INSTITUTE OF PHYSICS PUBLISHING
SUPERCONDUCTOR SCIENCE AND TECHNOLOGY
Supercond. Sci. Technol. 15 (2002) 315–319
PII: S0953-2048(02)28059-8
Magnetic relaxation and critical current
density of the new superconductor MgB2
H H Wen, S L Li, Z W Zhao, H Jin, Y M Ni, Z A Ren,
G C Che and Z X Zhao
National Laboratory for Superconductivity, Institute of Physics and Center for Condensed
Matter Physics, Chinese Academy of Sciences, PO Box 603, Beijing 100080, People’s
Republic of China
E-mail: hhwen@aphy.iphy.ac.cn
Received 20 August 2001
Published 25 January 2002
Online at stacks.iop.org/SUST/15/315
Abstract
Magnetic relaxation rate, critical current density and transport properties
have been investigated on MgB2 bulks from 1.6 K to Tc at magnetic fields up
to 8 T. A vortex phase diagram is depicted based on these measurements. A
large separation between the bulk irreversibility field Hirr(T ) and the upper
critical field Hc2(T ) has been found. It is thus proposed that there is a
quantum vortex liquid due to strong quantum fluctuation of vortices at 0 K.
It is also found that the magnetic relaxation rate is weakly dependent on
temperature but strongly dependent on field indicating a trivial influence of
thermal fluctuation on the vortex depinning process. Therefore, the phase
line Hirr(T ) is attributed to quantum vortex melting in the rather clean
system at a finite temperature.
1. Introduction
The recently discovered new superconductor MgB2 generates
enormous interest in the field of superconductivity [1].
Many important thermodynamic parameters have already been
derived, such as the upper critical field Hc2(0) = 13–20.4 T
[2], the Ginzburg–Landau parameter κ ≈ 26 [5] and the bulk
critical superconducting current density jc ≈ 8 × 104 A cm−2
at 4.2 K and 12 T [6] in thin films. However, one big issue is
concerned with how fast the critical current will decay under
a magnetic field and in which region on the field–temperature
(H–T ) phase diagram the superconductor can carry a large
critical current density ( jc). This jc is determined by the
mobility of the magnetic vortices, and vanishes at the melting
point between the vortex solid and liquid. A finite linear
resistivity ρlin = (E/j )j →0 will appear and the relaxation rate
will reach 100% at this melting point showing the starting
of the reversible flux motion. In this paper we present an
investigation on the flux dynamics by magnetic relaxation
and transport measurement. A vortex phase diagram will be
depicted based on the magnetic relaxation data.
2. Experimental details
Samples investigated here were fabricated by both highpressure (HP) (P = 6 GPa at 950 ◦ C for 0.5 h) and
0953-2048/02/030315+05$30.00 © 2002 IOP Publishing Ltd
ambient-pressure (AP) syntheses [7]. High-pressure synthesis
is a good technique for producing the MgB2 superconductor
since it can make the sample more dense and uniform (in
submicron scale) and also prevent the oxidization of Mg
element during the solid reaction. Our HP samples are
very dense and look like metals with shiny surfaces after
polishing. Scanning electron microscopy (SEM) shows that
the HP sample is uniform in the submicron scale, but some
disordered fine structures are found in the 10 nm scale, which
are similar to the internal structure of large grains seen in the
AP sample. X-ray diffraction (XRD) analysis on both type of
samples show that they are nearly in a single phase with the
second phase (probably MgO or MgB4) less than 1 wt%. For
simplicity we present mainly the results from the HP sample
in this paper.
The resistive measurements were carried out using the
standard four-probe technique with a Keithley 220 dc current
source and a Keithley 182 nanovoltmeter, and the magnetic
field was applied with a vibrating sample magnetometer
(VSM, Oxford 3001), with the field range varying from 0 to 8 T.
For transport measurements the sample was given a rectangular shape with dimensions of 4 mm × 3 mm × 0.5 mm.
Four silver pads were deposited onto the sample’s surface for
electric contacts with low contacting resistance.
