inclusions finely reside with higher density than otherareas [5, 10].
Figure 8 shows the temperature data which were measured
at T1 as functions of the sweep rates and temperature ranges.
Although the tendency is apparently the same as that in eachtemperature range, we can see a big difference between the

kept rising and the average temperature rise finally reached7.5 K until the field started decreasing.
We also note that the magnetic flux density Bz has only
reached just above 1.4 T in spite of an intense field of 5 T
being applied. This is due to the shielding effect of the bulk
magnet. The magnetic flux density measured on the sample
surface began to rise when the applied magnetic field started
rising. Although the profile of the magnetic flux density has
also saturated at around 1.2 T when the applied field reached
5 T, it has gradually kept increasing for about two hundred
minutes even after the applied field stopped growing as wellas the temperature profiles. This implies that the invading
fluxes still keep moving towards the central portion of thesample even in the static field. This results in the fact that the
distribution of the trapped field exhibits a trapezoid shape after
ZFC activation, as shown in figures 2 and 3.
When the external field reached zero, the temperatures
sharply fell and returned back to their initial states. Thismeans that heat draining effectively occurs when the heatgeneration disappears and suggests that the improvement of
the heat propagation property of the bulk material would
have suppressed the temperature rises more effectively andenhanced the resultant flux trapping ability. Although we haveno clear evidence of the position dependence from this roughfigure with respect to the measured temperatures, it is inferredthat the thermal propagation speed is too fast to recognize thedifferences among the positions on the sample surface as far as
we trace the temperature changes over the timescale of several
hundred minutes.
3.2.1. Time evolution of temperature for various sweep rates
and temperatures.
Figure 5 shows the detailed thermal changes on its (a)ascending and (b) descending field processes in the ZFC
operation which was shown in figure 4. At the very beginningof field application, since the applied weak field is repelled
at the sample surface, we can see no distinct temperaturerise. After rapid temperature rises which start at 400 s,
one sees apparent kinks at 1000 s and the temperatures once
again decrease for several hundred seconds. This phenomenon
can be understood by an explanation that the heat generation
uniformly happens at various portions of the sample, and it
diffuses into the various positions of the whole cooling system
4

Supercond. Sci. Technol. 22 (2009) 065014

T Oka et al

Figure 6. Profiles of (a) ascending and (b) descending field processes at 50 K at a sweep rate of 11.3 mT s−1 .

corresponds to the heat generation between the sweep rates of
5.06 and 11.3 mT s−1 .
3.2.2. Time evolutions of trapped magnetic flux density forvarious sweep rates and temperatures.
Figure 9 shows the trapped magnetic field data near the centerof the sample surface. As shown in figure 9(a), the magnetic
flux density has reached over 2 T when the applied field washeld at 5 T at 60 K, whereas it was 1.4 T at 50 K. Thisimplies that the shielding effect was weakened at 60 K incomparison with that at 50 K and the flux invasion was allowed
to some extent at the higher temperature. At the beginningof the profile, the Hall sensor remained still for a while dueto the shielding effect as well as the temperature behavior.
As the magnetic fields reached the same data at 3000 s inspite of different sweep rates, the field trapping condition is
independent of the sweeping speed and is determined only by
the shielding property caused by the pinning effect in the 5 T
static field.
In figure 9(b), the resultant trapped fields are observed
to be slightly different between the sweep rates. It is
understandable that the amount of heat generation apparently
affects the remnant trapped fields in the descending fieldprocess. As seen in figure 8(b), since the temperatures in
the faster processes, noted by closed symbols, during thesweeping time once exceed the profiles of the slower processes
at around 500 s, the temperatures which the sample experiencesat the faster sweeping rate are higher than those at the slower
sweeping rate. This certainly results in different values of the
final trapped magnetic flux.

