Physica C 426–431 (2005) 594–601
www.elsevier.com/locate/physc

Approach from temperature measurement to trapped ﬁeld
enhancement in HTSC bulks by pulse ﬁeld magnetizing
Hiroyuki Fujishiro a,*, Kazuya Yokoyama b, Masahiko Kaneyama a,
Manabu Ikebe a, Tetsuo Oka c, Koshichi Noto a,daFaculty of Engineering, Iwate University, 4-3-5 Ueda, Morioka 020-8551, Japan
National Institute for Materials Science, 3-13, Sakura, Tsukuba 305-0003, Japanc
IMRA MATERIAL R & D CO., LTD., 5-50 Hachiken-cho, Kariya 448-0021, Japand
Iwate Industrial Promotion Center, 3-35-2 Iiokashinden, Morioka 020-0852, Japanb

Received 23 November 2004; received in revised form 24 January 2005; accepted 24 January 2005
Available online 18 July 2005

Abstract
The time dependences of the temperature rise DT(t) and the magnetization M(t) on the surface of the cryo-cooled
SmBaCuO bulk superconductor have been investigated during the ﬁve successive magnetic pulse applications (No1–
No5) of equal strength ranging from Bex = 3.83–6.07 T. The pinning loss (Qp) is estimated by the hysteresis loss
QMH obtained by the M vs. applied ﬁeld l0Ha curve and the viscous loss (Qv) is estimated by subtracting QMH fromthe total Q which is estimated using the maximum temperature rise DTmax and the speciﬁc heat C. For the ﬁrst pulse(No1) application, Qp is a main origin of the heat generation and Qv is dominant for the No5 pulse. The temperature
measurements combined with the measurements of the M–l0Ha curve have been proved to give us the valuable information as for the enhancement of the trapped ﬁeld by PFM.
Ó 2005 Elsevier B.V. All rights reserved.
PACS: 74.25.Bt; 74.80.Bj; 74.60.Ge
Keywords: Pulse ﬁeld magnetizing; Heat generation; Pinning and viscous loss; Hysteresis loss

1. Introduction*

Corresponding author. Tel./fax: +81 19 621 6363.
E-mail address: fujishiro@iwate-u.ac.jp (H. Fujishiro).

In view of the applicational use of high-Tc bulk
superconductors (HTSCs) as a high-strength bulk
magnet for a magnetic separation system to clean
up waste water [1] and a magnetron sputtering

0921-4534/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved.
doi:10.1016/j.physc.2005.05.023

H. Fujishiro et al. / Physica C 426–431 (2005) 594–601

apparatus [2] and so on, the pulse ﬁeld magnetizing (PFM) have been intensively investigated aswell as the static ﬁeld-cooled magnetizing (FCM)
because of the relatively compact, inexpensive
and mobile setup. The trapped ﬁeld BPT and total
trapped ﬂux UPT by PFM are, however, generally
smaller than those attained by FCM at lower temperatures than 77 K possibly because of the large
temperature rise DT due to the dynamical motionof the magnetic ﬂuxes against the vortex pinning
force Fp and the viscous force Fv. In order to enhance BPT and UPT by PFM, DT reduction is anindispensable issue and several approaches suchas the iteratively magnetizing pulsed-ﬁeld methodwith reducing amplitude (IMRA) [3] and a multipulse technique with step-wise cooling (MPSC)[4] have been attempted. We investigated the eﬀectof metal ring setting onto the bulk disk on BPT andDT [5]. The BPT values are 10–20% enhanced by the
SUS304 ring because of the heat transfer to thering.
The heat generation Q during PFM is considered to be the sum of the pinning loss Qp andthe viscous loss Qv. It is desirable to evaluate thetemperature and applied ﬁeld dependences of the
Qp and Qv values to understand the PFM mechanism and to attain the optimal BPT and UPT values.
Mizutani et al. estimated Qp and Qv during PFM
using the ﬂux velocity v in the bulk measured by
the pick-up coil method [6]. We have studied thetime evolution and spatial distribution of the temperature rise DT(t) on the surface of the cryocooled YBaCuO [7,8], SmBaCuO [5,9–11] andGdBaCuO [8] bulks during PFM. The DT(t)behavior changed depending on the initial bulk
temperature Ts, the strength of the pulse ﬁeld Bex
and the trapped ﬁeld distribution before the magnetic pulse application. We have estimated thetotal generated heat Q using the maximum DT
and the speciﬁc heat C of the bulk. Analyzing
the pulse number dependence of Q for the ﬁve successive pulse applications with the ﬁxed amplitude
Bex, the contributions of Qp and Qv to the total Q
have been roughly separated [10]. Qp can be estimated from the hysteresis loop of the magnetization M vs. the applied ﬁeld l0Ha, while Qv is notdirectly related with the hysteresis loop. By combining the temperature and magnetic measure-595

