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Trapped magnetic field and vortex pinning properties of MgB2 superconducting bulk
fabricated by a capsule method

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2012 Supercond. Sci. Technol. 25 095012(http://iopscience.iop.org/0953-2048/25/9/095012)
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IOP PUBLISHING

SUPERCONDUCTOR SCIENCE AND TECHNOLOGYSupercond. Sci. Technol. 25 (2012) 095012 (6pp)

doi:10.1088/0953-2048/25/9/095012

Trapped magnetic field and vortex
pinning properties of MgB2
superconducting bulk fabricated by acapsule method
Tomoyuki Naito1,2 , Tomohisa Sasaki1 and Hiroyuki Fujishiro1,2
1

Department of Materials Science and Engineering, Faculty of Engineering, Iwate University, Morioka
020-8551, Japan
2
Soft-Path Engineering Research Centre (SPERC), Faculty of Engineering, Iwate University, Morioka
020-8551, Japan
E-mail: tnaito@iwate-u.ac.jp

Received 25 April 2012, in final form 15 June 2012
Published 6 July 2012
Online at stacks.iop.org/SUST/25/095012
Abstract
We have studied the trapped magnetic field and the critical current density for an MgB2
superconducting bulk disc fabricated by a capsule method. The maximum trapped magnetic
fields at the centre of bulk surfaces 20 and 30 mm in diameter were, respectively, 1.43 T at
13.4 K and 1.50 T at 16.4 K. The critical current densities, Jc s, were estimated to be 5.5 × 104
and 4.2 × 104 A cm−2 at 20 K for the 20 and 30 mm diameter bulks, respectively, from themeasured trapped field at the top surface, by using the analytical equation. The estimated Jc
was as small as about 30–60% of the measured Jc in the self-field which was determined fromthe magnetization hysteresis loop of small pieces cut from the bulk. The results suggest that an
MgB2 bulk magnet over 3 T can be realized at 20 K by means of the enhancement of both theJc values and the mass density.
(Some figures may appear in colour only in the online journal)

1. Introduction

substitutional elements, and control of the crystallographic
orientation enable us to enhance Jc . The values of Jc and BT
for REBCO bulks have already exceeded 105 A cm−2 and
3 T, respectively, at 77 K in the self-field [5]. The latter value
was one order of magnitude higher than that of a Nd–Fe–B
permanent magnet. Furthermore, a YBCO bulk (26.5 mm indiameter and 15 mm in thickness), which was reinforced with
an epoxy resin in order to overcome the high yield stress,
recorded the highest trapped field of 17 T at 29 K [6]. REBCO
bulks 45–60 mm in diameter are commercially available, canbe used to produce tesla-order quasi-permanent magnets, andhave already been used in prototypes for novel applications
such as drug delivery systems [7], sputtering cathodes [8] andmagnetic separation [9]. Although a large single-domain bulk
over 100 mm in diameter was difficult to fabricate, a large

A type II superconductor can trap quantized vortices andrealizes a strong quasi-permanent magnet after the magnetizing process. Bean’s critical state model [1] suggests that thetrapped field, BT , depends linearly on both the diameter andthe critical current density, Jc , of the superconducting bulk
disc. Therefore a larger superconducting bulk with higher Jc
is preferable.
Single-domain RE–Ba–Cu–O (REBCO; RE: rare earth
element) superconducting bulks grown by a melt process [2–4] have been intensively studied with a view toachieving higher trapped field, BT , because of their highcritical temperature, Tc , above 90 K, their high Jc andthe moderate Jc deterioration under magnetic fields. The
introduction of fine RE2 BaCuO5 (RE211) particles and0953-2048/12/095012+06$33.00

