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Rise-Time Elongation Effects on Trapped Field and Temperature Rise in Pulse Field
Magnetization for High Temperature Superconducting Bulk

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2005 Jpn. J. Appl. Phys. 44 4919
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Japanese Journal of Applied Physics
Vol. 44, No. 7A, 2005, pp. 4919–4925#2005 The Japan Society of Applied Physics

Rise-Time Elongation Eﬀects on Trapped Field and Temperature Risein Pulse Field Magnetization for High Temperature Superconducting Bulk
Hiroyuki FUJISHIRO, Masahiko K ANEYAMA, Kazuya Y OKOYAMA1 , Tetsuo OKA2 and Koshichi N OTO
Faculty of Engineering, Iwate University, 4-3-5 Ueda, Morioka 020-8551, Japan
1
National Institute for Materials Science, 3-13 Sakura, Tsukuba, Ibaraki 305-0003, Japan
2
IMRA Material R&D Co., Ltd., 5-50 Hachiken-cho, Kariya, Aichi 448-0021, Japan(Received February 3, 2005; accepted April 8, 2005; published July 8, 2005)

Pulse ﬁeld magnetization (PFM) using a magnetic pulse of Bex ¼ 3:83{5:53 T with various rise times tr (¼ 6{20 ms) has been
performed for the cryocooled SmBaCuO bulk superconductor starting at the initial temperature of 40 K. The time evolutionsof temperature TðtÞ and local ﬁeld BPL ðtÞ have been measured on the bulk surface after applying the magnetic pulse. With
increasing tr , the temperature rise T and the trapped ﬁeld BPT increase for Bex  4:70 T and decrease for Bex ¼ 5:53 T. The
rise time tr required to realize the optimum BPT has been found to become longer for a smaller pulse ﬁeld Bex . From theanalyses of the generated heat Q after ﬁve successive applications of pulses (Nos. 1–5) with the same amplitude, the Q(No. 5)
value, which can be regarded as the viscous loss Qv , decreases with increasing tr , due mainly to the decrease in the ﬂux
propagation velocity v in the bulk with longer tr . [DOI: 10.1143/JJAP.44.4919]
KEYWORDS: bulk superconductor, pulse field magnetization, rise time, temperature measurement, heat generation, pinning loss,
viscous loss

1.

Introduction

The practical application of high-Tc bulk superconductors
as a high-strength bulk magnet has been attempted for amagnetic separation system to purify waste water1) and for amagnetron sputtering apparatus,2) for example. Static ﬁeldcooled magnetization (FCM) is usually applied to magnetize
the high-Tc bulks, which can realize a high trapped ﬁeld
corresponding to the maximum trapping ability of magnetic
ﬁeld. Recently, the pulse ﬁeld magnetization (PFM) technique has been intensively investigated and applied becauseof its relatively compact, inexpensive and mobile setup. The
trapped ﬁeld BPT and total trapped ﬂux PT induced by PFM
are, however, generally smaller than those attained by FCM
at low temperatures below 77 K. This is possibly the result of
the large temperature rise T 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 PT
induced by PFM, T reduction is essential. Several
approaches have been attempted, such as an iteratively
magnetizing pulsed-ﬁeld method with reduced amplitude(IMRA)3) and a multi pulse technique with step wise cooling(MPSC).4) We proposed to set a metal ring onto the bulk
disk for T reduction.5) The BPT and PT values wereenhanced 10–20% with the presence of a stainless-steel ring
because of the transfer of heat generated in the peripheral
region of the bulk into the ring. Not only the strength ofmagnetic pulse Bex but also the shape of the pulse, such as
the rise time and pulse duration, must be taken into
consideration to analyze the PFM process.
The amount of heat generated Q during PFM is considered
to be given by the sum of the pinning loss Qp and the viscous
loss Qv , where Qv is proportional to the ﬂux propagation
velocity v. Thus the reduction of v in the bulk is a possible
approach to reducing heat generation. Yanagi and coworkers
measured the v value in SmBaCuO and YBaCuO bulks by
the pick-up coil technique and estimated the pinning andviscous losses.6,7) It is expected that v becomes faster withE-mail address: fujishiro@iwate-u.ac.jp