The magnetic measurements were carried out by
a superconducting quantum interference device (SQUID,
Printed in the UK
315
2.0
High Pressure Sample
1.5
FC
1.0
1.0
M ( emu )
2
0
-2
-4
-6
-8
-10
-12
-14
-16
0
0.8
R ( mΩ )
-3
M ( 10 emu )
H H Wen et al
0.6
0.4
0.2
ZFC
0.0
20
30
40
50
0.5
0.0
-0.5
dH / dt = 100 Oe / s
T = 2, 4, 6, 8, 10, 14, 18, 22,
26, 30, 32, 35, 37, 38 K
-1.0
-1.5
60
T(K)
-2.0
-2
10 20 30 40 50 60 70 80 90
0
2
10
6
10
5
10
4
10
3
316
22 K 18 K
14 K
35 K
32 K
10 K
8K
0.001
0.000
-0.001
10
2
10
1
-0.002
-0.003
0
0.01
T = 30 K
M ( emu )
Figure 1 shows the diamagnetic transition of one of the HP
samples measured in the field-cooled (FC) and zero-fieldcooled (ZFC) processes. All of the other samples show almost
similar quality. In the FC process, the temperature was lowered
from above Tc to a desired temperature below Tc under a
magnetic field, and the data were collected in the warming
up process with a field. Its signal generally describes the
surface shielding current and the internal frozen magnetic flux
profile. In the ZFC process, the temperature was lowered from
above Tc to a desired temperature below Tc at a zero field and
the data were collected in the warming up process with a field.
Its signal generally describes the internal magnetic flux profile
which is ultimately related to the flux motion. The inset shows
the resistive measurement on the sample. In zero field, the
superconducting transition temperature Tc0 and Tc (onset) are
38.9 and 39.9 K, respectively. Both resistive and diamagnetic
measurements show that the transition is very sharp with a
perfect diamagnetic signal.
In figure 2 we show the magnetization hysteresis loops
(MHLs) measured at temperatures ranging from 2 to 38 K. The
symmetric MHLs observed at temperatures up to 38 K indicate
the dominance of the bulk current instead of the surface
shielding current. The MHLs measured at low temperatures,
such as 2 and 4 K, show quite a strong flux jump which will
be discussed elsewhere [8]. It is easy to see that the MHLs
measured at low temperatures (e.g., 2–10 K) are too close
to be distinguishable. This indicates that both the critical
current density jc and the irreversibility field Hirr are weak
30 K 26 K
37 K
2
3. Results
8
Figure 2. Magnetization hysteresis loops measured at 2, 4, 6, 8, 10,
14, 18, 22, 26, 30, 32, 35, 37 and 38 K (from outer to inner). All
curves show a symmetric behaviour indicating the importance of
bulk current instead of surface shielding current. The MHLs
measured at low temperatures (e.g., 2–10 K) are too close to be
distinguishable. Strong flux jump has been observed at 2 and 4 K
near the central peak.
Jc( A/cm )
Quantum Design MPMS 5.5 T) and a vibrating sample
magnetometer (VSM 8T, Oxford 3001). To precisely calculate
the critical current density jc, the sample was cut with a
diamond saw into a rectangular shape with dimensions of
3.2 mm (length) × 2.7 mm (width) × 0.4 mm (thickness).
6
µ0H ( T )
T(K)
Figure 1. Temperature dependence of the superconducting
diamagnetic moment measured in the ZFC and FC processes at a
field of 10 Oe. A perfect diamagnetic signal can be observed here.
The inset shows the resistive transition with Tc0 and Tc (onset) are
38.9 and 39.9 K, respectively.
4
6K
4K
2K
1
2
3
µ0H ( T )
0.1
1
µ0H( T )
10
Figure 3. Critical current density jc calculated based on the Bean
critical state model. At each temperature the data has been measured
with three field sweeping rates: 200, 100 and 50 Oe s−1. The faster
sweeping rate corresponds to a higher dissipation and thus higher
current density. From these data one can calculate the dynamical
magnetic relaxation rate Q. The jc(H) curves measured at low
temperatures are very close to each other showing a rather stable
value of Hirr(T ) when T approaches 0 K. The dashed horizontal line
marks the criterion of jc = 30 A cm−2 for determining the Hirr(T ).
temperature-dependent functions in low-temperature region.
From these MHLs one can calculate jc as jc = 20M/Va (1 −
a/3b) based on the Bean critical state model, where M is
the width of the MHL, V , a and b are the volume, width and
length of the sample, respectively. The results of calculated
jc(H) are shown in figure 3. It is clear that the bulk critical
current density jc of our sample is rather high. To investigate
the flux dynamics, the jc(H) curves have been measured with
three different field sweeping rates 200, 100 and 50 Oe s−1.
The so-called irreversibility line Hirr(T ) has been determined
by taking a criterion of jc = 30 A cm−2. Hc2(T ) is determined
20
18
Hc2
16
14 V
ort
12
ex
Li q
10
u id
8
6
4
Vortex Solid
2
0
0
5 10 15
1.0
2K
Hc2-Bulk-SQUID
Hc2-Takano
Hc2-Bulk-Trans
Hirr-Bulk-VSM
Hirr-Bulk-SQUID
Hirr-Bulk-Trans
0.8
Relaxation Rate
0
Magnetic relaxation and critical current density of the new superconductor MgB2
0.6
0.4
0.2
0.0
20
25
30
35
40
T(K)
Figure 4. H–T phase diagram for the new superconductor MgB2.