1

c 2012 IOP Publishing Ltd Printed in the UK & the USA

Supercond. Sci. Technol. 25 (2012) 095012

T Naito et albulk has been realized by a multi-seeding technique [10] andin a microgravity environment in space [11].
MgB2 superconductors have mainly been studied forpractical application in superconducting tapes and thin films
owing to their high Tc of about 40 K and their having ahigh upper critical field among metallic superconductors. The
typical Jc value of the polycrystalline MgB2 samples is over
105 A cm−2 below 20 K in the self-field [12, 13], which is ashigh as that of the single-domain REBCO bulks at 77 K [14].
Furthermore, because of their long coherence length, ξ ,the problem of weak links at the grain boundaries can beignored even for the polycrystalline samples [15]. These
results enable us to produce better and larger polycrystalline
MgB2 bulk magnets below 20 K. The most important featureof MgB2 is light weight, compared to REBCO; that is,
the ideal mass densities of MgB2 and YBCO are 2.62
and 6.38 g cm−3 , respectively. The large polycrystalline
MgB2 bulk has an advantage as regards being cheap andsuited to mass production. Since the operating temperatureof 20 K is easily obtained by using liquid H2 or cryocooler
cooling, MgB2 bulk magnets are expected to be applicable inmagnetically levitated (MAGLEV) trains and so on.
Several groups have already reported the trapped fieldon the MgB2 bulk [16–18]. The BT value of about 2.3 T at
6 K was obtained for the MgB2 bulk (28 mm in diameterand 11 mm in thickness) which was sintered under a highpressure of 2 GPa [16]. Recently, Yamamoto et al reported
a 1.2 T MgB2 magnet (20 mm in diameter and 5 mm inthickness) at 17 K [17]. Dense MgB2 bulks fabricated by
the reactive Mg liquid infiltration (Mg-RLI) technique havealso been reported [19], on which the maximum BT was
about 1.3 T at 15 K after field cooling under a magnetic
field of 1.4 T for an MgB2 disc (55 mm in diameter and
15 mm in thickness) [18]. The reported BT values for MgB2
bulks are smaller than those of REBCO bulks at the present
stage. However, they are promising materials for producing
a strong and large superconducting bulk magnet, because
the BT value must be enhanced by the improvement of thefilling factor and the connectivity between the grains [20] andby the enlargement of the diameter. MgB2 has usually been
fabricated in a vacuum-sealed quartz or metal tube to preventthe oxidization and/or nitridization of Mg and B; however thismethod is not suitable for large bulk, several centimetres indiameter.
For the fabrication of large polycrystalline MgB2 bulk,
we proposed a simple and convenient capsule method [21],which does not require special techniques such as sealing-off
or welding and gives us a kind of hot-press annealing effectby suppressing the expansion of the precursor pellet. We
demonstrated that a 1.65 T MgB2 bulk magnet 30 mm indiameter was successfully produced at 14 K by this method;
however the relationship between the trapped field and thevortex pinning properties has not been examined in theprevious report [21]. In this paper, we measure the trappedfield, BT , for large MgB2 bulks 20–30 mm in diameter andthe critical current density, Jc , of small pieces cut from thebulk, and discuss their correlation.

Figure 1. Schematic illustration of the closed capsule.

2. Experimental details
2.1. The process of fabrication of MgB2 bulks
MgB2 bulks were fabricated by the in situ capsulemethod [21]. A schematic image of the capsule is shownin figure 1. The capsule consists of two commercial stainlesssteel flanges (70 mm in diameter and 10 mm in thickness; ICF
flange), two stainless steel plates and a copper gasket. Raw
powders of Mg (99% purity, ≤180 µm grain size, Kojundo
Chemical Laboratory Co., Ltd) and amorphous B (99% purity,
300 mesh, Furuuchi Chemical Corp.) were weighted at 1.1:2.0
in molar ratio and ground using an agate mortar and pestle for
1 h. The mixed powder was pressed into pellets 20–30 mm indiameter and 5–9 mm in thickness under uniaxial pressure ofabout 12 MPa. The precursor pellet was set in the hole of thestainless steel flange, covered by the stainless steel plates, andfinally closed in by means of the other flange with the copper
gasket, using the bolts and nuts. The stainless steel plates wereinserted to prevent reaction of Mg with Cu. The precursor
pellet was prepared in air and the capsule was sealed in an
Ar atmosphere using a glove box. The MgB2 precursor in theclosed capsule was sintered at 800 ◦ C for 6 h in a box furnaceand cooled down to room temperature by furnace cooling. The
MgB2 bulks 20 and 30 mm in diameter were named MB-20
and MB-30, respectively. Sample specifications are listed intable 1. Figure 2 shows a photograph of the MB-20 bulk withthe stainless steel flange after the sintering.
2.2. Measurements
The MgB2 bulk was magnetized by field cooling (FC) in amagnetic field of 5 T parallel to the thickness direction using
a 10 T cryogen-free superconducting magnet (JMTD-10T100,
Japan Superconductor Technology (JASTEC), Inc.) and thenthe applied magnetic field was decreased to 0 T at a rateof −0.22 T min−1 . The bulk was set on the cold-head of a
Gifford–McMahon type helium refrigerator by inserting a thin
In plate to achieve good thermal contact. The trapped field
was measured by using a cryogenic Hall sensor (BHT-921,
FW Bell Inc.) mounted on the centre of the bulk surface using
2Supercond. Sci. Technol. 25 (2012) 095012

T Naito et al

Table 1. Specifications of the MgB2 bulks. Tc is the critical temperature, 1Tc is the width of the transition and BT is the trapped field.
Sample name

Diameter (mm)Thickness (mm)Tc (K)

1Tc (K)

Max. of BT

MB-20
MB-30

20.2
30.4

5
9

38.2
38.4

0.9
1.0

1.43 T at 13.4 K
1.50 T at 16.4 K

Figure 2. Photograph of the MB-20 MgB2 bulk (centre circle) withthe stainless steel flange.

