INSTITUTE OF PHYSICS PUBLISHING
SUPERCONDUCTOR SCIENCE AND TECHNOLOGY
Supercond. Sci. Technol. 18 (2005) 839–849
doi:10.1088/0953-2048/18/6/009
Pulsed field magnetization of a 36 mm
diameter single-domain Sm–Ba–Cu–O
bulk superconductor at 30, 35 and 77 K
Y Yanagi1 , Y Itoh1 , M Yoshikawa1 , T Oka1 , H Ikuta2 and
U Mizutani2
1
IMRA Material R&D Co., Ltd, 5-50 Hachiken-cho, Kariya, Aichi 448-0021, Japan
Department of Crystalline Materials Science, Nagoya University, Furo-cho, Chikusa-ku,
Nagoya 464-8603, Japan
2
Received 10 August 2004, in final form 8 April 2005
Published 29 April 2005
Online at stacks.iop.org/SUST/18/839
Abstract
A c-axis oriented single-domain Sm–Ba–Cu–O bulk superconductor 36 mm
in diameter was magnetized by the pulsed field magnetization (PFM)
method at 30, 35 and 77 K. The trapped field distributions after applying
pulsed fields with different amplitudes were measured by scanning a Hall
sensor 0.5 mm above the surface of the sample. We also measured the time
evolution of magnetic fields during the PFM by using an oscilloscope
connected to two Hall sensors mounted on the bulk superconductor surface.
Fluxes are found to penetrate into the bulk superconductor and to escape
from it by choosing passes through the direction inclined at 45◦ to growth
sector boundaries (GSBs) of the sample. At 35 K, the temperature rise of the
sample caused by heat generation due to flux motion becomes more
substantial than that at 77 K. Thus, flux jumps occurred through the passes
and assisted magnetic fluxes to reach rather easily the centre of the bulk
superconductor. As a result, the magnetic field necessary for PFM is lower
than that to fully magnetize the sample by means of the static
zero-field-cooling magnetization method. The optimized multi-PFM with
reducing amplitudes, which was specifically referred to as the IMRA
technique, turned out to be very effective in achieving excellent trapped field
characteristics by PFM at low temperatures. We could achieve a maximum
trapped field of 3.6 T together with a well conical trapped field distribution
at 30 K.
1. Introduction
For the last decade, c-axis oriented large single-domain RE–
Ba–Cu–O bulk superconductors, which exhibit a high critical
current density Jc far exceeding 104 A cm−2 at 77 K, have
been relatively easily synthesized by utilizing the fabrication
techniques known as QMG [1] and/or OCMG [2] processes.
This state of the art material has been considered for use as
a quasi-permanent magnet producing much stronger magnetic
fields than the ordinary magnets like Nd–Fe–B [3, 4]. Thanks
to the progress in sample fabrication coupled with mechanical
reinforcement techniques, very high trapped fields of the bulk
superconductors have been achieved by several groups [5–9].
The development of compact refrigerators has also encouraged
0953-2048/05/060839+11$30.00 © 2005 IOP Publishing Ltd
us to use a magnetized bulk superconductor as a quasipermanent magnet at as low temperatures as 20–40 K, since
Jc and trapped fields are known to be significantly enhanced
with lowering temperature.
Indeed, we have reported several applications including
superconducting motors [10], magnetic field generators [11]
and magnetron sputtering [12] by using magnetized bulk
superconductors as quasi-permanent magnets. Here the
choice of the magnetization method is of critical importance
in the installation of a bulk superconductor as a magnet
in actual devices. The pulsed field magnetization (PFM)
technique [13] was originally developed to magnetize a series
of bulk superconductors by feeding a pulsed current into a
solenoid immersed in liquid nitrogen in the housing of a
Printed in the UK
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Y Yanagi et al
superconducting motor. However, we immediately realized
that substantial heat is generated [13–16] due to rapid flux
motion during the PFM operation, resulting in degradation of
the trapped field. To suppress heat generation, many attempts
have been made, including the development of the present
multi-PFM technique named iteratively magnetizing pulsedfield operation with reducing amplitudes (IMRA) [17, 18],
locating yoke pieces around a bulk superconductor [19], use
of vortex-type coils [20] and repeating pulses with step-wise
cooling [21].