Figure 7. Detailed temperature changes in the descending fieldprocess at a rate of −11.3 mT s−1 , shown in figure 6(b).

profiles of sweep rates 5.06 and 11.3 mT s−1 . It is clear that thetemperature rises apparently correspond to the balance of theheat generation rate and the heat draining rate. When the sweep
rate is faster, the temperatures would change faster according
to the faster heat generation speed while the applied field issweeping. In the ascending stage, as shown in figure 8(a),the temperature changes are slightly different between thesweeping rates. When the sweep rate is slower, plotted by open
symbols, the temperatures reach the slightly higher values at
3000 s than those of the faster rate, shown by closed symbols,
in both temperature ranges. This means that the total amountof generated heat during the slower field sweeping is greaterthan that of the faster one, because the heat draining speedsin each case are the same in both cooling conditions. The
duration of heating is responsible for this phenomenon. On
the descending stage, figure 8(b), the heat generation rates
apparently exceed the draining rates in the faster sweeping
process, whereas they show an inverse behavior in the slower
sweeping in both temperature ranges. The heat draining speed

3.3. Estimation of generated heat
As Fujishiro et al reported, the heat generation Q is describedas follows [11]:Q= Ts +Tmax

C(T )V dT,

Ts

where C(T ) is the specific heat of the bulk magnet at thistemperature range, V is the volume, and Ts and Tmax
mean the initial temperature and the highest temperaturerise, respectively. The specific heat and the heat capacity
5Supercond. Sci. Technol. 22 (2009) 065014

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Figure 8. Temperature profiles measured at T1 in (a) ascending and (b) descending field processes as a function of the sweep rate.

Figure 9. Magnetic field profiles in (a) ascending and (b) descending field processes.

of bulk magnets at around 50 K are estimated as 0.8 ×
10−3 J mm−3 K−1 [11] and 19 J K−1 , respectively, whereas thevolume of the sample is 23.8 × 103 mm3 . As the cooling rateis derived to be 0.01 K s−1 from figure 7, the calculated heatdraining of 0.19 W mainly corresponds to 2.7% of the coolingpower of the GM cryocooler, which nominally generates 7 W
at 50 K [12]. The major portion of cooling energy is spent onheat draining against the heat invasion from outside the vacuum
insulation system.

This assists the hypothesis that the time period being heatedby the moving fluxes strongly affects the total amount of heatgeneration, which acts contrary to the FC case. As the different
behaviors of the temperature changes were observed between
its ascending and descending field processes, it is suggested
that the magnetic fluxes invade in and diffuse out in different
manners between their ascending and descending stages. It isalso inferred that the difference between the specific heats at 50
and 60 K must correspond to the temperature rises at the slow
sweeping rate.
Figure 11 shows the averaged temperature changes during
the ascending and descending periods as functions of the initialcold head temperatures and the sweep rates. The data showsa good example to imply that there are different behaviors
between slow and fast sweep rates in the descending stage.
In the field ascending period, closed notes, heat generation ismainly caused on the periphery of the sample and propagatesto the central portion. Then we do not see any substantial

3.4. Temperature changes
Figure 10 shows the temperature rise as functions of various
sweep rates, positions and initial temperatures. The FC data,
denoted as (+), were added for comparison with the ZFC in
the figure. The highest value of the averaged temperature rises
was recorded as 7.5 K, which was obtained when the process
was operated at the slow sweep rate of 5.06 mT s−1 at 50 K.
6

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T Oka et al

(a)

(b)

Figure 10. Maximum temperature rises at various positions of thermocouples against sweep rates in ZFC cooled to (a) 50 K and (b) 60 K.

B/T

µ 0HM

4

2
2

1

Figure 11. Averaged temperature changes during ascending field(up) and descending field (down) periods in ZFC at 50 and 60 K.
0Table 1. Temperature changes (K) measured on the bulk sample
surface. (Note: Ti : initial temperature, Rs : sweep rate, Tave : averaged
data, TFC : compared with field-cooling method [5].)TiRs (mT s−1 )

T1

T2

T3

T4

T5

Tave

TFC

50
50
60
60

5.06
11.3
5.06
11.3

7.1
5.0
5.9
4.9

7.5
5.0
6.0
5.3

8.2
6.2
6.6
5.8

7.2
5.2
5.9
5.1

7.4
5.6
5.4
4.7

7.5
5.4
6.0
5.2

4.1
5.9
—
—

-a

0

a

Figure 12. Illustration of the magnetic flux behavior.
Table 2. Temperature changes (K) during sweeping magnetic field.
(Note: Rs : sweep rate, up: ascending field, down: descending field.)