Figure 3. Temperature dependence of the trapped magnetic field,
BT (T), for the MgB2 bulks. The reported BT (T) lines are alsopresented.

GE7031 varnish. During FC, the temperature of the bulk wascontrolled by a Cernox thermometer which adhered beside theHall sensor on the bulk surface. After the FC magnetization
experiments, the bulks were cut into several small pieces,
and we evaluated the superconducting properties such as
the critical temperature, Tc , and the critical current density,
Jc , by measuring the magnetization, M, using a commercial
SQUID magnetometer (MPMS-XL, Quantum Design Inc.).
Jc was estimated from the hysteresis loop using the extended
Bean model, Jc = 201M/a(1 − a/3b), where 1M is thewidth of the hysteresis loop, and a and b (a < b) are thecross-sectional dimensions of the sample perpendicular to theapplied magnetic field.

corresponds to the one reported (20 mm in diameter and 5 mmin thickness) [17], but those for the MB-30 bulk are obviously
smaller than those for the MgB2 bulk reported on, which is
28 mm in diameter [16]. This might arise from the fact thatthe density (approximately 1.3–1.4 g cm−3 ) of the MB-30
bulk is lower than that of the bulk in [16] fabricated underhigh pressure. Higher BT could be realized by increase of thedensity of the bulk.
The superconducting properties of the MgB2 bulks were
evaluated using small pieces cut from the bulk after themeasurements of the trapped field. Figure 4 shows the powder
x-ray diffraction patterns taken at the room temperature using
Cu Kα radiation. The observed peaks were mainly indexed
to the MgB2 phase, and small amounts of impurity phasessuch as Mg, MgO and MgCu2 were also observed. The small
peak at 2θ = 37◦ for the MB-20 bulk represents the (101)plane of Mg, originating from the unreacting Mg. The peakat 2θ = 63◦ for both bulks represents the (111) plane of
MgO, which might be created in the mixture grinding or
the sintering process. The peaks at 2θ = 22◦ and 44◦ foundonly for the MB-30 bulk arise, respectively, from the (111)and (222) planes of MgCu2 , resulting from the reaction ofliquid Mg and the Cu gasket. The reason for the MgCu2 phaseappearing only in the MB-30 bulk is that the distance between
the precursor pellet and the Cu gasket for the MB-30 bulk isless than that for the MB-20 bulk, i.e., the liquid Mg easily
reacts with Cu.
Figure 5 presents the temperature dependence of thenormalized magnetization, M(T), in a magnetic field of
0.4 mT after zero-field cooling. Six pieces were cut from

3. Results and discussion
Figure 3 shows the temperature dependence of the trappedfield, BT (T), for two MgB2 bulks. The BT (T) lines reported
previously [16, 17] are also shown for comparison. For
both bulks, BT (T) increases with decreasing temperature;
this effect originates from the enhancement of Jc at low
temperatures. The highest BT (T) values for MB-20 and
MB-30 bulks, respectively, are 1.43 T at 13.4 K and 1.50 T
at 16.4 K. The magnitude of BT for the MB-30 bulk isapproximately 1.2–1.3 times larger than that for the MB-20
bulk at the same temperature, which is 13–20% smaller than
the 1.5 expected from the ratio of the diameters; BT should be
proportional to the diameter in terms of Bean’s critical statemodel if Jc is identical in both bulks. The results suggest that
the Jc value for the MB-30 bulk is smaller than that for the
MB-20 bulk. The BT (T) value for the MB-20 bulk almost3Supercond. Sci. Technol. 25 (2012) 095012

T Naito et al

the MB-20 bulk and 1.0 K for the MB-30 bulk. The resultthat Tc is slightly lower than the optimal Tc of 39 K may arise
from the existence of the impurity phases. It is noteworthy that
the MgCu2 phase seems not to degrade the Tc for the MB-30
bulk.
Figure 6 depicts the magnetic field dependence ofthe critical current density, Jc (H), at 20 K. The samples
measured are the same as those used for making the M(T)measurements. For the MB-20 bulk, as found in figures 6(a)and (b), the Jc is about 1.2–1.6 × 105 A cm−2 at µ0 H = 0 T,
and decreases monotonically with increasing magnetic field.
The Jc curves hardly depend on the sample position except
for above 2.5 T. The irreversibility field, µ0 Hirr , defined at
the Jc = 10 A cm−2 value is 3.3–3.6 T. For the MB-30 bulk,
as shown in figures 6(c) and (d), the Jc (H)s also decrease
monotonically with increasing magnetic field. The propertiesof the vortex pinning of the edge region are slightly inferior
to those of the centre region; the Jc (0 T) and µ0 Hirr values,
respectively, are 1.1–1.3 × 105 A cm−2 and 3.3–3.5 T for thecentre samples and are 0.7–1.0 × 105 A cm−2 and 3.2–3.3 T
for the edge samples. Both the Jc (0 T) and µ0 Hirr values for
the MB-30 bulk are somewhat small compared with those for
the MB-20 bulk, which can explain the relatively low BT valueof the MB-30 bulk. The MgCu2 impurity phase in the MB-30
bulk seems not to act as a pinning centre.
We compare the microscopic Jc (micro-Jc ) determinedfrom the magnetization of the small pieces with themacroscopic Jc (macro-Jc ) which gives the trapped field.
Under the assumption of a uniform Jc distribution in thebulk, which is supported by the uniform two-dimensional
BT distribution for the other MgB2 bulk in our previous
paper [21], we estimate the macro-Jc value of the bulks fromthe experimentally obtained BT using the following analyticalFigure 4. X-ray diffraction patterns taken at room temperature for
the MgB2 bulks.