The motion of fluxes driven by PFM in a disc-shaped
bulk superconductor kept in liquid nitrogen at 77 K has been
extensively studied [13–16, 19, 20, 22]. In most cases, the
trapped field thus obtained has been analysed by assuming
uniform and lateral penetration of fluxes into a disc-shaped
bulk superconductor. However, a careful inspection of the
data even at 77 K revealed that the trapped field produced
by PFM is slightly distorted as a result of unavoidable
position-dependent distribution of pinning centres over the
superconducting matrix [19, 23]. Another group using a short
pulse for magnetization also reported a strong deformation
of the trapped-field distribution of the bulk superconductor
at 77 K [24]. If temperature were lowered far below 77 K,
the effect would probably become more serious because of
increasing heat generation during PFM [18, 25, 26].
To achieve as high a trapped field as possible at low
temperatures around 20–40 K, it is of critical importance
to study the detailed magnetization process due to the PFM
operation. In the present experiment, we have studied the
trapped field distribution as a function of both temperature
and amplitudes of the pulsed field over the temperature
range 30–77 K and also investigated the dynamical motion
of fluxes propagating in the bulk superconductor during the
PFM at 35 K. In addition, we also report on the trapped
field distribution achieved by optimizing the IMRA technique
mentioned above, and conclude that a newly elaborated IMRA
technique is very powerful to achieve a fairly conical trapped
field distribution over a 36 mm diameter bulk superconductor
by the PFM at 30 K.
2. Experimental details
Powders of SmBa2 Cu3 Ox and Sm2 BaCuO5 with the molar
ratio 3:1 were thoroughly mixed together with 0.5 wt% Pt and
10 wt% Ag2 O. A compressed cylindrical pellet was subjected
to the melt texturing method by using a NdBa2 Cu3 O y crystal
as a seed under flowing Ar gas atmosphere to produce a c-axis
oriented single-domain Sm–Ba–Cu–O bulk superconductor of
36 mm in diameter and 16 mm in thickness. More details about
the sample fabrication have been described elsewhere [5]. The
bulk superconductor obtained after appropriate heat treatment
in flowing oxygen atmosphere was embedded into a stainlesssteel ring of 43 mm in outer diameter and 2 mm in thickness,
and the gap between the bulk superconductor and the ring was
filled with epoxy resin. Its photograph is shown in figure 1.
Figure 2 shows the trapped field distribution obtained after the
sample was magnetized by field cooling (FC) to liquid nitrogen
temperature in the presence of a static magnetic field of 4 T.
One can see that the present bulk superconductor is essentially
free from any serious weak links. However, a closer look
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Growth Sector
Boundary (GSB)
Growth Sector
Y
X
A
B
36 mm
Figure 1. A photograph of a 36 mm diameter c-axis oriented
single-domain Sm–Ba–Cu–O bulk superconductor, which is
embedded into a stainless steel ring with epoxy resin for
reinforcement against fracture during cooling and magnetization.
There are four a-axis growth sectors on the sample surface. Their
boundaries (GSBs) are clearly seen. The time evolution of magnetic
field during the pulsed field operation was measured by using the
Hall sensors mounted at position A at the centre of the sample and
position B 7.5 mm away from the centre and 45◦ inclined from the
GSB. The x–y coordinates are introduced to match along GSBs for
the trapped field distribution measurements in this study.
Figure 2. The trapped field distribution obtained by static field
cooling magnetization for the present bulk superconductor immersed
in liquid nitrogen. The data were taken by scanning the Hall sensor
(F W Bell, BHA921) 0.5 mm above the surface of the bulk
superconductor. The x–y coordinates are chosen to coincide with
that in figure 1. The dashed circle indicates the edge of the sample.
into figure 2 reveals the existence of directions pointing to the
rounded corners of slightly squared iso-field lines. These were
chosen as x- and y-directions in figure 2 and coincide with the
directions along the growth sector boundaries (GSBs).