ments, more precise Qp and Qv analyses should
become possible.
In this paper, we investigate the time dependences of DT(t) and M(t) for the cryo-cooled SmBaCuO bulk superconductor during the successive
magnetic pulse applications with equal strengthand estimate the Qp and Qv values. We compare
the estimated Qp values by the temperature measurement with those by the M–l0Ha hysteresis
loop. We also discuss the possibility to the BPT
enhancement on the basis of the temperature measurement data.

2. Experimental
A highly c-axis oriented SmBaCuO bulk superconductor with 45 mm in diameter and 18 mm inthickness was used for measurements, which consisted of four growth sector regions (GSRs) divided
by the growth sector boundaries (GSBs). The composition and the detailed fabrication method of thebulk are described elsewhere [12]. The SUS304 ring
was set onto the bulk in order to enhance thetrapped ﬁeld by the reduction of the temperaturerise [5] and, at the same time, to reinforce the bulk
mechanically. The bulk disk was tightly stacked on
the sapphire plate attached to the cold stage of aGM-cycle helium refrigerator. The initial stage
temperature Ts was ﬁxed at 40 K before every pulse
application. The inset of Fig. 1(a) shows the positions on the bulk for the temperature and thetrapped ﬁeld measurements. The time evolutionof temperatures, T0 at the center of the bulk (P0)and, T1–T4 at P1–P4 were recorded using ﬁne
chromel-constantan thermocouples adhered by
GE7031 varnish just after applying the pulse ﬁeld.
P1–P4 were situated on the central radial lines ofeach GSR by 9 mm apart from P0. The time evolution of the trapped ﬁeld BPT ðtÞ on the bulk surface
was measured by the Hall sensor (F.W. Bell, model
BHA 921) adhered to the position at PH 2.5 mm
distant from P0 using a digital oscilloscope. The
total trapped ﬂux UPT and the distribution of thetrapped ﬁeld B3T mm were measured using an axialtype Hall sensor, which scanned 3 mm above thebulk surface stepwise with a pitch of 1.2 mm. Five
iterative magnetic pulses l0Ha(t) (No1  No5)

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pure superposition of the pulse ﬁeld and it is easy toanalyze the ﬂux trapping mechanism. Bex was monitored by measuring the current I(t) ﬂowing
through the shunt resister.

3. Results and discussion
3.1. Temperature rise and trapped ﬁeld by
iterative PFM

Fig. 1. The time evolutions of T0(t)–T4(t) after applying theNo1 and No5 pulse ﬁelds of: (a) Bex = 3.83 T, (b) 4.70 T, (c)6.07 T, respectively.

with the same maximum amplitude Bex from 3.83 T
to 6.07 T (a rise time: tp = 12 ms, a pulse duration:
100 ms) were applied sequentially after re-coolingthe bulk to Ts, where we can obtain the eﬀect of theFig. 1(a)–(c) shows the time evolutions of T0(t)–T4(t) on the bulk for Ts = 40 K after applying theNo1 and No5 pulse ﬁelds of (a) Bex = 3.83 T, (b)4.70 T, (c) 6.07 T, respectively. The insets of eachﬁgure show the distribution of B3T mm for the No1
pulse. In Fig. 1(a), for the No1 pulse of Bex =3.83 T, T 2(t) and T3(t) rise up ﬁrst with the maximum temperature rise DTmax = 12–14 K, followedby T4(t) and T0(t), and T1(t) rises up latest. T2(t)and T3(t) take a maximum at t = 1.8 s. But theothers slowly increase and then reach a maximum
at t = 5–10 s. Since the ﬂux motion necessarily
generates heat inside the bulk through the mechanisms of Qp and Qv, such a rapid temperature riseof T2 and T3 suggests the existence of the easy
paths for the ﬂux intrusion due to relatively
weaker pinning force Fp in GSR2 and GSR3.
The distribution B3T mm shows a small peak aroundP3, which suggests that only the small amount of
ﬂux intrudes through the easy path near P3. In
Fig. 1(b), for the No1 pulse of Bex = 4.70 T,
T2(t), T3(t) and T4(t) rise up faster with a peak(DTmax = 20–24 K), followed by T1(t) and T0(t)rise up latest (DTmax = 19K). The slow rising upof T1(t) indicates the existence of a hard path forthe ﬂux intrusion around P1. The trapped ﬁeld increases and the distribution takes a cone shape for
Bex = 4.70 T. In Fig. 1(a) and (b), DTmax for theNo5 pulse decreases and shows no distinct anomaly in T(t). In Fig. 1(c) for the No1 pulse of
Bex = 6.07 T, DTmax is as large as 26–34 K andthe rise time of T(t) becomes short at all the positions which results from the uniform ﬂux intrusion
into the bulk similarly to that in Fig. 1(b) and thecone shape in the B3T mm proﬁle is also maintained.
A large and distinct peak in T3(t) can be seen
for the No5 pulse, compared with that forH. Fujishiro et al. / Physica C 426–431 (2005) 594–601