the centre and the edge of each bulk; the positions areschematically shown in the figure. We named the samples
from higher, at and below the bulk centre C1, C2 and C3,
respectively. The edge samples, E1, E2 and E3, are also
named in a similar manner. The sample dimensions weretypically 2 × 2 × 2 mm3 . All the small samples show the
sharp superconducting transition, although the C1 and E1
samples of the MB-20 bulk show a broad tail. The criticaltemperatures, Tc s, defined at the mid-point of the transition areabout 38.2 K for the MB-20 bulk and 38.4 K for the MB-30
bulk. The widths of the transition, 1Tc s, are about 0.9 K for

Figure 5. Temperature dependence of the normalized magnetization in the magnetic field of µ0 H = 0.4 mT after zero-field cooling for the
MB-20 ((a) and (b)) and MB-30 ((c) and (d)) bulks. The sample positions are shown in the figure.
4Supercond. Sci. Technol. 25 (2012) 095012

T Naito et al

Figure 6. Magnetic field dependence of the critical current density, Jc (H), at T = 20 K for the MB-20 ((a) and (b)) and MB-30 ((c) and (d))
bulks. The sample positions are shown in the figure.

equation based on the Biot–Savart law:
p

µ0 Jc
(D/2) + (D/2)2 + (z + t)2
BT (z) =(z + t) log
2
z+t
p

(D/2) + (D/2)2 + z2,
(1)
− z logz(ii) The critical current density, Jc , which was measured
using small pieces cut from the bulk was approximately
1 × 105 A cm−2 at 20 K in the self-field.
(iii) The macroscopic Jc was estimated to be 5.5 ×
104 A cm−2 for the 20 mm diameter MgB2 bulk at
20 K from the trapped field of 1.09 T and was 4.2 ×
104 A cm−2 for the 30 mm diameter one at 20 K, from thetrapped field of 1.33 T, using the analytical equation. The
estimated Jc values were as small as about 30–60% of
the microscopic Jc which was measured using the small
pieces cut from the bulk.
(iv) To produce a strong and large MgB2 bulk magnet over
50 mm in diameter, improvement of the critical current
density, mass density and connectivity is needed.

where D and t are the diameter and thickness of the
disc-shaped superconductor and z is the distance from thecentre of the top surface of the bulk. For the MB-20 bulk,
the macro-Jc at 20 K is estimated to be 5.5 × 104 A cm−2
using the experimentally obtained BT (z = 0) of 1.09 T. For
the MB-30 bulk, on the other hand, the estimated macro-Jc
at 20 K is about 4.2 × 104 A cm−2 from the measured BT(z = 0) of 1.33 T. The estimated macro-Jc value is about
30–60% of the measured micro-Jc for both bulks; similar
results were also observed for the REBCO bulks [10]. The
small macro-Jc compared to the micro-Jc is probably causedby the degree of connectivity at the interface of the grains [20],because it prevents the supercurrent from circulating. The
results of analysis suggest that the 3 T class MgB2 bulk
magnets 20–30 mm in diameter can be produced at 20 K by
improving the macro-Jc , which is as large as the micro-Jc .

Acknowledgments
This work was partially supported by Japan Scienceand Technology Agency under Research for Promoting
Technological Seeds 2009 (02-051) and the Adaptable
and Seamless Technology Transfer Program through targetdriven R&D for Exploratory Research at the FS stage(AS232Z02579B). We thank Dr S Kobayashi for his help
with the magnetization measurements using the SQUID
magnetometer.

4. Summary
We measured the trapped magnetic field and the criticalcurrent density of the large MgB2 bulks (20–30 mm indiameter and 5–9 mm in thickness) fabricated by the capsulemethod. The important results are described below.

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5Supercond. Sci. Technol. 25 (2012) 095012

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