Figure 3 illustrates schematically the present experimental
set-up to measure the trapped field distribution of the sample
over 30–77 K. The sample was mounted on doubly stacked
sapphire blocks 50 mm in total thickness and 40 mm in
diameter and tightly anchored onto the cold head of a Gifford–
McMahon (GM) refrigerator (AISIN, GR301). We used
sapphire blocks instead of Cu to get rid of two serious
difficulties inherent in PFM: first, a temperature rise of the
Cu blocks due to induced eddy current, which in turn causes
sample heating, and second, buckling of the thin-wall cylinder
of the GM refrigerator due to a large compressive force
caused by an electro-magnetic repulsive force between the Cu
Pulsed field magnetization of a 36 mm diameter single-domain Sm–Ba–Cu–O bulk superconductor at 30, 35 and 77 K
Figure 3. Schematic illustration of the experimental set-up for the measurement of magnetic field distribution on the bulk superconductor
mounted on the cold head of a Gifford–McMahon refrigerator. A supporting rod of 650 mm in length is in vacuum inside the bellows and is
movable by driving the motor assisted with a computer. The space above the bulk superconductor in the vacuum chamber is 84 mm in
diameter, inside which the Hall sensor mounted at the end of the supporting rod can be moved. The temperature of the sapphire block
2.5 mm below the sample was monitored by a thermometer inserted into a hole on its sidewall.
block and the magnetizing coil. The temperature of the bulk
superconductor was controlled over the range from 30 to 77 K
by monitoring a thermometer and using a heater wound around
the cold head of the GM refrigerator. We could not directly
measure the temperature of the superconductor, since it was
embedded in a stainless-steel ring and there is no free surface
on its sidewall. Thus, we had to be content with measuring the
temperature in the sapphire block 2.5 mm below the sample
by inserting an additional thermometer (Scientific Instruments,
RO105) into a hole on its sidewall. By using this sensor, we
measured the maximum temperature rise, which was typically
reached within a few seconds after applying a pulsed field.
The temperature rise T is defined as the difference between
the maximum temperature thus recorded and the temperature
before the start of the PFM.
The magnetizing coil for PFM was placed outside the
vacuum chamber of the GM refrigerator in such a way that
the central axis of the resulting field coincides with that of the
sample. The sample was magnetized by feeding a pulse current
through the coil with a rise time of 13 ms, as shown in figure 4.
Here, we define the applied field (µ0 Ha ) as the peak value of the
pulsed field, which was calculated as a product of the maximum
current in the magnetizing coil and its coil constant. After each
PFM, the trapped field component Bz parallel to the c-axis
of the bulk superconductor was measured by scanning a Hall
sensor (F W Bell, BHA 921). In the present experiment, we
specifically constructed a Hall sensor scanning device shown
in figure 3, which has an x–y stage with a flexible bellows.
This originally developed device enables us to scan the Hall
sensor 0.5 mm above the surface of the bulk superconductor
Figure 4. A typical current pulse. The coil constant for the
magnetizing coil is 1.4 × 10−3 T A−1 .
located inside the vacuum chamber of the GM refrigerator,
the distance being typically employed for the measurement of
the sample immersed in liquid nitrogen. Once the trapped field
distribution measurement was over, the Hall sensor was moved
to the position where the maximum trapped field was achieved,
and subsequently the maximum surface trapped field (BTmax )
was measured by lowering the sensor directly onto the surface
of the superconductor. The total flux was calculated from
the trapped field distribution map by integrating Bz over the
region where its value was positive.
We also measured the time evolution of magnetic field
on the sample surface during PFMs by using a similar
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Y Yanagi et al
Figure 5. Trapped field distributions ((a)–(f)) produced by a set of single PFMs with different amplitudes for the bulk superconductor in the
unmagnetized state at 77 K. The main panel shows the maximum trapped field BTmax ( ) and the maximum temperature rise T () as a
function of the applied field.
•
experimental set-up for the field mapping measurement. In
this measurement, two Hall sensors (F W Bell, BHT 921)
were attached at positions A and B marked in figure 1, and
their signal lines were connected to a digital oscilloscope
(Yokogawa Electric, DL4100).