Bex 6 4.70 T shown in Fig. 1(a) and (b). This result
suggests that the rampant ﬂux motion takes placearound P3 even during No5 pulse, supporting
again that there is the easiest path near around.
In this way, the ﬂux motion can be ﬁgured out
by monitoring the temperature evolution.
Fig. 2(a) and (b) show the pulse number dependence of the maximum temperature rise DTmax andthe trapped ﬁeld BPT , respectively, for various Bex
values. We deﬁne D Tmax in Fig. 2(a) as the averaged one from DT0max to DT4max. For each Bex,
DTmax is the largest for the No1 pulse and de-597

creases with increasing pulse number, approaching
an ultimate value for the No4 and No5 pulses. In
Fig. 2(b), a large amount of the magnetic ﬁeld istrapped by applying the No1 pulse. BPT is graduallyenhanced with increasing pulse number and thensaturates. These saturation tendencies in BPT muchresemble the behaviors of DTmax and it can be seenthat the ﬂux trapping and temperature rise are closely connected with each other.
Fig. 2(c) summarizes the relation between BPT
and the maximum temperature Tmax(=Ts + DTmax)
during PFM on the basis of the results of Fig. 2(a)Fig. 2. The pulse number dependence of: (a) the maximum temperature rise DTmax, (b) the trapped ﬁeld BPT for various Bex = valuesand (c) the summary of the relation between BPT and the maximum temperature Tmax(= Ts + DTmax) during PFM. The arrows indicate
the change of data sets of (T max ; BPT ) from No1 to No5 pulse for each Bex.

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H. Fujishiro et al. / Physica C 426–431 (2005) 594–601

and (b). For each Bex data sets of (T max ; BPT ) from
No1 to No5 pulse are plotted. The measured
trapped ﬁeld BFC
T by FCM as a function of Tmax is
also presented, which corresponds to the maximum
ability of the ﬂux trapping of this SmBaCuO bulk.
The data sets for the No1 pulse of Bex = 3.83 T and
4.70 T are situated below the BFC
T –T max line. For the
succeeding pulses, Tmax monotonically decreases
and BPT slightly increases and then both values saturate for the No5 pulse. For Bex = 5.53 T and 6.07 T,
the BPT value for the No1 pulse is smaller than thatfor Bex = 4.70 T because Tmax touches the BFC
T –T max line and BPT decreases following the line withthe further increase of temperature. After the succeeding pulse application, BPT increases withincreasing pulse number and the highest value of
3.09 T can be obtained for the No5 pulse of
Bex = 5.53 T. These analyses demonstrate that theﬂux trapping ability by the PFM technique can besystematically explained as limited by the BFC
T 
T max line.
3.2. Estimation of pinning loss Qp and viscous
loss Qv based on the temperature measurement
In order to elucidate the magnetizing mechanism by PFM and to enhance BPT , it is important
to know the generated heat Q, because Q contains
more exact information than DT indispensable fordetailed analyses. If we assume that the heat generation occurs under the adiabatic condition, the Q
value is represented by the following equation [10]:Z T s þDT max
Q¼CðT ÞV dT ¼ QP þ QV ;
ð1Þ
Ts

where C(T) is the speciﬁc heat and V is the volumeof the bulk disk. C(T) was estimated using the relation C ¼ K=a, i.e., the thermal conductivity K divided by the thermal diﬀusivity a, both of whichwere measured simultaneously [13,14].
Fig. 3 presents the estimated Q(No1) andQ(No5) values after the No1 and No5 pulse
together with the diﬀerence dQ(= Q(No1) 
Q(No5)) as a function of Bex. The inset displays
C(t) of the SmBaCuO bulk. Both Q(No1) andQ(No5) increase with increasing Bex. However,the Q(No1)–Bex curve is convex and the Q(No5)–
Bex curve is concave. The heat generation during

Fig. 3. The estimated Q(No1) and Q(No5) values after the No1and No5 pulse and the diﬀerence dQ (=Q(No1)-Q(No5)) as afunction of Bex. The speciﬁc heat C(T) of the SmBaCuO bulk
used in this study is also shown in the inset.