shorter rise time tr of the magnetic pulse. Itoh et al.
performed PFM at 77 K with tr ¼ 1:3 and 3.6 ms with thesame Bex and measured the total magnetic ﬂux PT .8)
However, no diﬀerence in PT was observed in this rangeof tr . We studied the time evolution and spatial distributionof the temperature rise TðtÞ on the surface of cryocooled
YBaCuO,9,10) SmBaCuO11,12) and GdBaCuO10) bulks during
PFM, where tr was ﬁxed at 12 ms. The TðtÞ behavior
changed depending on the initial bulk temperature Ts , thestrength of the pulse ﬁeld Bex and the trapped ﬁeld
distribution before the application of magnetic pulse. We
also estimated the total generated heat Q using the maximum
T based on the speciﬁc heat C of the bulk. By analyzing
the pulse number dependence of Q for successive applications of pulses with a ﬁxed amplitude Bex , the contributionsof Qp and Qv to the total Q were separated.10) Qp could be
precisely estimated from the hysteresis loop of magnetization M vs applied ﬁeld 0 Ha , and Qv was determinedby subtracting the pinning loss Qp ðMHÞ, estimated from theM–0 Ha hysteresis loop, from the total Q obtained intemperature measurements.13)
In this paper, we investigate the time dependences of TðtÞand the local ﬁeld BPL ðtÞ and the trapped ﬁeld BPT [¼ BPL(inﬁnity)] on the surface of the cryocooled SmBaCuO bulk
superconductor during successive applications of magnetic
pulses of the same strength. We estimate the Qp and Qv
values and discuss the tr dependences of these values. We
also discuss the possibility of BPT enhancement from theviewpoint of tr dependence.
2.

Experimental

A SmBaCuO bulk superconductor (Sm-bulk) of a disk
shape (45 mm in diameter and 18 mm in thickness) with ahighly c-axis-oriented structure was used. (fabricated by
Dowa Mining Co., Ltd.) which consisted of 4 growth sector
regions (GSR1-GSR4). The bulk crystal was composed of
SmBa2 Cu3 Oy (Sm123) and Sm2 BaCuO5 (Sm211) with themolar ratio of Sm123 : Sm211 ¼ 1:0 : 0:3, 15.0 wt % Ag2 O
powder and 0.5 wt % Pt powder. The bulk was uniformly
impregnated with epoxy resin in vacuum. However, epoxy

4919

4920

Jpn. J. Appl. Phys., Vol. 44, No. 7A (2005)

H. FUJISHIRO et al.

Fig. 2. Examples of the time dependence of current IðtÞ for each tr in thecase of Bex ¼ 3:83 T.

Fig. 1. (a) Experimental setup of the PFM technique. Rise time of thepulse ﬁeld tr was changed from 6 to 20 ms by combining the reactance ofthe dummy coil and/or the capacitance of the condenser bank. (b)Measurement positions of the temperature (P0–P4) and magnetic ﬁeld
(PH) on the bulk.

resin on the upper and bottom surfaces was removed toenhance the thermal response. Figure 1(a) shows theexperimental setup for the PFM technique. The Sm-bulk
was tightly stacked on the sapphire plate on the cold stage ofthe helium refrigerator in vacuum. The initial stage temperature Ts was held at 40 K. The bulk crystal was magnetizedusing a pulse magnetization coil (L ¼ 1:08 mH, 39 mm inbore radius) dipped in liquid N2 . The rise time of the pulse
ﬁeld tr was changed from 6 to 20 ms by combining thereactance of a dummy coil (L ¼ 0{2:2 mH) and/or thecapacitance of the condenser bank (C0 ¼ 20 or 60 mF).
Figure 1(b) shows the positions of the temperature andmagnetic ﬁeld measurements on the bulk. The temperature
T0 at the bulk center (P0) and the temperatures, T1–T4, at
P1–P4 in the four GSRs were measured using ﬁne chromelconstantan thermocouples (76 mm in diameter) attached tothe bulk surface using GE7031 varnish. P1, P2, P3 and P4
were situated at the center of each GSR, 9 mm from P0. Eachtemperature was recorded about 7 times/s just after applying
the pulse ﬁeld. The Hall sensor (F.W. Bell, model BHA 921)
was attached at position PH on the growth sector boundary(GSB) 2.5 mm from P0. The time evolution of the local ﬁeld

