INSTITUTE OF PHYSICS PUBLISHING
SUPERCONDUCTOR SCIENCE AND TECHNOLOGY
Supercond. Sci. Technol. 14 (2001) 722–725
PII: S0953-2048(01)26551-8
Creep properties of MgB2 bulk near the
irreversibility line
G Ghigo1,2,3 , D Botta1,2,3 , A Chiodoni1,2,3 , R Gerbaldo1,2,3 ,
L Gozzelino1,2,3 , E Mezzetti1,2,3 , B Minetti1,2,3 , S Ceresara4 ,
G Giunchi4 and G Ripamonti4
1
Istituto Nazionale per la Fisica della Materia, U.d.R. Torino-Politecnico, c.so Duca Degli
Abruzzi 24, 10129 Torino, Italy
2
Istituto Nazionale di Fisica Nucleare, Sez. Torino, via P. Guiria 1, 10125 Torino, Italy
3
Dipartimento di Fisica, Politecnico di Torino, c.so Duca degli Abruzzi 24, 10129 Torino,
Italy
4
Edison S.p.A. Foro Buonaparte 31, 20121 Milano, Italy
Received 4 June 2001
Published 22 August 2001
Online at stacks.iop.org/SUST/14/722
Abstract
Using susceptometric measurements at different frequencies and fields we
investigate the creep properties of MgB2 near the irreversibility line. The
data analysis allows to find the dependence of the pinning energy U on field
and temperature. Remarkably, it turns out that the dependence on B and T
cannot be separated as U (B, T ) = U0 (B)f (T ). An analysis aimed at
understanding the mechanisms underlying this lack of a scaling law is tried.
Self-consistent experimental hints prove that different creep mechanisms are
active in low-frequency/low-field and high-frequency/high-field regions.
1. Introduction
One of the main issues from the beginning of the short history
of MgB2 is the correlation/competition between structural
and magnetic granularity [1]. Scanning electron microscopy
(SEM) images indeed reveal the granular microstructure of the
bulk material.
In our samples, large grains of about 10 µm in diameter
are framed inside a matrix of microcrystals, whose size is
one order of magnitude lower than the grains. On the
other hand careful magneto-optical (MO) studies showed
that the polycrystalline material enters into a critical state
without revealing the penetration of flux among magnetically
decoupled grains: without a doubt, a polycrystalline sample
enters into the critical state as a whole [2]. However the flux
profile obtained by MO analysis in proximity of the critical
state shows some puzzling features. These features consist in
the local fluctuation of the light intensity resulting in local
fluctuation of the field profile. The patterns can be either
attributed to experimental uncertainties or to the contribution of
local shielding currents due to fully shielded grains inside the
network of flux penetrated bulk [3]. In order to investigate the
effects of the structural granularity from another point of view,
we made a set of susceptometric measurements at different
frequencies, looking for the dynamic effects of the competition
between differently coupled, different size grains [4].
0953-2048/01/090722+04$30.00
© 2001 IOP Publishing Ltd
In this paper we report on the vortex dynamics near the
irreversibility line in bulk samples. We analyse the flux–creep
activation energy and its dependence on the dc magnetic field
and temperature. The data allow us to outline consistent,
although different, dynamic aspects that are preliminarily
discussed.
2. Experimental details
High-density MgB2 bulk pellets were prepared from the
elements B (99.5% pure) and Mg (99.9% pure), after their
reaction in a sealed stainless-steel container, lined with Nb
foil. The thermal treatment was performed for 2 h in the
range 850–950 ◦ C. The preparation procedures of highlydensity MgB2 pellets are reported elsewhere [5]. The
measurements were performed on a disc-shaped sample
(diameter = 2.93 mm, thickness = 0.34 mm), at different
frequencies and dc magnetic fields. The onset of the thirdharmonic generation was used for the identification of the
irreversibility temperature, Tirr .
3. Experimental results
We measured the in-phase (χ ) and out-of-phase (χ )
components of the ac susceptibility at different frequencies,
Printed in the UK
722
Creep properties of MgB2 bulk
40
0.4
Hac = 107 A/m
ν = 110 Hz
0.2
36
0T
0.02 T
0.125 T
0.25 T
0.5 T
1T
5T
-0.4
-0.6
-0.8
Tirr (K)
χ' , χ'' (SI)
0.0
-0.2
µ0Hdc
10
15
Tirr obtained from
experimental measurements
34
32
30
28
Hac = 107 A/m
26
-1.0
5
Tirr obtained as
a fitting parameter
38
20
25
30
35
24
40
0
1
2
T (K)
Figure 1. Typical applied field dependence of the in-phase (χ ) and
out-of-phase (χ ) components of the ac susceptibility.
