Physica C 369 (2002) 232–235
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Temperature, field and current dependence of the flux
creep activation energy in bulk MgB2
D. Botta a, A. Chiodoni a, R. Gerbaldo a, G. Giunchi b, G. Ghigo a,
L. Gozzelino a, F. Laviano a, B. Minetti a, E. Mezzetti a,*
a
INFM––U.d.R Torino-Politecnico; INFN––Sez. Torino; Politecnico di Torino, c.so Duca degli Abruzzi 24, 10129 Torino, Italy
b
Edison S.p.A., Foro Buonaparte 31, 20121 Milan, Italy
Abstract
In this paper we investigate the behavior of the flux creep activation energy as a function of T, B and J in the
temperature range from 4 K up to Tc . The experimental methodology is mainly based on ac susceptibility measurements
at different frequencies and applied field, though some dc measurements are referred to along the discussion. A new
analysis method is employed in the framework of the flux creep theory to explore the full range of temperature. It turns
out that the key energy scale U0 ðT ; BÞ at any external field exhibits a peak. The main outcome of the study is that the
peak values are laying along the dc irreversibility line (IL) curve, while the points where U0 ¼ 0 match the ac IL. Then
these two curves divide the phase diagram in three reference regions to be investigated in details. Ó 2001 Elsevier
Science B.V. All rights reserved.
Keywords: Flux creep activation energy; Flux pinning; Flux-line lattice dynamics; Magnesium diboride
The recent discovery of the superconductor
MgB2 [1] has aroused great interest and intensive
studies have been carried out on this material, as
prepared in different laboratories [2]. One of the
main issues concerning MgB2 is the determination
of its flux-pinning properties, because the motion
of the vortices (flux creep) over the pinning barriers induces dissipation and sets the limiting critical current density Jc . The interest is driven by the
need to understand the basic pinning mechanisms,
*
Corresponding author. Address: Department of Physics,
Politecnico di Torino, c.so Duca degli Abruzzi 24, 10129
Torino, Italy. Tel.: +39-011-564-7314/7349; fax: +39-011-5647399.
E-mail address: mezzetti@polito.it (E. Mezzetti).
as well as by the practical requirement to enhance
Jc [3,4]. In this paper we investigate the flux creep
activation energy and its dependence on temperature, field and current density. Aiming at obtaining
the most general information about the pinning
properties of our samples, we present a new analysis of the pinning energy in the whole temperature range, from 4.2 K up to the critical
temperature. The main results reported in the paper are based on ac susceptibility measurements at
different frequencies and dc magnetic fields.
High density MgB2 bulk pellets were prepared
starting from the elemental compounds B (99.5%
of purity) and Mg (99.9% of purity), after their
reaction in a sealed stainless steel container,
lined with a Nb foil. The thermal treatment was
0921-4534/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved.
PII: S 0 9 2 1 - 4 5 3 4 ( 0 1 ) 0 1 2 4 8 - 5
D. Botta et al. / Physica C 369 (2002) 232–235
Fig. 1. SEM of the MgB2 pellet. In the inset a magneto-optical
image is reported (l0 Hext ¼ 89 mT; T ¼ 35 K): bright regions
indicate presence of magnetic field, while dark regions indicate
shielded zones. Black lines mark the sample edge.
performed for 2 h in the range of 850–950 °C. The
superconducting transition temperature is Tc ¼
38:9 K, with DTc ¼ 0:3 K [5]. The apparent absence of magnetic granularity up to temperatures
very close to Tc was checked by means of a magneto-optical analysis (inset of Fig. 1): despite the
polycrystalline nature of the material, clearly visible in the scanning electron microscopy (SEM)
picture reported in Fig. 1, the flux enters the
sample in a single crystal like fashion, with a Bean
profile [5].
The ac susceptibility measurements have been
performed on a disk-shaped sample (diameter ¼
2:93 mm; thickness ¼ 0:34 mm) with l0 Hac ¼ 0:13
mT, at different frequencies (2, 10, 110, 1000, 5000
and 10 000 Hz) and dc magnetic fields (0, 0.125,
0.25, 0.5 and 1 T). Fig. 2 shows the characteristic
effects of the dc external magnetic field l0 Hext on
the ac susceptibility: as l0 Hext is increased, the
transition broadens and shifts towards lower
temperatures.
The real part of the first harmonic susceptibility
were analysed in the framework of the Clem and
Sanchez model for the case of a thin sample in a
transverse field [6,7] in order to obtain the critical
current density in the whole (T ; B; m) range. Fig. 3
shows the critical current density as a function of
temperature, at l0 Hext ¼ 0:5 T and for different
values of the frequency.
Irreversibility lines (ILs) have been determined
by both ac and dc methods, by means of the onset
233
Fig. 2. Ac susceptibility as a function of temperature, at different values of the external magnetic field.
of the third harmonic component of the susceptibility and from the closing up of the hysteresis
cycles, respectively.
Critical current values are analysed in the
framework of a thermally activated flux creep
model: flux lines jump to neighbouring states over
the energy barrier U via thermal activation. The
mean relaxation time is given by the Arrhenius
law:
s ¼ s0 expðU =kT Þ
ð1Þ
where s0 is the relaxation time scale. In the
framework of the collective creep model one can
assume the very general relation [8]:
l
1
Jc
U ðT ; B; J Þ ¼ U0 ðT ; BÞ
1
ð2Þ
l
J
where U0 is a characteristic energy scale, Jc is the
critical current density in the absence of thermally
activated creep processes and the exponent l is a
characteristic of the particular flux dynamics. Eq.