3. Results and discussion
3.1. Trapped field distribution achieved by a single PFM
First of all, we should note that a single PFM in this section
refers to the singly operated PFM for an unmagnetized bulk
superconductor. Figure 5 shows the applied field µ0 Ha
dependence of the maximum trapped field BTmax and maximum
temperature rise T after the single PFM with different
amplitudes was made at 77 K. The corresponding trapped
field distributions are shown in (a)–(f), which are arranged
in ascending order from low to high values of µ0 Ha . We point
out first that the trapped field remains absent in the central area
up to the applied field µ0 Ha of 2.2 T (figure 5(b)), and that
BTmax takes the maximum value of 1.0 T when µ0 Ha reaches
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2.7 T (figure 5(d)). Obviously, further increase in µ0 Ha results
in a decrease in BTmax . It is also important to mention that
magnetic fields were trapped mainly along the GSBs when
µ0 Ha is higher than 3 T (figures 5(e) and (f)), the same as
the previous report [19]. The temperature rise T is found to
increase monotonically with increasing µ0 Ha and to reach the
maximum value of 2.5 K at µ0 Ha = 6.4 T. However, the value
of T is negligibly small, as long as µ0 Ha is lower than 2 T.
The measurements described above were also made at
35 K. As shown in figure 6(a), the trapped field is limited only
in the peripheral region and is essentially zero in the central
region of the superconductor, when µ0 Ha is less than 3.4 T.
However, once µ0 Ha increases further only by 6%, i.e., 3.6 T,
the magnetic field jumps into the bulk superconductor and the
trapped field suddenly becomes finite in the central region,
resulting in a residual value of BTmax higher than 2.4 T. It is
also worthwhile emphasizing that the region where the trapped
fields remain high is not uniform but concentrated in the area
along the broken lines, the direction of which is inclined by
45◦ with respect to the GSBs, as indicated in figure 6(c).
Instead, we can see that the trapped fields are almost zero in the
Pulsed field magnetization of a 36 mm diameter single-domain Sm–Ba–Cu–O bulk superconductor at 30, 35 and 77 K
Figure 6. Trapped field distributions ((a)–(f)) produced by a set of single PFMs with different amplitudes for the bulk superconductor in the
unmagnetized state at 35 K. The main panel shows the maximum trapped field BTmax ( ) and the maximum temperature rise T () as a
function of the applied field.
•
peripheral region along the GSB, when µ0 Ha is in the range
of 3.6–3.9 T (figures 6(b) and (c)).
When µ0 Ha = 4.2 T in figure 6(d), we find that BTmax
takes its maximum value of 2.95 T. Surprisingly, this value
is as high as 70% of the applied field µ0 Ha . An extension
of the static zero-field cooling (ZFC) magnetization, which
requires the applied field at least twice as large as the trapped
field for full magnetization, would lead to the assumption
that an extremely high pulsed field is needed to magnetize
a bulk superconductor at low temperatures, since Jc increases
rapidly with decreasing temperature. However, this is not true.
The achievement of a high percentage reaching 70% is never
expected in the static ZFC magnetization. This means that the
PFM at low temperatures does not require a large field as in the
static ZFC method. This value of µ0 Ha is hereafter called the
optimum applied field µ0 Hopt . When µ0 Ha exceeds µ0 Hopt
as in figures 6(e) and (f), trapped fields are found to become
substantial along the GSB, similar to that at 77 K. As for the
temperature rise, T reaches 18 K when µ0 Ha = 6.9 T, which
is far larger than the maximum value of about 2.5 K at 77 K.
As can be seen from the applied field dependence of T in
figure 6, the range in µ0 Ha , where T is almost zero, reaches
3 T, which is much wider than 2 T at 77 K shown in figure 5.
The area in which magnetic fluxes are mainly trapped is
found to change drastically, depending on whether the applied
field µ0 Ha exceeds µ0 Hopt or not. This characteristic feature
is enhanced when the temperature is lowered from 77 to 35 K.
To gain a deeper insight into the mechanism for this unique
behaviour in the trapped field distribution, we consider it to
be important to discuss first the penetration of fluxes into a
cylindrical bulk superconductor.
