Supercond. Sci. Technol. 13 (2000) 202–208. Printed in the UK
PII: S0953-2048(00)08900-4
Current–voltage characteristics and
flux creep in melt-textured
YBa2Cu3O7−δ
H Yamasaki and Y Mawatari
Electrotechnical Laboratory, 1-1-4 Umezono, Tsukuba, Ibaraki 305-8568, Japan
E-mail: hyamasak@etl.go.jp
Received 21 October 1999
Abstract. We investigated the current–voltage (E–J ) characteristics in melt-textured
YBa2 Cu3 O7−δ strips by measuring the magnetic-field sweep rate dependence of
magnetization. We took account of the current density J distribution in the specimen using a
previously developed method (Mawatari Y et al 1997 Appl. Phys. Lett. 70 2300). For a wide
temperature and magnetic-field range (60–80 K, 0.2–5.0 T), the E–J curves in the
electric-field window E = 10−10 –10−5 V m−1 exhibited power-law behaviour E ∝ J n , and
the power index n generally became smaller at higher magnetic fields and temperatures. In
low magnetic fields (µ0 Ha 6 0.5 T) the n values were large (>20), and thus the Bean model
becomes a good approximation. The E–J characteristics in the lower E window were also
derived from the relaxation of magnetization, the flux creep, and we found that the
wide-range E–J characteristics exhibit near-power-law behaviour but that there exist slight
downward curvatures in the log E versus log J plots. This downward curvature reveals that
the dissipation approaches zero when the current is substantially reduced. The drastic
decrease of the flux creep, which was observed when the sample temperature was decreased
in a fixed magnetic field, is consistent with the observed E–J characteristics.
1. Introduction
The current–voltage (E–J ) characteristics of superconductors reveal how dissipation occurs as a result of current, and
thus it is an important parameter for power applications. For
melt-textured YBa2 Cu3 O7−δ (YBCO), however, the transport measurement, which can obtain the E–J characteristics
in relatively high-electric-field E regions (E > 1 µV m−1 ), is
difficult owing to its large critical current. The E–J characteristics can also be obtained from the magnetic-field sweep
rate β dependence of magnetization M or from the relaxation
of M [1–7]. However, when using magnetization measurements to extract the E–J characteristics, several previous
studies disregarded the effect of the current density J distribution inside the sample [1–3]. Superconducting rings were
used for precise measurement, because, in these rings, the J
and E distributions are negligible [5–7].
Recently, Mawatari et al proposed a new method
to obtain the E–J characteristics from the magnetic-field
sweep rate dependence of M, taking account of the J
and E distributions in the specimen [8, 9]. Using this
method we can precisely measure the E–J characteristics
of superconducting disks or strips, which can be prepared
with much less difficulty than rings [10]. In this study,
we investigated the E–J characteristics of melt-textured
YBCO strips. We found that, for a wide temperature
and magnetic-field range (60–80 K, 0.2–5.0 T), the E–J
0953-2048/00/020202+07$30.00
© 2000 IOP Publishing Ltd
curves in the electric-field window E = 10−10 –10−5 V m−1
exhibited power-law behaviour like that which has often
been observed in high-Tc superconductors [1, 2, 4, 11–14].
Using the same specimen, we also investigated the relaxation
of magnetization, the flux creep, and extracted the E–J
characteristics data in the still lower E region. Combining
both measurements, we found that the wide-range E–J
characteristics exhibit near-power-law behaviour but that
there exist slight downward curvatures in the log E versus
log J plots. This downward curvature reveals that the
dissipation approaches zero when the current is substantially
reduced and is consistent with the vortex-glass theory [15, 16]
and the collective flux-creep theory [17]. We observed a
drastic decrease in the flux creep by slightly decreasing the
sample temperature in a fixed magnetic field.
2. Experimental procedure
Superconducting strips used for the E–J characteristic
measurements were cut from a melt-textured, single-domain
bulk sample with a diameter of 44 mm and a height of
18 mm (Dowa Mining Co.). Most of the measurements were
performed on a strip with a thickness d of 0.5 mm, a width
w of 0.8 mm and a length l of 7.8 mm (sample A). Sample B
(d = 0.4 mm, w = 0.8 mm and l = 3.8 mm) and sample C
(d = 0.3 mm, w = 1.0 mm and l = 6.3 mm) were also
used. X-ray diffraction measurement showed that the YBCO
Current–voltage characteristics and flux creep in melt-textured YBCO
(a)
3. E–J characteristics obtained from the β
dependence of M
(b)
Magnetization (kA/m)
phase was well oriented with the c-axis perpendicular to
the strip plane and that sample C includes a large amount
of the oxygen-deficient YBCO phase. All three samples
contained a small amount of the 211 phase (Y2 BaCuO5 ).