PFM is given by the sum of Qp and Qv as presented by Eq. (1) and ﬂux trapping should be closely connected with Qp. Since no additional ﬂux
trapping takes place for the No5 pulse, it is reasonable to assume that the diﬀerence dQ roughly
stands for the pinning loss connected to the ﬂux
trapping for the No1 pulse. Then Q(No5) may
mainly consists of Qv.
3.3. Determination of pinning loss Qp using
M–l0Ha curve
Following the idea of the critical state model,
Qp can be qualitatively divided into two components, QTp and QLp , as schematically illustrated ona hypothetical M–l0Ha hysteresis loop for quasistatic magnetizing in Fig. 4,
QP ¼ QTP þ QLP ;ð2Þ

where QTp is the pinning loss inevitable for the ﬂux
trapping, while QLp is additional pining loss unrelated with the ﬂux trapping. In Fig. 4, it is anticipated that there is a threshold applied ﬁeld l0Hthwhich provides the boundary between QTp and QLp
on the M–l0Ha space. We have measured the timedependence of the applied ﬁeld l0Ha(t) and thetrapped ﬁeld B(t). The magnetization M in thebulk is given by
M ¼ B  l0 H a .

ð3ÞH. Fujishiro et al. / Physica C 426–431 (2005) 594–601

Fig. 4. The schematic view of the hypothetical M–l0Ha
hysteresis loop during quasi-static magnetizing. The hysteresis
loss Qp can be qualitatively divided into two components,
QTp and QLp (see text). The hysteresis loop starting from Mtrap
corresponds to the second run.

Fig. 5 shows the M vs. l0Ha curves for the No1,No2 and No5 pulses of Bex = 3.83–6.02 T. In Fig.
5(a), for Bex = 3.83 T, the magnetic ﬂuxes canhardly penetrate into the bulk center and the Mvalue is nearly equal to the applied ﬁeld
l0Ha(M  –l0Ha) and the hysteresis behavior
cannot be observed. In Fig. 5(b) and (c) for
Bex = 4.70 T and 5.53 T, a wide hysteresis loop in
M–l0Ha curve can be clearly seen for the No1
pulse which may mainly result from the ﬂux trapping by the bulk disk. The hysteresis loop isslightly enhanced with increasing Bex. For theNo2 pulse, the hysteresis loop becomes drastically599

narrow and no hysteresis behavior can be observed
for the No5 pulse. In contrast, the pulse number
dependence of the M–l0Ha curve of for
Bex = 6.07 T in Fig. 5(d) is somewhat diﬀerent; asizable hysteresis remains even for the No5 pulse.
Since the trapped ﬂux is not enhanced for theNo5 pulse of Bex = 6.07 T, the hysteresis loss for
the No5 pulse is attributable to QLp .
Fig. 6(a) shows the pulse number dependence of
the QMH values determined from the M–l0Ha hysteresis loop for each Bex. For Bex = 3.83 T, QMH isnegligibly small because of no observable hysteretic behavior. For Bex = 4.70 T and 5.53 T, theQMH value for the No1 pulse is the largest andsuddenly decreases after the No2 pulses and thenapproaches to zero. For Bex = 6.07 T, QMH decreases with increasing pulse number, but the ﬁnite
QMH value of 150 J exists even for the No5 pulse.
Fig. 6(b) displays the increment of the total
trapped ﬂux dUPT ¼ UPT ðNo iÞ  UPT ðNo i  1Þ asa function of the pulse number i. For the ﬁrst pulse(i = 1), dUPT is deﬁned as UPT (No1). The behaviors
of dUPT or the increment of the BPT value in Fig. 2(b)are much similar to QMH shown in Fig. 6(a), except for the QLp contribution which shows the oﬀset
for Bex = 6.07 T.
Fig. 7(a) and (b) present the total heat generation Q determined from the temperature measurement, QMH and the diﬀerence DQ = Q–QMH for
the No1 and No5 pulses, respectively, as a function of Bex. In Fig. 7(a), DQ is equal to the viscous
loss Qv(No1) because QMH = Qp. However, for
Bex = 3.83 T, the estimated Qp(No1) = 0 should

Fig. 5. The measured M–l0Ha curves for the No1, No2 and No5 pulses of Bex = 3.83–6.02 T.