As applied field increases, quantized magnetic fluxes start
to penetrate into the bulk superconductor from the peripheral
region. The magnetic flux moves in the bulk while satisfying
the relation FL + Fp + Fv = 0, where FL is the London
force [27, 28], Fp is the pinning force and Fv is the viscous
force [13]. FL acts to drive the magnetic flux towards a less
dense area as a result of repulsive interaction among fluxes,
while both Fp and Fv resist the motion due to FL . If the
pinning force is strong, magnetic fluxes will be pinned and
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Y Yanagi et al
their density naturally increases, resulting in an increase in
the driving force. The magnetic fluxes are forced to move
in the bulk when the driving force overcomes the pinning
force. Once it moves, heat is generated because of the presence
of the two losses: pinning loss proportional to the pinning
force and the velocity of the moving flux, and viscous loss
proportional to the square of the velocity [13]. They are
given as the product of the force and velocity and, hence,
should be referred to as the power loss in the unit of watts.
Hence, a temperature rise of the bulk superconductor would
be determined by integrating the power losses over the period
of the PFM operation. When the applied field is increased
quasi-statically and the velocity of the flux is negligibly small,
the heat generation in the bulk superconductor should be
essentially suppressed. In the case of the PFM, however,
the magnetic flux enters the bulk superconductor within a few
milliseconds. Hence, the heat generation becomes substantial
as a result of a high velocity of the moving flux [15], and
the temperature rise T in the bulk superconductor becomes
significant, since the heat generated during a PFM cannot
be instantly liberated. The heat generation should be more
serious at low temperatures due to the decrease in the specific
heat of the bulk superconductor. For example, the specific
heat of Sm–Ba–Cu–O bulk superconductor at 35 K becomes
less than 30% of the value at 77 K [26]. In addition, the
pinning force increases with decreasing temperature and thus
the heat generation becomes more substantial as a result of
the increasing pinning loss, even if the magnetic flux moves
with the same velocity as that at 77 K. Once the temperature
of the bulk superconductor increases by heat generation, the
pinning force is weakened and the magnetic fluxes can move
less resistively against the pinning force.
The results shown in figures 5 and 6 clearly indicate that
there is a difference in the flux trapping property between the
area including GSBs and the rest of the sample. Recently,
Eisterer et al have developed a new characterization method,
the magnetoscan method, and have observed that the shielding
current is stronger near GSBs [29], which means that the
critical current density is larger near GSBs. Therefore, we
assume that the pinning force is stronger along the x- and
y-directions, which are hereafter referred to as region SP
(strong pinning abbreviated as SP) while the rest as region WP
(weak pinning) involving the fewest GSBs, i.e., 45◦ away from
it. As a natural consequence, the temperature in region WP
would become higher than that in region SP due to selective
passage of the fluxes during the PFM, and the non-uniform
temperature distribution thus produced would become more
significant at low temperatures like 35 K. In other words,
the spatially changing time-dependent temperature distribution
should play an important role in determining the final trapped
field distribution. Indeed, the non-uniform temperature rise
after the PFM at around 40 K has already been reported by
other group [25, 26].
We are ready to discuss the results shown in figures 5 and 6
under the interpretation described above. As we can see from
figures 5(a) and (b), the trapped field distributions for µ0 Ha
lower than µ0 Hopt at 77 K are rather isotropic. However, at
35 K, anisotropic distribution is clearly seen in figures 6(b)
and (c). Judging from the distribution maps, we naturally
consider that magnetic fluxes have entered the central region
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through the WP region along dashed lines in figure 6(c). Since
the inherent local Jc in the bulk superconductor at a given
temperature must be fairly uniform throughout the bulk as
indicated in figure 2, the difference in the degree of the nonuniformity in trapped field distributions between 77 and 35 K
should be attributed to the difference in the locally occurring
heat generation during each PFM. As noted above, a sudden
penetration of the magnetic field into the centre of the bulk
superconductor was brought about only by a slight increase in
µ0 Ha at 35 K (see figures 6(b) and (c)). This is also interpreted
by taking into account the non-uniform temperature rise in
the bulk superconductor during the PFM, mentioned in the
previous paragraph.
When the applied field exceeds µ0 Hopt , the highest
trapped field region shifts from WP to SP, as clearly seen
in figures 5(f) and 6(e) and (f). This unique change in the
trapped field distribution can be explained by considering
that excessive heat generation takes place and raises the
temperature in region WP in the ascending stage of the PFM. In
turn, in the descending stage of the PFM, this heat generation
leads to weakening of the pinning force in this area and causes
magnetic fluxes in the central area to escape from the sample
through region WP. All the argument above is based on the
assumption that the pinning force is slightly higher along the
GSB but less so along the direction 45◦ away from it, thereby
resulting in the position-dependent temperature rise in the bulk
superconductor during PFM. We believe that region WP plays
an important role in determining the trapped field distribution;
it allows magnetic fluxes to penetrate preferentially into the
centre of the bulk but, at the same time, when the applied field
exceeds µ0 Hopt , it acts as the path for magnetic fluxes to escape
from the sample.