BPL ðtÞ was monitored using a digital oscilloscope (Yokogawa
Electric, DL1640). The time dependence of the applied ﬁeld
0 Ha ðtÞ was also monitored from the current IðtÞ ﬂowing inthe shunt resistor. The maximum strength of the pulse ﬁeld
0 Ha ðtÞ was deﬁned as Bex , and it ranged from 3.83 to
5.53 T. Five magnetic pulses (Nos. 1–5) with the same Bex
were applied sequentially after recooling to Ts , and TðtÞ andBPL ðtÞ were measured at each stage.
The trapped ﬁeld BPT was also measured at PH using thesame Hall sensor. The two-dimensional distribution of thetrapped ﬁeld B3T mm was monitored at each stage using anaxial Hall sensor scanned stepwise 3 mm above the bulk
surface with a pitch of 1.2 mm. The trapped ﬁeld BFC
T by
FCM was also measured at several temperatures using the
cryocooled superconducting magnet. During FCM, the static
magnetic ﬁeld of 5 T was decreased to 0 T in 18 min(0.278 T/min).
Figure 2 shows examples of the time dependence of
current IðtÞ for each tr in the case of Bex ¼ 3:83 T. Eachpulse is a maximum at tr ¼ 6{20 ms and then recovers tozero in 120 ms.
3.

Results and Discussion

3.1 Temperature rise and trapped ﬁeld
Figures 3(a)–3(d) show examples of the time evolutionsof T0ðtÞ–T4ðtÞ on the bulk after applying the No. 1 and No. 5
pulse ﬁelds of (a) Bex ¼ 3:83 T with tr ¼ 6 ms, (b) Bex ¼
3:83 T with tr ¼ 20 ms, (c) Bex ¼ 4:70 T with tr ¼ 6 ms, and(d) Bex ¼ 4:70 T with tr ¼ 20 ms. The distribution of B3T mm
for the No. 1 pulse is shown in the inset of each ﬁgure. For
Bex ¼ 3:83 T shown in Figs. 3(a) and 3(b), T3ðtÞ clearlyshows a peak with a faster rise for the No. 1 pulse, whichsuggests that the powerful heat source is located in thevicinity of P3. The magnetic ﬂuxes preferentially intrude
into the bulk through the path around P3, where heatgeneration takes place. The maximum temperature riseTmax at T3 for tr ¼ 20 ms (¼ 18 K) is larger than that fortr ¼ 6 ms (¼ 14 K) and the T values at all the positions
increase with increasing tr . The trapped ﬁeld B3T mm at thebulk center is always small but B3T mm for tr ¼ 20 ms is larger
than that for tr ¼ 6 ms.
For the No. 1 pulse of Bex ¼ 4:70 T shown in Figs. 3(c)and 3(d), the temperature rise T at each position increasesJpn. J. Appl. Phys., Vol. 44, No. 7A (2005)

H. FUJISHIRO et al.

4921

Fig. 3. Time evolutions of temperatures T0ðtÞ–T4ðtÞ after applying the No. 1 and No. 5 pulse ﬁelds: (a) tr ¼ 6 ms with Bex ¼ 3:83 T,(b) tr ¼ 20 ms with Bex ¼ 3:83 T, (c) tr ¼ 6 ms with Bex ¼ 4:70 T and (d) tr ¼ 20 ms with Bex ¼ 4:70 T. For the No. 5 pulse, only T0ðtÞ
and T3ðtÞ are shown in each ﬁgure.

compared with that for Bex ¼ 3:83 T. T2ðtÞ also shows apeak, as does T3ðtÞ. T0ðtÞ at the bulk center shows a slower
temperature rise for tr ¼ 6 ms, which suggests that the mainheat source is far from the bulk center. On the other hand,
T0ðtÞ for tr ¼ 20 ms rises faster with a faint peak whichsuggests that ﬂux motion and heat generation take place also
around the center. The distribution of B3T mm in both ﬁgures
shows a conical shape but the peak value in B3T mm fortr ¼ 20 ms is somewhat larger than that for tr ¼ 6 ms. The
temperature rise T decreases with increasing pulse number
and shows a tendency to a saturate after the third (No. 3)
pulse application. There is no peak in TðtÞ for the No. 5
pulse, which suggests that ﬂux motion and heat generation
take place in all GSRs equally.
Figure 4(a) shows the maximum temperature rise T0max
at P0 for the No. 1 and No. 5 pulses as a function of tr .
For the No. 1 pulse of Bex ¼ 3:83 T and 4.70 T, T0max
increases with increasing tr and with increasing Bex .
However, for the No. 1 pulse of Bex ¼ 5:53 T, T0max
slightly decreases with increasing tr . On the other hand,
T0max for the No. 5 pulse, which is far smaller than that for
the No. 1 pulse, decreases with increasing tr particularly for
Bex ¼ 4:70 T. Figure 4(b) shows the trapped ﬁeld BPT at theposition PH as a function of tr for each Bex . For the No. 1
pulse of Bex ¼ 3:83 T, BPT increases monotonically withincreasing tr . For Bex ¼ 4:70 T, the markedly enhanced BPT