Magnetization M was measured using an Oxford vibrating
sample magnetometer with magnetic fields applied parallel
to the c-axis of the YBCO phase, perpendicular to the strip
plane. We measured M with a magnetic-field sweep rate
β from 0.6 T min−1 to 0.0001 T min−1 with a field width
that was sufficiently large for the sample to be in the fullpenetration condition, in which the shielding current flows in
a simple circular direction. For the flux-creep measurements
the applied magnetic field was increased with a constant
sweep rate (β = 0.5 T min−1 ), the field sweep was terminated
at a specific magnetic field and the relaxation of M was
measured.
80
40
T = 77.3 K, H II c-axis
0
β = µ0d Ha/dt = 0.0001–0.6 T/min
-40
-80
0.1
0.15
0.2
0.25
0.3
Applied field (T)
5
Let us consider a superconducting strip that is in an applied
magnetic field Ha perpendicular to the strip plane (parallel
to the z-axis) and in the full-penetration condition. When
Ha is swept with a constant sweep rate β = µ0 dHa /dt, the
electric field E induced in the superconductor in the steady
state (see the next paragraph) has a simple distribution and
is proportional to β, where µ0 is the magnetic permeability
for vacuum. The magnetization M of the sample is nearly
proportional to the shielding current density J inside the
sample. Therefore, the β dependence of M reflects the E–J
characteristics of the superconducting specimen.
Here, we assume a steady state where β is much larger
than the time derivative of the magnetic flux density due to the
shielding current: |β| |∂Bz /∂t −β| ∼ (1−D)µ0 |∂M/∂t|,
where Bz is the z component of the magnetic flux density
and D is the demagnetization factor [8, 9]. It should be
noted that this condition is not satisfied immediately after
the change of the magnetic-field sweep direction, where
|∂M/∂Ha | ∼ 1/(1 − D) and (1 − D)µ0 |∂M/∂t| ∼ |β|
[9].
We also assume that the E–J characteristics (and the
critical current density Jc defined by a certain criterion) only
weakly depend on the magnetic field and that the effect of the
self-field (shielding currents) and the local field variation in
the sample can be ignored. This assumption is well justified
in higher magnetic fields (µ0 Ha > 1 T), where the self-field
is much smaller than Ha . As for the influence of the self-field
in lower magnetic fields (µ0 Ha 6 0.5 T), see [10]. When the
magnetic field is perpendicular to a strip of length l, width
w and thickness d (l w > d), E and J at the edge of
the superconducting strip in the steady state are expressed as
[8, 9]
E = −βw/2
(1)
J = (2 + α)2M/w
α=
β ∂M
∂(ln |M|)
=
.
∂(ln |β|)
M ∂β
(2)
We can extract the precise E–J characteristics using
equations (1) and (2). In this method, the E and J
distributions in the superconducting specimen are considered
Magnetization (kA/m)
4
3.1. Correction for the E and J distribution
3
2
1
0
T = 77.3 K
β = 0.0001–
0.6 T/min
H II c-axis
-1
-2
-3
4.8
4.9
5
5.1
5.2
Applied field (T)
Figure 1. Effect of the magnetic-field sweep rate β on
magnetization M, measured in sample A at 77.3 K and around
(a) µ0 Ha = 0.2 T and (b) µ0 Ha = 5 T. β values were 0.0001,
0.0003, 0.0006, 0.0012, 0.003, 0.006, 0.012, 0.03, 0.06, 0.12, 0.3
and 0.6 T min−1 . M depends strongly on β at µ0 Ha = 5 T,
reflecting the broad E–J characteristics in such a high magnetic
field.
[8, 9]. If α → 0 in equation (2), then the average current
density hJ i = 4M/w, and equation (2) results in the wellknown Bean model equation as
Jc = 4M/w.
(3)
The parameter α in equation (2) reflects the inhomogeneous
J distribution in the specimen. In the case of the powerlaw E–J characteristics with a power index n (E ∝ J n ), we
obtain α = 1/n [8, 9]. This result indicates that the deviation
from the simple Bean model (neglecting the J distribution
inside the specimen) becomes large with small n values which
indicate broad E–J characteristics.