Before ending this section, we wish to point out that
the results obtained in the present experiment may be
universally obtained in any c-axis oriented single-domain
bulk superconductors. This is because a top-seeded bulk
superconductor is characterized by the possession of mutually
perpendicular GSBs which always gives rise to regions WP
and SP. The subtle difference in the structure is reflected in the
trapped field profile by PFM. The effect is more strongly and
more clearly observed especially at low temperatures.
3.2. Flux motion behaviour during the single PFM process
To confirm further the interpretation described in section 3.1,
we have measured the time evolution of magnetic field during
PFM at 35 K at two positions A and B on the surface of the bulk
superconductor, as marked in figure 1. Figures 7(a)–(f) show
the results taken at different values of applied field µ0 Ha . We
see from figure 7(a) that fluxes have not reached both positions
A and B when µ0 Ha is 3.4 T. This is in good agreement with the
trapped field distribution shown in figure 6(a). Figure 7(b) was
taken when µ0 Ha is increased to 3.6 T, i.e., only 0.2 T higher
than that in figure 7(a). Now a sharp increase in magnetic field
is observed 13 and 15 ms after the start of PFM at position B
and A, as marked with arrows (1) and (2), respectively. The
magnetic field in both positions A and B remains substantially
unchanged, except for a slight decrease by flux creep. This
means that most of the magnetic fluxes, once they have reached
these two positions, remain trapped after PFM.
Pulsed field magnetization of a 36 mm diameter single-domain Sm–Ba–Cu–O bulk superconductor at 30, 35 and 77 K
Figure 7. Time evolution of the magnetic field measured at two different positions A and B shown in figure 1 in the course of a single PFM.
A step-like noise, the magnitude being proportional to the time derivative of applied field dB/dt, appeared only for the data at position B.
The data are shown after the elimination of this noise.
As the applied field increases further, the time needed for
magnetic flux to reach these two positions is slightly shortened.
When the applied field exceeds 4.5 T, magnetic field detected
at positions A and B reaches more or less the same magnitude
as the applied field. Indeed, as shown in figure 7(d) for
µ0 Ha = 4.5 T, magnetic field of 4 T reaching position A did not
decay significantly and magnetic flux density of 3.5 T could be
trapped 180 ms after the start of PFM. However, the magnetic
field at position B rapidly decreased in the descending stage of
PFM and ended up with trapped fluxes of only 1.2 T.
A more noticeable phenomenon was observed in
figures 7(e) and (f), when the applied field was further increased
to 4.7 and 6.7 T, respectively. A sharp drop in the magnetic field
suddenly occurred at position A in the descending stage of PFM
as marked with arrows (3)–(5). Surprisingly, no corresponding
anomaly was detected at position B. Thus, we believe that
fluxes in the central region of the sample escaped through
the WP other than position B. The present interpretation is
apparently consistent with the data reported by Fujishiro et al
[27], who studied the effect of the PFM on the temperature
rise of the bulk superconductor at 40 K and revealed that
the temperature rise on the bulk surface immediately after a
PFM is different, depending on the growth sector regions,
and suggested that flux preferentially passes through some
particular growth sector region in the bulk superconductor
during a PFM at low temperatures. It is also noted that the
time dependence of magnetic field measured at position B
follows well that of the applied field, particularly when the
highest value of 6.4 T is used as µ0 Ha . This indicates that the
magnetic fluxes move almost freely with the applied field, as
if the pinning force were lost along the region starting from
position B to the sample edge. This strongly suggests that
magnetic fluxes should escape from the sample through region
WP. A sharp increase in magnetic field is always observed at the
early stage of PFM, as marked with (1) and (2) in figure 7(b).