value further increases and then saturates with increasing tr .
For the No. 1 pulse of Bex ¼ 5:53 T, BPT decreases withdecreasing tr .
Figure 5 summarizes the relationship between BPT and the
maximum temperature T0max after applying the No. 1 pulse
for various tr values. Using the data shown in Figs. 4(a) and
4(b), data sets of (T0max , BPT ) are plotted for each Bex and tr .
The measured trapped ﬁeld BFC
T ðTÞ is also presented, whichcorresponds to the maximum ﬂux trapping ability of thepresent SmBaCuO bulk. The data sets of Bex ¼ 3:83 and4.70 T are situated below the BFC
T –T0max line. When Bex ¼
4:70 T is applied, BPT becomes the largest for tr ¼ 20 ms andthen decreases with decreasing tr . On the other hand, forBex ¼ 5:53 T, the BPT value becomes the largest for tr ¼ 6 ms
and then decreases with increasing tr . The BPT values fortr ¼ 12 and 16 ms are smaller than those for Bex ¼ 4:70 T
because of the increase of heat generation; T0max touches theP
BFC
T –T0max line and the BT decrease follows it with thefurther increase of temperature. The results of these analyses
demonstrate that the ﬂux trapping ability by the PFM
technique can be systematically explained as being limitedby the BFC
T –T0max line.
Figure 6 shows the time evolutions of the applied ﬁeld
0 Ha ðtÞ and the local ﬁeld BPL ðtÞ at PH for (a) tr ¼ 6 ms with
Bex ¼ 4:70 T, (b) tr ¼ 16 ms with Bex ¼ 4:70 T, (c) tr ¼ 6 ms
with Bex ¼ 5:53 T and (d) tr ¼ 16 ms with Bex ¼ 5:53 T for4922

Jpn. J. Appl. Phys., Vol. 44, No. 7A (2005)

Fig. 4. (a) Maximum temperature rise T0max at P0 and (b) trapped ﬁeld
BPT at PH for the No. 1 and No. 5 pulses as a function of rise time tr .

H. FUJISHIRO et al.

reduced to 3.2 T, as shown in Fig. 4(b). Similar behaviors
were also conﬁrmed for Bex ¼ 5:53 T with tr ¼ 6 ms and16 ms, as shown in Figs. 6(c) and 6(d), respectively; trB(¼ 10 ms) for tr ¼ 16 ms is elongated compared with trB(¼ 6:5 ms) for tr ¼ 6 ms. For Bex ¼ 5:53 T with tr ¼ 16 ms,
the maximum of the local ﬁeld attains almost 5.5 T, but thishigh value of BPL causes a more intense ﬂux creep, resulting
in a smaller trapped ﬁeld BPL (2:1 T) than that (2:8 T) fortr ¼ 6 ms.
In Figs. 6(a)–6(d), we note that the increase of BPL ðtÞ starts
at about the applied pulse ﬁeld 0 Ha ðtÞ  4:3 T regardless ofthe maximum pulse ﬁeld Bex and the rise time tr . Thissuggests that the surface barrier against ﬂux penetration
breaks down at about 4.3 T in the virgin run. The strength of
the surface barrier results from the critical current density Jcof the bulk and is independent of the Bex and tr values. The
existence of the surface barrier of 4:3 T is consistent withthe drastic increase of BPT between Bex ¼ 3:83 and 4.70 T. In
Fig. 6(e), for the No. 5 pulse of Bex ¼ 4:70 T, the variationof BPL ðtÞ is very small but the response of BPL ðtÞ shows nodelay against the magnetic pulse. The surface barrier seems
to be removed owing to the magnetic ﬂux already trapped in
the bulk.
Assuming the relation v ¼ d=trB , where d (¼ 20 mm) is the
distance between the bulk edge and the position PH, the ﬂux
velocity v is roughly estimated to be 3.1 m/s for tr ¼ 6 ms
and 2.2 m/s for tr ¼ 16 ms, which are reasonable values
compared with those determined by the pick-up coiltechnique.6) It should be noted that the propagation speed
v of magnetic ﬂux in the bulk only modestly changes
in contrast to the large change of tr . In the following
subsection, we estimate the total generated heat Q andseparate the pinning loss Qp and the viscous loss Qv from thetotal Q.
3.2 Estimation of generated heat Q
If we assume that the heat generation occurs during PFM
under the adiabatic condition, the total generated heat Q,
which is the sum of Qp and Qv , is given by10)
Z Ts þTmax
Q¼
CðTÞV dT ¼ Qp þ Qv
ð3:1Þ
Ts