3.2. Power-law E –J characteristics observed for
E = 10−10 –10−5 V m−1
Figure 1 shows the effect of the magnetic-field sweep rate
β on magnetization M at 77.3 K in sample A. |M| is larger
203
1 05
(a) 1 0-5
0.2 T, α = 0.033
1 04
↓ 3 T, α = 0.083
2 T, α = 0.098
5 T, α = 0.188
H II c-axis
77.3 K & 80 K
3
10
1 0-6
1 0-5
1 0-4
1 0-3
10
-7
Figure 2. Magnetic-field sweep rate β dependence of
magnetization hysteresis width 1M, measured at T = 77.3 K and
80 K. Open symbols represent the data at 77.3 K and at
µ0 Ha = 0.2, 0.3, 0.5, 1, 2, 3 and 5 T. Full symbols represent the
data at 80 K and at µ0 Ha = 0.2, 0.3, 0.5 and 2 T.
with larger sweep rate β, because larger β leads to larger
E (see equation (1)), which in turn leads to larger J (M).
The M dependence on β was pronounced at µ0 Ha = 5 T
(figure 1(b)) owing to the broad E–J characteristics in such
high magnetic fields. Then, the hysteresis widths 1M =
M− − M+ at µ0 Ha = 0.2–5.0 T and at T = 77.3 K and
80 K are plotted against β in figure 2, where M− (M+ ) is the
magnetization in the magnetic-field decreasing (increasing)
branch. The β dependence of 1M exhibits clear power-law
behaviour. The power index directly gives the parameter α
in equation (2), which is constant and does not depend on β.
Next, we calculated E and J at the edge of the
superconducting strip using equations (1) and (2), replacing
2M with 1M. Figure 3 shows the E–J curves at various
fields at 65, 70, 77.3 and 80 K in sample A. In this electricfield window E = 10−10 –10−5 V m−1 , power-law behaviour
E ∝ J n is observed over the entire magnetic-field range
covered (µ0 Ha = 0.2–5.0 T). In lower magnetic fields
(µ0 Ha 6 1 T) the power index n was large (>25), which
indicates that the E–J curves are steep. In this case, the
parameter α = 1/n is small compared with 2 in equation (2),
and the correction for the J distribution is quite small (<2%).
Therefore, the Bean model equation (equation (3)) is a good
approximation for the calculation of J . In high magnetic
fields, however, n is not as large and the correction from
equation (3) becomes substantial, e.g. ∼10% at 77.3 K and
5 T (figure 3(a)). For the power-law E–J characteristics,
the correction for the J distribution consists of a simple
multiplication by a constant (2 + α)/2. Thus, the n values
derived from the experimental results do not depend on
whether or not the data were corrected.
Equations (1) and (2) can be used for long
superconducting strips whose length l is much larger than
width w. If l is not sufficiently long compared with w,
a correction is necessary. If anisotropy in the critical
T = 77.3 K
and 80 K
No correction
(Bean model)
5T
1 0-8
2T
n=
10.2
1 0-9
0.2 T
5T
n = 5.3
1 0-10 6
10
n=
30.8
3T 2T
n = 12.3 n = 20.3
1 07
1 08
1 09
Current density (A/m2)
1 0-2
Magnetic-field-sweep rate, β (T/sec)
204
Electric field (V/m)
1 0-6
(b) 1 0-5
T = 70 K
and 65 K
1 0-6
Electric field (V/m)
Hysteresis width, ∆M (A/m)
H Yamasaki and Y Mawatari
1 0-7
5T
1 0-8
n = 17.4
1 0-9
3T
1 0-10
1 T 0.5 T
0.2 T
n = 25.5 n = 29.2 n = 28.4 n = 40.4
1 08
1 09
2
Current density (A/m )
Figure 3. Current–voltage characteristics of sample A in applied
fields of µ0 Ha = 0.2–5.0 T at (a) T = 77.3 K and 80 K and
(b) T = 65 K and 70 K, calculated using equations (1) and (2).
Data calculated by the Bean model equation (3) are also shown
(crosses in (a)). Open symbols represent the data at µ0 Ha = 0.2,
0.3, 0.5, 1.0, 2.0, 3.0 and 5.0 T at T = (a) 77.3 K and (b) 70 K.