The filled circles represent the bulk irreversibility lines Hirr(T )
measured by the VSM; half-filled circles represent Hirr(T ) for
another sample measured by SQUID; open diamond represent Hirr
of the HP sample measured by resistive transport. The filled squares
represent the Hc2(T ) data of Takano et al [4] from resistive
measurement; open squares represent this work from the M(T )
measurement by SQUID; filled diamond represent this work by
transport measurement. All the lines are guide to the eye.
from the M(T ) curve at the point where the magnetization
starts to deviate from the normal state linear background.
Another method to determine Hirr(T ) and Hc2(T ) is
to measure the resistive transitions at different magnetic
fields. Hirr(T ) was determined by taking a minimum value
of resistivity as the criterion, while for the upper critical
field Hc2(T ), we (and Takano et al [4]) determined the upper
critical point Tc2 from the point at which the resistance starts
to deviate from the normal state resistance. All the phase
lines determined by using these methods are presented and
discussed below.
4. Discussion
4.1. Vortex phase diagram of MgB2
The phase lines of Hirr(T ) and Hc2(T ) determined by the
methods mentioned above are shown in figure 4. It is
clear that the irreversibility line Hirr(T ) determined from
the MHL is very close to that determined by resistive
measurement. This strongly indicates that Hirr(T ) is a
vortex melting line which signals the appearance of a
finite linear resistivity. Plotted together in figure 4 are
the upper critical field Hc2(T ) determined from (1) the
temperature-dependent magnetization by defining Hc2(T )
as the point at which the magnetization starts to deviate
from the normal state linear background [9], and (2) the
resistive measurement by Takano et al [4] and by us on HP
samples. Although the samples are from different groups and
different techniques have been used to obtain the data, the
vortex phase diagram derived here has a good consistency.
A striking result from this vortex phase diagram is that Hirr(T )
extrapolates to a rather low field at 0 K, here, for example,
Hirr(0) ≈ 8 T, while Hc2(T ) extrapolates to a much higher value
Hc2(0)
Hirr(0)
T = 2, 4, 6, 8, 10, 14, 18,
22, 26, 30, 32,35,37 K
0
2
4
6
8
10
12
14
16
18
20
µ0H ( T )
Figure 5. Field dependence of the relaxation rate at temperatures 2,
4, 6, 8, 10, 14, 18, 22, 26, 30, 32, 35 and 37 K. The dashed line is a
guide to the eye for 2 K. It is clear that Q will rise to 100% at 8 T
and 2 K. Since Hirr(T ) is rather stable at low temperatures, it is
anticipated that Hirr(0) ≈ 8 T, which is much smaller than Hc2(0)
≈ 15 T.
(Hc2(0) ≈ 15 T) [2] at 0 K. There is a large separation between
the two fields Hirr(0) and Hc2(0). If following the hypothesis
of the vortex liquid above Hirr(T ), we would conclude that
there is a large region of magnetic field for the existence of
a vortex liquid at 0 K. This can be attributed to a quantum
fluctuation effect of vortices in bulk MgB2. Although the
lowest temperature in our present experiment is 1.6 K, from
the experimental data one cannot find any tendency for Hirr(T )
to turn upward rapidly to meet Hc2(0). One may argue that
the Hirr(T ) probably can be increased to higher values by
introducing more pinning centres into this sample. This is
basically correct since recently a higher irreversibility line
Hirr(T ) has been found in some MgB2 thin films [6] and bulk
samples irradiated by protons [10]. Actually in our recent
experiment on MgB2 thin films, the irreversibility line Hirr(T )
is also close to that of bulks. This indicates that the large
separation between Hirr(0) and Hc2(0) may be an intrinsic
property of MgB2 in the clean limit.
4.2. Large separation between Hirr(0) and Hc2(0) and
possible evidence for strong quantum fluctuation of vortices
In order to investigate the flux dynamics in the vortex solid
state below Hirr(T ) and to see more clearly the evidence for the
quantum vortex melting in a relatively pure system, we have
carried out the dynamical relaxation measurement. According
to Schnack et al [11] and Jirsa et al [12], in a field sweeping
process, if the field sweeping rate is high enough, the quantity
Q = d ln M/d ln(dH/dt) is close to the relaxation rate S =
−d lnM/d ln t measured in the conventional relaxation method,
where Q is called the dynamical relaxation rate, M is the
width of the MHL and dH/dt is the field sweeping rate. The
raw data with three different sweeping rates (200, 100 and
50 Oe s−1) are shown in figure 3. The Q values versus field for
different temperatures are determined and shown in figure 5.