Fig. 5. BPT value as a function of maximum temperature T0max for theNo. 1 pulse with various tr .

the No. 1 pulse. In Fig. 6(a) for tr ¼ 6 ms with Bex ¼ 4:70 T,
the maximum BPL ðtÞ is about one-half of Bex . The rise time of
BPL ðtÞ is about trB ¼ 6:5 ms. On the other hand, for tr ¼ 16 ms
shown in Fig. 6(b), the rise time of BPL ðtÞ increases to about
trB ¼ 9 ms and the magnetic ﬁeld of 4:5 T, which is almost
as large as Bex , enters the bulk and then slowly decreases due
to ﬂux creep. As a result, the trapped ﬁeld BPT is ultimately

where CðTÞ is the speciﬁc heat and V is the volume of
the bulk disk. CðTÞ was estimated using the relation C ¼
=, i.e., the thermal conductivity  divided by the thermal
diﬀusivity , which were measured simultaneously.14)
Figure 7 presents the estimated Q(No. 1) and Q(No. 5)
values after the No. 1 and No. 5 pulses and the diﬀerencedQ [¼ Q(No. 1)  Q(No. 5)] for Bex ¼ 4:70 T as a functionof tr . Since no additional ﬂux trapping takes place with theNo. 5 pulse, as described in the previous paper,12) Q(No. 5)
may consist mainly of viscous loss Qv and dQ can beroughly regarded as the pinning loss Qp for the No. 1 pulse.
In Fig. 7, Q(No. 1) and dQ increase with increasing tr . On
the other hand, it should be noted that Q(No. 5) decreases
with increasing tr . The decrease of v for longer tr may bemainly responsible for the decrease of Q(No. 5) (’ Qv )because Qv is proportional to v.
The magnetization M at PH can be estimated from the0 Ha ðtÞ and BPL ðtÞ values usingJpn. J. Appl. Phys., Vol. 44, No. 7A (2005)

H. FUJISHIRO et al.

4923

Fig. 6. Time evolutions of the applied ﬁeld 0 Ha ðtÞ and local ﬁeld BPL ðtÞ for (a) tr ¼ 6 ms with Bex ¼ 4:70 T, (b) tr ¼ 16 ms with
Bex ¼ 4:70 T, (c) tr ¼ 6 ms with Bex ¼ 5:53 T and (d) tr ¼ 16 ms with Bex ¼ 5:53 T for the No. 1 pulse. (e) Time evolution of 0 Ha ðtÞand BPL ðtÞ upon applying the No. 5 pulse of tr ¼ 6 ms with Bex ¼ 4:70 T.

M ¼ BPT  0 Ha :

ð3:2ÞFigure 8(a) shows the M vs 0 Ha curves for the No. 1 pulseof Bex ¼ 4:70 T with tr ¼ 6 ms, 12 ms and 16 ms. Following
the critical state model, the pinning loss Qp ðMHÞ can beobtained from the area of the M–0 Ha hysteresis loop. A
wide hysteresis loop in the M–0 Ha curve can be clearlyseen for each tr , which results from ﬂux trapping in the bulk
disk. The area of the hysteresis loop is enhanced withincreasing tr , corresponding to the enhancement of BPT in