Rs (mT s−1 )50 K up

60 K up

5.06
11.3

3.8
3.5

4.2
4.6

50 K down

−2.1
1.6

60 K down

−1.4
1.0

3.5. Behavior of trapped magnetic flux

differences between the temperatures nor sweep rates. In
the descending time, however, when the sweep rate is slow,
the heat generation is much weaker than that of the fasterone. The sweep rate affects the temperature rise because
the temperature change depends on the balance between heatgeneration and draining. Noudem et al [13] reported thatembedding metal membranes into the holes which were drilledin the samples is effective at improving the mechanical strengthof the materials. Thanks to the heat conduction property ofmetals, the heat draining of such samples would be improved,
and it would be possible to reduce their heating up during
the magnetizing processes. The data of temperature changes
are listed in tables 1 and 2, which correspond to figures 10
and 11.

The schematic illustration which explains the flux motion in thesample is shown in figure 12. The ascending and descending
magnetic flux are indicated on the left- and right-hand sidesof the figure, respectively. When the field is initially applied,the fluxes are prevented from invading the sample. When thefield reaches 5 T, the magnetic fluxes still keep penetrating
into the sample even after the external field stops increasing,and fall into the central portion, showing a flux creeping
phenomenon like a snow slide. This flux creeping releases thefluxoids from the pinning centers and then generates the heat
which corresponds to the pinning energy. So we can trace thespecified paths through which the magnetic fluxes disperse outof the sample by measuring the temperature distribution.
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On the descending stage from 5 T to zero, since the central
portion of the sample is shielded by the surrounding fields
and the heat generation is not intense in the high field region
over 2 T, the trapped field in the center tends to keep its value
and sluggishly decreases as if it were frozen. Therefore, thisbehavior of the magnetic flux results in the trapezoid or Mshaped distribution after the ZFC operation, whereas they show
a cone shape when magnetized in the FC process.
The inhomogeneous temperature and flux distributions in
the bulk sample have been reported by Laurent et al [14] withrespect to the weak ac field application. They have pointed
out that the trapped dc field before ac field application reduces
the temperature increases. This is another example of heatgeneration by the flux motion in bulk samples.

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4. Conclusions
The temperature rises of an Sm–Ba–Cu–O single-domain bulk
superconductor have been precisely measured during the ZFC
process. The highest temperature rise has been reported as
7.5 K when the sample was magnetized at a sweeping rateof 5.06 mT s−1 at 50 K. We have so far emphasized thatthe temperature change is never negligible even in the ZFC
magnetizing operation as well as the FC. The conclusions of
this study are listed as follows.
Both the temperatures and the magnetic fields have
gradually kept increasing even after the applied magnetic field
stopped growing at 5 T. The magnetic fluxes fall into the central
portion of the sample even in the static field, showing the flux
creeping like a snow slide.
It is clarified that the time period while being heated by
the moving fluxes strongly affects the total amount of heatgeneration, which acts contrary to the FC case. Different
temperature gradients were observed in its descending period,
which inferred the presence of various heat draining paths
through which the magnetic fluxes diffuse outside. It is alsosuggested that the paths of invading and diffusing fluxes aredifferent between its ascending and descending processes.
The trapped field distribution which exhibits a trapezoid
shape was discussed and consistently explained by flux
motions during the ZFC process. This behavior implies thatthe improvements of the heat propagation property of the HTS
bulk materials and the cooling systems must suppress thetemperature increases and enhance the resultant flux trapping
abilities.

Acknowledgments
This work has been partially supported by grants-in-aid fromthe Japan Science and Technology Agency (JST) and Iwate
Industrial Promotion Centre.

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