It is clear that the relaxation rate increases monotonically with
317
H H Wen et al
is probably induced by a strong pinning barrier relative to the
thermal energy, i.e. kBT Uc, where Uc is the intrinsic pinning
energy. Recently, it was concluded [15, 16] that Uc is in the
scale of 1000 K, which is much higher than the thermal energy
kBT. Therefore, for the new superconductor MgB2 the pinning
well is too deep leading to a trivial influence of the thermal
activation and fluctuation. It thus naturally suggests that the
quantum fluctuation and tunnelling of vortices are quite strong
in MgB2. We strongly suggest that the melting between a
vortex solid and a liquid is due to the quantum fluctuation
instead of the thermal fluctuation.
Relaxation Rate
1.0
6T
5T
10
15
4T 3T
2T
1T
30
35
0.8
0.6
0.4
0.2
0.0
0
5
20
25
40
T(K)
Figure 6. Temperature dependence of the relaxation rate at fields 1,
2, 3, 4, 5 and 6 T. The dashed lines are guide to the eye. The arrows
point at the bulk irreversibility temperatures Tirr determined from the
jc(H) curve.
the external magnetic field and extrapolates to 100% at the
bulk melting point Hirr(T ). At 2 K it is found from the Q(H )
data that the vortex melting field (where Q = 100%) is about
8 T, which is very close to Hirr(T = 2 K) determined from
the jc(H) curve. It is known that Hirr(T ) is rather stable in a
low-temperature region; therefore we can anticipate a rather
low value of Hirr(0) which is below 9 T being much lower than
Hc2(0). Again one can see a large separation between Hirr(0)
and Hc2(0). This effect has recently been found also in rather
pure MgB2 films [13] with Tc(0) = 38 K and jc(0 T, 14 K) =
1.8 × 107 A cm−2. All these may strongly suggest the existence
of the quantum vortex liquid due to strong quantum fluctuation
of vortices in the pure system of MgB2. The reason for the
strong quantum fluctuation is still unknown. It may share the
same reason as the relatively low upper critical field.
4.3. Residual relaxation rate at 0 K and weak temperature
dependence of the relaxation rate
Figure 6 shows the temperature dependence of the dynamical
relaxation rate Q. The arrows point at the irreversibility
temperatures at the corresponding fields Hirr(T ). It is clear
that the relaxation rate extrapolates to a finite value at 0 K for
all fields. This effect was also observed in high-Tc cuprate
superconductors and attributed to the quantum tunnelling of
vortices. The difference between the MgB2 and the HTS is that
the residual relaxation rate Q at 0 K in the former case has a
strong field dependence, but in the latter it is weakly dependent
on the field, especially for the 3D YBa2Cu3O7 system. Another
striking point for MgB2 is that in a wide temperature region the
relaxation rate is rather stable against the thermal activation
and fluctuation. However, when the bulk melting point Hirr(T )
is approached the relaxation rate will quickly jump to 100%.
The small relaxation rate at a relatively low field has also been
measured by Thompson et al [14] who regarded it as a highly
stable superconducting current density in MgB2. Actually the
relaxation rate can be rather high when the magnetic field is
increased to a higher value. The extremely small relaxation
rate and weak temperature dependence at a finite temperature
318
5. Conclusion
In conclusion, in rather pure samples of MgB2, the
irreversibility field is rather low compared to the upper critical
field in the low-temperature region showing the possible
existence of the quantum vortex liquid due to strong quantum
fluctuation of vortices. The temperature and field dependence
of the relaxation rate may further suggest that the vortex
melting at a finite temperature is also induced by strong
quantum fluctuation in pure systems, such as single crystals
and bulks.
Magnetic relaxation measurement shows that the pinning
barrier is much higher than the thermal energy; this may also
interpret the trivial importance of the thermal activation and
thermal fluctuation. In comparison the quantum tunnelling and
the fluctuation show a much stronger influence. The reason
for such a strong quantum effect is still unknown, but it may
be related to the superconducting mechanism of MgB2, such
as a relatively low upper critical field.
Acknowledgments
This work is supported by the National Science Foundation
of China (NSFC 19825111) and the Ministry of Science
and Technology of China (project: NKBRSF-G1999064602).
HHW gratefully acknowledges the K C Wong education
foundation of Hong Kong for financial support.
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