Full symbols represent the data at (a) µ0 Ha = 0.2, 0.3, 0.5 and
2.0 T at 80 K and (b) µ0 Ha = 0.2, 0.3 and 0.5 T at 65 K.
current density within the a–b-plane is neglected, then the
magnetization hysteresis width is calculated based on the
Bean model: 1M = (wJc /2)(1 − w/3l) [18]. Therefore,
the correction factor is 1/(1 − w/3l), and it is found that the
current density J of figure 3 in sample A (l = 7.8 mm and
w = 0.8 mm) is underestimated by ∼3.4%.
We measured the E–J characteristics for 0.2 T 6
µ0 Ha 6 5.0 T and for temperatures 60 K 6 T 6 80 K
in sample A and for 0.2 T 6 µ0 Ha 6 0.5 T and 70 K 6
T 6 80 K in samples B and C. In almost all cases, powerlaw behaviour was observed in the electric-field window
E = 10−10 –10−5 V m−1 . The downward curvature in the
log E versus log J plots, which is regarded as a characteristic
of the vortex-glass state [15, 16] or the collective flux creep
[17], was only slightly exhibited (figure 3). The observed
values of n for samples A, B and C are summarized in
table 1. In general, n was smaller at higher magnetic fields
Current–voltage characteristics and flux creep in melt-textured YBCO
Table 1. The n values of E–J curves in melt-textured YBCO samples measured by magnetic-field sweep rate dependence of magnetization.
(1) Sample A: Jc ∼ 2.5 × 108 A m−2 at 77.3 K, 0.3 T (E = 1 µV m−1 criterion).
n for the following T (K)
B (T)
60
65
70
75
77.3
77.3 (second)
80
0.2
0.3
0.5
1
2
3
5
44
40.4
33.5
30.3
29.9
32.7
36.6
40.4
37.4
32.6
—
—
—
—
37.1
35
28.4
29.2
26.2
25.5
17.4
31.9
31
25.8
—
—
—
—
30.2
27.9
25.1
24.9
21.8
12
5.31
30.8
25.5
27.2
25.3
20.3
12
—
27.2
25.8
27.5
—
10.2
—
—
(2) Sample B: Jc ∼ 1.7 × 108 A m−2 at 77.3 K, 0.3 T (E = 1 µV m−1
criterion).
n for the following T (K)
B (T)
70
75
77.3
80
0.2
0.3
0.5
38.3
34.4
30.1
34.4
31.0
29.3
33.3
29.6
26.1
30.3
26.6
25.5
(3) Sample C (containing oxygen-deficient YBCO): Jc ∼ 5.8 × 106 A m−2
at 77.3 K, 0.3 T (E = 1 µV m−1 criterion).
n for the following T (K)
B (T)
70
77.3
80
0.2
0.3
0.5
25.7
23.7
21.6
25.4
21.7
20.0
23.2
22.0
19.2
The power-law E–J characteristics indicate that
the activation energy U for the flux motion depends
logarithmically on J [11, 12], U = U0 ln(J0 /J ), where U0 is
a J -independent activation energy. Then, the induced electric
field E and the n value are expressed as
E = E0 exp[(U0 /kT ) ln(J /J0 )] = E0 (J /J0 )n
n = U0 /kT .
(4)
This indicates that the n value is directly related to the pinning
strength through U0 . Since U0 generally becomes smaller
in higher magnetic fields and temperatures, the observed
field and temperature dependence of n can be qualitatively
explained by equation (4).
3.3. Calculation of hysteresis loss for the power-law
E –J characteristics
Figure 4. Relaxation of M at T = 60 K and 77.3 K measured in
sample A.
and temperatures, with the exception of high magnetic fields
(µ0 Ha > 2 T) at 60 K in sample A, in which n increased.
This may be related to the broad peak effects in the M–H
curves that were observed in high magnetic fields and low
temperatures (µ0 Ha > 5 T at 60 K and µ0 Ha > 4 T at
50 K).
Superconducting magnetic-levitation applications, such as
superconducting magnetic bearings in flywheel energy
storage systems, are regarded as one of the most important
applications of melt-textured YBCO. In these systems, the
magnetic field is generated by permanent magnets and is
usually limited to less than 0.7 T [19–21]. It is evident from
table 1 that, in such low magnetic fields, the n values are quite
large (>25) in good-quality samples (samples A and B), and
that even a poor-quality sample with very low Jc (sample C)
has rather large n values (>19). In this case, the effect of
the J dependence of E becomes small, and the simple Bean
model becomes a good approximation.