(2) becomes U ðJ Þ ¼ U0 lnðJc =J Þ as l ! 0.
The experimental critical currents (Fig. 3) exhibit a noticeable dependence on the frequency.
This characteristic can be considered the signature of creep effects that can be introduced into a
critical state model by considering a frequencydependent ‘‘critical current’’ Jc ðT ; B; mÞ [9]:
kT
m0
ln
Jc ðT ; B; mÞ Jc ðT ; BÞg
U0 ðT ; BÞ
m
234
D. Botta et al. / Physica C 369 (2002) 232–235
Fig. 3. Critical current density as a function of temperature,
at l0 Hext ¼ 0:5 T and for different values of the frequency.
where the function gðxÞ reflects the relaxation of
the flux profile during the time 1=m. This expression incorporates Eq. (1), with s ! 1=m and s0 !
1=m0 . By assuming Eq. (2), it becomes
1=l
lkT
m0
ln
Jc ðT ; B; mÞ ¼ Jc ðT ; BÞ 1 þ
ð3Þ
U0 ðT ; BÞ
m
Jc ðT ; BÞ Jc ðT ; B; m ¼ m0 Þ represents the critical
current density in absence of flux creep, while
J Jc ðT ; B; mÞ can be interpreted as the effective
critical current density when thermally activated
processes are present. Eq. (3) could be used to
determine U0 and l, if the value of m0 is known.
However, in order to minimize numerical instabilities, we adopted the following equivalent approach. At any fixed value of temperature and
external field we independently determine from the
experimental data the ratio
Jcexp ðT ; B; mÞ
J
Jcexp ðT ; B; m0 Þ Jc
and the value of the activation energy
U ðT ; B; J Þ ¼ kT ln
s
m0
¼ kT ln
s0
m
as deduced from Eq. (1). To obtain general information about the pinning properties of our
samples, we did not assume any a priori functional
dependence of the pinning energy on temperature
and field. At any given value of T and B, we fit the
data U vs. J =Jc by means of Eq. (2), with U0 and l
Fig. 4. Typical U vs. J =Jc fit of experimental data by means of
Eq. (2) (see text) at fixed value of the external magnetic field
(l0 H ¼ 0:25 T) and temperature (T ¼ 25 K).
as fitting parameters (a typical example is reported
in Fig. 4). We assumed m0 ¼ 10 kHz, as driven
from a detailed v00 -peak analysis on the same sample, reported in a recent paper [4]. It turns out that
the value of m0 is significantly lower than that
usually reported for HTSs [9].
As already pointed out above, the main result
of this approach is the determination of the activation energy U in the whole temperature range,
at different values of the external magnetic field.
The main feature of the energy scale parameter
U0 ðT ; BÞ is the presence of a sharp peak, dividing
the temperature range into two distinct regions
(Fig. 5). It turns out that the peak position exactly
corresponds, in a temperature–field phase diagram, to the IL, determined in the same sample by
a dc method, i.e. by the closing-up point of the
hysteresis cycles (Fig. 6).
The exponent l maintains a nearly constant
value (in the range from 1.4 to 2.2), up to temperatures close to the U0 peak. Above this temperature it drops to very low values, resulting in a
logarithmic dependence of the energy activation
on the current.
In the high temperature region (above the peak)
the present analysis is in good agreement with the
results we reported in Ref. [4], obtained by a different approach based on the v00 -peak analy2 a
sis, where we assumed U ¼ U 0 ½1 ðT =Tx Þ . Here
a and Tx are field-dependent parameters. Tx repre-
D. Botta et al. / Physica C 369 (2002) 232–235
Fig. 5. Activation energy scale U0 , determined as a fit parameter (see Fig. 4) by the procedure described in the text, as a
function of temperature for different values of the external
magnetic field. Dotted lines represent the extrapolation used
to determine the temperature where U0 ¼ 0.
235
the power-law decrease of the pinning energy
U0 with temperature, notwithstanding the different analysis method.
In the low-temperature region (below the peak),
the U0 curves at a fixed external field are increasing
functions of temperature (it is worthwhile to remind that along these curves the internal field,
i.e. the average number of vortices, is not constant). This result takes one back to U ðT Þ dependences obtained for YBCO in Ref. [10].
Some insight into the vortex matter behavior
in correspondence of the two regimes, below and
above the U0 peak, are provided by the comparison
between the features observed in the U0 ðT ; BÞ
curves and the ILs, as evaluated by ac and dc
methods (Fig. 6). In particular, as already pointed
out, the points of the U0 peaks exactly match the dc
IL, while the points where U0 ðT Þ ¼ 0 match the ac
IL. Therefore the results point toward the presence
of three main regions in the vortex–phase diagram,
all of them in a context of relatively weak pinning:
the first one (I) is characterized by a pinning energy
increasing with T up to the dc IL, the second one
(II) by a pinning energy collapsing toward zero at
the ac IL, the third one (III) corresponding to a
reversible region with unpinned vortices.
References
Fig. 6. Vortex–phase diagram determined by the comparison
among different independent analysis: onset of the third harmonic susceptibility (IL ac), hysteresis cycles (IL dc), U0 ðT ; BÞ
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A qualitative agreement is also found with the
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