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H. Fujishiro et al. / Physica C 426–431 (2005) 594–601

Fig. 6. (a) The pulse number dependence of QMH determinedfrom the M–l0Ha loop. (b) The increment of the total trapped
ﬂux dUPT ¼ UPT ðNo iÞ  UPT ðNo i  1Þ as a function of pulse
number.

For the No5 pulse shown in Fig. 7(b), becauseof the absence of QMH(No5), our previous
assumption [10] that Q(No5) = Qv may be acceptable for Bex 6 5.53 T. For Bex = 6.07 T, Qv(No5)
is estimated by the relation of Qv(No5) =Q(No5)–QMH(No5) and Bex dependence of
Qv(No5) again falls on a nearly linear function.
It is clear that the Q(No5)–Bex concave curve originates from the appearance of QMH for Bex =6.07 T. We also notice that QMH(No5) for Bex =6.07 T corresponds to QLp notlinked with the ﬂux
trapping. Since QLp of this size is considered to bealso contained in QMH(No1), this QLp must be subtracted from QMH(No1) to estimate the trapping
loss QTp (No1) for Bex = 6.07 T as shown in Fig.
7(a). The QTp (No1) value for Bex = 6.07 T is smaller
than those for Bex = 4.70 T and 5.53 T because of
the smaller amount of the trapped ﬂux.

4. Summary
The time dependences of the temperature riseDT(t) and the magnetization M(t) on the surfaceof the cryo-cooled SmBaCuO bulk superconductor have been investigated during the identicalmagnetic pulse successive applications (No1–
No5) from Bex = 3.83–6.07 T. Main experimental
results and conclusions obtained in this study aresummarized as follows.
Fig. 7. Total Q, QMH and the diﬀerence DQ = Q  QMH as afunction of Bex for the (a) No1 and (b) No5 pulses. The QTp ; QLp
and Qv values are estimated for each pulse (see text).

be underestimated because a sizable amount ofmagnetic ﬂux is actually trapped as is seen in
Fig. 6(b) in spite of apparent non-hysteresis behavior of the M–l0Ha curve. Because the position PH,
which is deﬁned in the inset in Fig. 1(a), is locatednear the hard path around P1, the measuring position dependence of M(t) should be taken accountof. It is also to be noticed that Qv(No1) is represented by nearly a linear function of Bex as awhole. In this ﬁgure, QMH(No1) can be regarded
as the trapping pinning loss QTp (No1) except for
Bex = 6.07 T because of the absence of the hysteresis loss QMH(No5) for the No5 pulse below
Bex = 5.53 T shown in Fig. 7(b).

(1) The simultaneous temperature T(t) and magnetization M(t) measurements during pulse
ﬁeld magnetizing enable us to separate thegenerated heat due to the ﬂux pinning loss
Qp and the viscous loss Qv more precisely.
(2) For the No1 pulse application to the virginstate bulk, the pinning loss Qp determinedfrom the M vs. applied ﬁeld l0Ha curve isthe main origin of the heat generation and
Qv, which is estimated by the subtraction of
QMH from the total Q, is the dominant origin
for the No5 pulse.
(3) There is a threshold ﬁeld Bth = l0Hth above
which the pinning loss QLp unrelated to theﬂux pinning increases rapidly. Bth is locatedjust above Bex = 5.53 T for the present SmBaCuO bulk with 45 mm in diameter.

H. Fujishiro et al. / Physica C 426–431 (2005) 594–601(4) The spatial dependence of DT(t) enable us tolocate the easy paths and the hard path forthe ﬂux intrusion and it is found that thetemperature measurements combined withthe measurement of the M–l0Ha curve give
us valuable information in order to enhance
the trapped ﬁeld by PFM.

Acknowledgements
This work is partially supported by Japan Science and Technology Corporation under the
Joint-research Project for Regional Intensive in
the Iwate Prefecture on ‘‘Development of practicalapplications of magnetic ﬁeld technology for use in
the region and in everyday living’’.

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