205
H Yamasaki and Y Mawatari
1 0-5
Electric field (V/m)
1 0-6
n = 21.8
(β depend.)
n=
24.9
n=
27.2
n=
30.8
n=
25.5
⇒
1 0-8
1 0-9
1 0-11
10
-12
1 0-13
n=
44.0
T =
60K
1 0-7
1 0-10
n=
33.5
77.3K
n = 26.9
(flux creep)
2 T
n=
34.4
n=
34.1
1 T
0.5 T
1 08
⇐
n=
32.5
n=
36.2
n=
34.5
0.2 T
0.3 T
0.5 T
Current density (A/m2)
n = 57.2
(flux creep)
0.2 T
1 09
Figure 5. Wide-range E–J characteristics of sample A measured by both the β dependence of M and the flux creep.
Rhyner calculated the ac losses of superconductors
with the power-law E–J characteristics of equation (4)
and derived an analytic equation for a semi-infinite
superconductor exposed to an oscillating external field
(B0 sin(ωt)) parallel to its surface [22]. The losses per cycle
per unit surface area A are
B03
Qc
E0 µ0 J0 1/(1+n)
=
(1.33 + 3.11n−0.55 ). (5)
A
2µ20 J0
ωB02
We note that the hysteresis loss of the superconductor, which
results from the nonuniform distribution of the magnetic field
and can be estimated by equation (5), causes the rotation
loss of the rotor in the superconducting magnetic bearing
[19, 21]. Typical values of the parameters for the rotationloss calculation are E0 = 10−6 V m−1 , J0 = 2 × 108 A m−2 ,
ω/2π = 100 Hz and B0 = 0.02 T. The induced electric field
is estimated to be
ωB02 E0 µ0 J0 1/(1+n)
≈ 7.2 × 10−4 V m−1
ωB0 z∗ =
µ0 J0
ωB02
where z∗ is the ac penetration length [22] and n = 20 is
used. If we assume that the observed power-law behaviour
continues to occur in the E range two orders of magnitude
higher than that of figure 3, then equation (5) can be used for
the calculation. Then, the correction factor from the Bean
critical state (n → ∞) is 0.720 × 1.93/1.33 = 1.04 for
n = 20 and 1.09 for n = 30.
4. E–J characteristics obtained from the flux-creep
data
Next, we measured the time dependence of magnetization,
the flux creep. The log |M+ | versus log t plots measured at
various fields at 60 K and 77.3 K in sample A reveal that
the |M|–t relation also exhibits power-law behaviour, except
for small-t regions (figure 4). If the E–J characteristics are
expressed by a power law with n 1, then the J distribution
inside the sample can be neglected and the electric field can
206
be expressed as E = E0 (M/M0 )n . Combining this equation
with Faraday’s law
E = −(µ0 w/2) dM/ dt
(6)
we can calculate the relaxation of magnetization as
t0 = µ0 wM0 /2(n − 1)E0 .
(7)
For our experimental conditions for sample A, w = 0.8 mm,
β = 0.5 T min−1 , E0 = 4 × 10−6 V m−1 , M0 ≈ 4 ×
104 A m−1 and n ≈ 30, we obtain t0 ≈ 0.17 s. Then, t/t0 1 for most of the measured time period, and the t dependence
of M (i.e. equation (7)) can be expressed by a power law
with the index of 1/(1 − n). The straight lines in figure 4
illustrate that the time dependence predicted by equation (7)
is actually observed, and the n values can be obtained from
the slopes of these lines. Note that the normalized flux-creep
rate S = −∂ log |M|/∂ log t = 1/(n − 1), and S is nearly
inversely proportional to n.
An interesting phenomenon is that the values of n
obtained from the relaxation of M (figure 4) were larger than
those obtained from the β dependence of M (table 1). This
is due to the difference in the related electric-field windows.