Fig. 4(b). Figure 8(b) presents the pulse number dependenceof the M vs 0 Ha curves for tr ¼ 12 ms with Bex ¼ 4:70 T.
The hysteresis loop becomes drastically narrow for the No. 2
pulse and no hysteresis behavior can be observed for the
No. 5 pulse. These behaviors are consistent with the pulse
number dependences of BPT and support the hysteresis loop
being directly related to ﬂux trapping.12) The Qp ðMHÞ values
estimated from the area of the hysteresis loop are alsoplotted in Fig. 7. It should be noted that the Qp ðMHÞ values
are nearly equal to dQ determined from the temperature

4924

Jpn. J. Appl. Phys., Vol. 44, No. 7A (2005)

Fig. 7. Estimated Q(No. 1) and Q(No. 5) values after the No. 1 and No. 5
pulses and the diﬀerence dQ [¼ Q(No. 1)  Q(No. 5)] for Bex ¼ 4:70 T
as a function of tr . The Qp ðMHÞ values estimated from the M–0 Ha
hysteresis loop [in Fig. 8(a)] are also plotted.

H. FUJISHIRO et al.

place because of the large T. These results can besystematically explained on the basis of the diagram of
the trapped ﬁeld induced by the ﬁeld-cooled magnetization (FCM) BFC
T vs maximum temperature T0max .
(3) The BPT value for the virgin-state bulk is governed not
only by the pulse ﬁeld strength Bex but also by the risetime tr . The maximum BPT can be achieved with the
optimum combination of Bex and tr . In other word,
there is a characteristic Bex for each tr which maximizes the BPT value.
(4) In the present SmBaCuO bulk in the virgin state, there
exists a surface barrier against ﬂux penetration, but it
is destroyed by the applied magnetic pulse of 4:3 T.
For the following pulse ﬁeld application, the barrier iseliminated by the previously trapped ﬂux.
(5) The ﬁve pulse ﬁelds (Nos. 1–5) with the ﬁxed strength
Bex were applied to the bulk and the generated heat Q
was estimated using the maximum temperature riseT0max and the speciﬁc heat C. Heat generation
Q(No. 5) after the No. 5 pulse, which is mainly
contributed by the viscous loss Qv , decreases withincreasing tr . The tr dependence of Q(No. 5) may
mainly result from the decrease of the ﬂux propagation
velocity v, which was conﬁrmed from the timedependence of the local ﬁeld BPL ðtÞ at position PH
in the bulk. The dQ [¼ Q(No. 1)  Q(No. 5)] value,
which is regarded as the pinning loss Qp for the No. 1
pulse, increases with increasing tr for Bex ¼ 4:70 T, in
accord with the observed tr dependence of BPT .
(6) The pinning loss Qp ðMHÞ was estimated from thehysteresis loop of the magnetization M vs the appliedﬁeld 0 Ha . The Qp ðMHÞ value is nearly equal to dQ
estimated from the measured temperature. This result
is consistent with our assumption that dQ can be
regarded as the pinning loss and that the viscous loss
Qv can be given by Q(No. 5).
Acknowledgements

Fig. 8. (a) M vs 0 Ha curves for tr ¼ 6, 12 and 16 ms with Bex ¼ 4:70 T
for the No. 1 pulse. (b) Pulse number dependence of M vs 0 Ha curves
for Bex ¼ 4:70 T with tr ¼ 12 ms.

measurement. These results suggest the validity of estimating pinning loss from the measured temperature. Thus theviscous loss Qv can be reliably estimated on the basis of theQ(No. 5) value.
4.

Summary

The rise-time elongation eﬀect of the magnetic pulse(Bex ¼ 3:83{5:53 T) on the temperature rise T and thetrapped ﬁeld BPT has been investigated for various rise times
tr (¼ 6{20 ms) for the cryocooled SmBaCuO bulk superconductor. Main experimental results and conclusions
obtained in this study are summarized as follows.
(1) Under identical magnetic pulse strengths Bex , thetemperature rise T and the trapped ﬁeld BPT change
depending on the rise time tr of the magnetic pulse.
(2) For Bex  4:70 T, T and BPT increase with increasing
tr . On the other hand, for Bex ¼ 5:53 T, T and BPT
decrease with increasing tr . The reduction of BPT takes

The valuable suggestions by Professor M. Ikebe of Iwate
University are greatly acknowledged. This work is partially
supported by Japan Science and Technology Agency under
the Joint-Research Project for Regional Entities in Iwate
Prefecture on development of practical applications ofmagnetic ﬁeld technology for use in the region and ineveryday living.
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