We believe that all these sharp changes in magnetic field at
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Y Yanagi et al
Figure 8. A set of the trapped field distributions, and the applied field dependence of the maximum trapped field BTmax , and the total flux at 35 K, after applying an initial pulse field equal to µ0 Hopt of 4.4 T with the superposition of several PFMs with reducing amplitudes.
both ascending and descending stages of PFM are caused by
flux jumping in the area where heat generation locally lowers
the pinning force. The present experiment, particularly at
35 K, clearly demonstrates that magnetic fluxes select the path
where the pinning force is weak, upon penetration into the
bulk superconductor and also upon escape from it. The results
discussed above lend strong support to the interpretation in
section 3.1.
3.3. Optimization of the multi-PFM IMRA technique
In this section, we discuss the results obtained when the
bulk superconductor is subjected to the multi-PFM IMRA
method. It may be noted that multi-PFM itself is effective for
increasing the trapped field but that multi-pulses with reducing
amplitudes are more powerful to enhance the trapped field of
the bulk superconductor as much as possible. This technique
was specifically named iteratively the pulsed-field magnetizing
operation with reducing amplitudes (IMRA) [17, 18]. In
the present multi-PFM IMRA method, pulsed fields were
repeated with a time interval long enough to resume the sample
temperature to the value before applying the previous pulse.
This is typically 5 min. Figure 8 shows a series of trapped
field distributions in the course of the IMRA process under the
condition that the applied field µ0 Ha was initially chosen to be
4.4 T around µ0 Hopt and then to reduce its amplitude stepwise
from 4.5 T in the subsequent iterative pulsed field operations.
As can be seen in figure 8, trapped field distributions BTmax
and total flux did not change any more after the third PFM
846
operation. The value of BTmax was obtained at the centre of
the bulk superconductor and turned out to be higher than 3 T.
However, the trapped fields near the GSB or region SP in the
peripheral area did not increase even after successive PFM
operations.
Further IMRA experiments were carried out under the
condition that the bulk superconductor was subjected to
an initial applied field of 6.9 T much larger than µ0 Hopt
and subsequent iterative PFM operations with reducing
amplitudes. The results are shown in figure 9. In sharp contrast
to the data in figure 8, magnetic fluxes were now trapped
even in region SP after the initial PFM, and the trapped field
distributions were further improved in the course of the IMRA
process. The final distribution marked as (6) in figure 9 turned
out to be far more isotropic than the data shown in figure 8.
The total flux of the final distribution was 1.3 times as large
as that in figure 8. However, the value of BTmax in the final
distribution could not be increased beyond that obtained in
figure 8. It remained only 2.8 T, which is 0.4 T smaller than
that in figure 8.
The results described above are interpreted as follows.
In the experiment shown in figure 8, the initial pulsed field
was chosen to be close to µ0 Hopt . This is the minimum
applied field needed to push fluxes into the centre of the bulk
superconductor through region WP, but is not large enough to
overcome the peripheral area in the region SP involving the
GSB where the pinning force is stronger. Once the trapped
field, like that shown in figure 8(a), is achieved in the initial
PFM, we can no longer produce a field gradient to drive further
Pulsed field magnetization of a 36 mm diameter single-domain Sm–Ba–Cu–O bulk superconductor at 30, 35 and 77 K
Figure 9. A set of the trapped field distributions, and the applied field dependence of the maximum trapped field BTmax , and the total flux at 35 K, after applying an initial pulse field of 6.9 T with the superposition of several PFMs with reducing amplitudes.
penetration of fluxes, no matter how many times fields of the
same magnitude or less are repeatedly applied. This explains
why the trapped field is not increased any more in the peripheral
region SP even after 14-fold repetition of the PFM operations
in figure 8.
In the case of the experiment shown in figure 9, the
application of the initial field far exceeding µ0 Hopt allowed us
to push magnetic fluxes into region SP but, instead, the value
of BTmax at the centre of the bulk superconductor remained
low because of unavoidable excessive heat generation. The
trapped field can be effectively enhanced in region WP after
the repetition of the PFM operations. However, the already
existing field at the centre of the bulk superconductor could
not give rise to a large field gradient. This explains well why
the total flux can be enhanced but the value of BTmax could not
increase up to the value of 3.2 T which the previous procedure
described in figure 8 attained. The conclusion above has been
confirmed by analysing the data on the time evolution of the
magnetic field by using the Hall sensors mounted onto the
surface of the bulk superconductor in the same way as that
discussed in the single-PFM experiment.