It is also possible to extract the E–J characteristics from the
flux-creep data, using equation (6). The E–J curves obtained
by both the β dependence of M and the flux creep are depicted
in figures 5 and 6 for samples A and B, respectively. It can be
seen that the electric-field window of the E–J curves from
the flux-creep data is about two orders of magnitude lower
than that obtained from the β dependence of M. Combining
both measurements, we found that there is a slight downward
curvature in the wide-range log E versus log J plots. This
downward curvature is expected according to the vortex-glass
theory [15, 16] and the collective flux-creep theory [17], in
which the J -dependent potential barrier diverges at J → 0,
as U (J ) ∼ J −µ . Several researchers have reported the
observation of this J dependence of the activation energy
by measuring the β dependence of magnetization and flux
creep in melt-textured YBCO samples [23, 24].
M = M0 (t/t0 + 1)1/(1−n)
Current–voltage characteristics and flux creep in melt-textured YBCO
Electric field (V/m)
1 0-6
1 0-7
1 0-8
1 05
n=
29.6
n=
31.0
n = 34.4
(β depend.)
70 K
n = 40.2
80 K
75 K
µ 0H a =
0.3 T
1 0-9
1 0-10
1 0-11
1 0-12
10
n=
38.0
µ 0 H a = 0.3 T
6 104
n=
26.6
|M+| (A/m)
1 0-5
n=
37.5
n = 40.2
(flux creep)
77.3 K 75 K 70 K
n = 37.5
77.3 → 70, 75 K
77.3 K
80 → 77.3 K
2 104
1
10
100
1 03
1 04
n = 38.0
1 05
1 06
-13
1 08
Current density (A/m2)
Time (sec)
1 09
Figure 6. Wide-range E–J characteristics of sample B measured
Figure 7. Retarding the flux creep by decreasing the temperature
in a fixed magnetic field (sample B).
at µ0 Ha = 0.3 T and at T = 70–80 K.
−9
−7
−1
In the electric-field window range of 10 –10 V m ,
the E–J curves obtained from the flux creep do not
completely match those obtained from the β dependence
of M. One reason for this disagreement is that the former
were extracted from the M+ data only whereas that the latter
were obtained from the 1M = M− − M+ data. Because of
the contribution from the reversible magnetization, |M+ | is
larger than |M− |, and this results in the overestimation of J
in the former case, which can be observed in figures 5 and 6.
However, both curves did not coincide even when the above
effect was corrected. This is due to experimental error.
5. Retarding the flux creep by decreasing the
temperature in a fixed magnetic field
It is found that the wide-range E–J characteristics exhibit
near-power-law behaviour but that there are slight downward
curvatures in the log E versus log J plots. This downward
curvature reveals that the dissipation approaches zero when
the current is substantially reduced. Thus, it is expected that
the flux creep can be eliminated if we can substantially reduce
the shielding current density from the critical state.
Figure 6 shows that the diamagnetic shielding current
density J immediately after the magnetic field of µ0 Ha =
0.3 T is applied at T = 77.3 K is about 1.6 × 108 A m−2
and that the induced electric field E with this J is very small
at 75 K. Therefore, we predict that the flux creep will be
greatly retarded if we apply the magnetic field of 0.3 T at
77.3 K and then decrease the sample temperature to 75 K.
A drastic decrease in the flux creep was observed when the
sample temperature was decreased from 77.3 K to 75 K (or
70 K) in a fixed magnetic field of 0.3 T (figure 7). The same
phenomenon was observed when the sample temperature was
reduced from 80 K to 77.3 K, and this can be understood in
the same way on the basis of the E–J characteristic data
of figure 6. Several researchers previously observed the
reduction of the flux creep by temperature change [25–28],
but none of them explained the phenomenon in terms of the
E–J characteristics.
6. Summary
We investigated the E–J characteristics in melt-textured
YBCO superconducting strips by measuring the magneticfield sweep rate β dependence of magnetization M. We
took account of the current density distribution in the
specimen using a novel method. For a wide temperature
and magnetic-field range (60–80 K, 0.2–5.0 T), the E–J
curves in the electric-field window E = 10−10 –10−5 V m−1
exhibited power-law behaviour E ∝ J n . The observed
n values are generally high (>25) in low magnetic fields
(60.5 T) with which most superconducting magneticlevitation applications are concerned. This suggests that the
Bean critical-state model is a good approximation. The E–J
characteristics in the lower E window were also derived
from the flux-creep data. Although the wide-range E–J
characteristics exhibit near-power-law behaviour, there are
slight downward curvatures in the log E versus log J plots,
which reveal that the dissipation approaches zero when the
current is substantially reduced. We observed a drastic
decrease in the flux creep when the sample temperature was
decreased in a fixed magnetic field.
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