Based on the experiments and discussions above, we
propose the following magnetization procedure at low
temperatures in achieving the best trapped field distribution
by the PFM operation.
(1) The PFM with the applied field equal to µ0 Hopt is repeated
a few times to achieve the highest trapped field at the centre
of the bulk superconductor in the unmagnetized state.
(2) A field higher than µ0 Hopt to the extent not to lose the
field trapped in the central region in the first process is
subsequently applied at least once to allow the penetration
of fluxes into the SP region involving the GSB.
(3) The successive PFMs with the reducing amplitudes are
then superimposed.
The trapped field distribution obtained at 35 K by following the
procedure above is shown in figure 10. As expected from the
present work, we could achieve the highest magnetic fluxes of
3.3 T at the centre of the bulk superconductor and the highest
total fluxes of 1.5 mWb over its surface. We could also confirm
a quite isotropic and conical trapped field distribution for its
z-component or the component parallel to the c-axis of the
bulk superconductor at 0.5 mm above the sample surface. The
trapped field distribution attained by the present method at 30 K
is shown in figure 11. BTmax reaches 3.6 T on the surface of
the sample.
Before ending this section, the temperature dependence of
BTmax for the present bulk superconductor obtained after the
application of the IMRA method discussed above is plotted
in figure 12 in comparison with the data of the static FC
847
Y Yanagi et al
Figure 10. A set of trapped field distributions and applied field dependence of the maximum trapped field BTmax , and the total flux , after
applying the optimized IMRA-PFM at 35 K, as proposed in the text.
3.5
30 K
3.0
2.5
Bz(T)
2.0
1.5
1.0
0.5
0.0
-20
-10
10
0
x(mm
)
10
20
20
0
-10
m)
-20
y(m
Figure 11. The trapped magnetic field distribution of the
z-component obtained immediately after the optimized IMRA-PFM
at 30 K, as proposed in the text. The data were taken by scanning the
Hall sensor 0.5 mm above the surface of the bulk superconductor.
Figure 12. Temperature dependence of the maximum trapped field
BTmax for the present bulk superconductor magnetized by the
proposed multi-PFM IMRA method and by the static field cooling
method. Here, static field cooling was conducted in a field large
enough for magnetizing the sample as much as possible at each
temperature.
magnetization method. The temperature was measured by
using the thermometer embedded in the sapphire block in the
cold head. Though BTmax attained by the IMRA technique
is still lower than that by FC, we see that the maximum
848
Pulsed field magnetization of a 36 mm diameter single-domain Sm–Ba–Cu–O bulk superconductor at 30, 35 and 77 K
trapped field BTmax increases almost linearly with decreasing
temperature and reaches the value of 3.6 T at 30 K.
4. Conclusion
We have carried out the trapped field distribution measurement
on a 36 mm diameter Sm–Ba–Cu–O bulk superconductor
magnetized by the pulsed field at temperatures of 30, 35 and
77 K and analysed the results by taking the time evolution
data of the magnetic field on the surface of the superconductor
during the application of the pulsed field. The magnetic
field jumped into the bulk superconductor locally through
the region where the pinning force was relatively low, when
the applied pulsed field exceeds some critical value at low
temperatures. This is the region inclined at 45◦ relative to
the GSB and designated as the weak pinning or WP region.
We found the existence of an optimum applied field µ0 Hopt ,
which is large enough to push magnetic fluxes comparable
to its magnitude into the centre of the unmagnetized bulk
superconductor. This suggests that the PFM operation does not
need an applied field high enough to fully magnetize by means
of the static ZFC magnetization. However, we also revealed
that the existence of non-uniformity in the pinning force over
the bulk superconductor yields a large disorder in the trapped
field distribution when PFM is carried out at low temperatures
like 35 K. It is also found that an applied field much higher
than µ0 Hopt is needed to trap magnetic fluxes in the region
involving the GSB where the pinning force is relatively high.
The optimized IMRA technique turned out to be very effective
in mending the disorder in the trapped field distribution caused
by the low temperature PFM. We could achieve the maximum
trapped field of 3.6 T on the sample surface together with a
well conical trapped field distribution at 30 K.
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