χ '' (SI)
6
ν = 10 Hz
ν = 110 Hz
Hac = 107 A/m
µ 0Hdc = 0.5 T
0.3
5
ν = 10 Hz
ν = 110 Hz
0.2
4
0.1
0.0
33
7
α
0.4
5
(a)
µ 0Hdc = 0.02 T
Hac = 107 A/m
4
µ 0H (T)
0.5
3
3
34
35
36
37
38
39
40
T (K)
Figure 2. χ (T ) curves for two different dc magnetic fields (0.02 T
and 0.5 T) and two different frequencies (10 Hz and 110 Hz).
ranging from 2 Hz to 10 kHz, and at various applied dc fields
up to 5 T. The ac field was 107 A m−1 . The value of the ac
field determine the Jc value in correspondence of the χ peaks.
The analysis concerning χ is referred to the peak position and
then to a constant value of Jc .
The general trend of the curve dependence on frequency
is rather conventional: as the frequency increases the χ peaks
shift toward higher T and the onset temperature of the χ transition shifts toward higher values of T . The critical temperature,
Tc , evaluated as the temperature corresponding to the dχ /dT
maximum, is 38.9 K. The onset temperature T0 is 39.4 K. The
dχ /dT full-width at half-maximum (FWHM) is 0.3 K.
Figure 1 shows a typical field dependence of the in-phase
(χ ) and out-of-phase (χ ) components of the ac susceptibility.
Figure 2 shows the χ (T ) curves for two different dc magnetic
fields (0.02 T and 0.5 T) and two different frequencies (10 Hz
and 110 Hz). At a field of less than 0.5 T, the χ (T ) curves
exhibit a shoulder reminiscent of a double peak. As the dc
magnetic field increases the double peak disappears and a
larger smooth peak is observed instead. In a sintered HTSC
scheme two separated peaks are the signature of a percolating
intergrain current path followed at higher temperatures by a
non-percolating intragrain current.
0
1
2
3
4
5
µ 0H (T)
(b)
Figure 3. (a) Dc magnetic field dependence of the fitting parameter
Tirr and comparison with experimental values obtained from the
onset of the third harmonic of the ac susceptibility, (b) field
dependence of the fitting parameter α.
In this case, the absence of a sharp separation between
two peaks inside a narrow range of temperature points toward
a ‘continuous’ temperature driven transition. In other words,
as the temperature increases differently coupled grains could
contribute to the critical state, as will be discussed. Thus the
basic issue is to understand the macroscopic dynamics of such
a complex system.
Looking to this goal we analyse our experimental data
in the framework of thermally activated flux motion with a
suitable energy barrier U (T , B). Accordingly, the following
Arrhenius law is considered
ν = ν0 exp[−U (T , B)/kB T ]
(1)
where U (T , B) is the effective activation energy which
depends on the temperature and magnetic field, and νo is
an attempt frequency [6, 7]. U (T , B) changes slightly with
temperature for T Tirr and drops rapidly as T approaches
Tirr [8]. In order to account for the explicit dependence of U
on T and B, we adopt the following function, suitable when T
723
10
10
8
10
1
0
Hac = 107 A/m
ν = 110 Hz
0T
0.02 T
0.25 T
0.5 T
1T
5T
6
4
2
-1
U (eV)
ln [ν (Hz)]
G Ghigo et al
10
27K
29K
31K
-3
10
33K
39K
-4
0.030
0.035
0.040
0.045
0.050
-1
1/T (K )
(a)
Hac = 107 A/m
µ0Hdc = 0.5 T
ν = 110 Hz
8
6
4
Fitting Parameters
ln(ν0) = 9.2 ± 0.8
2
U0/kB = (1.9 ± 0.2)⋅10 K
Tirr = (37.1 ± 0.3) K
= 2.15 ± 0.05
α
7
0
0.0272
-1
0.0276
0.0280
0.0284
-1
1/T (K )
(b)
Figure 4. (a) ln(ν) against 1/T measured at different dc magnetic
fields. The broken curves are the fitting curves obtained by means of
equation (3) (see text). (b) Enlargement of ln(ν) against 1/T for
µ0 Hdc = 0.5 T. The broken curve is the fitting curve obtained by
means of equation (3). The values of the fitting parameters are
indicated in the figure.
approaches Tirr [6, 8]:
U (T , B) = U0 (B)[1 − (T /Tirr )2 ]α .
(2)
Here U0 (B) would represent the value of the activation energy
at T = 0 K if the adopted equation (2) was valid also at very
low temperatures, and therefore has no physical meaning by
itself; Tirr is the field dependent irreversibility temperature.
The adopted equation (2) allows checking if a scaling law as
U/U0 (B) = f (T /Tirr (B)) describes the system as whole,
depending on the possible change of the exponent α with the
applied field.
We fit our experimental data, at each constant dc field
(B = µ0 Hdc ), with equations (1) and (2) rewritten as
ln(ν) = ln(νo ) −
0
37K
35K
1
2
3
µ0H (T)
4
5
Figure 5. Dependence of the effective activation energy, U (B, T ),
on the dc magnetic field at constant Jc .
10
ln [ν (Hz)]
T=25K
-2
10
0
0.025
U0 (B)[1 − (T /Tirr )2 ]α
kB T
(3)
where νo , U0 , Tirr and α are fitting parameters. The parameter
U0 (B) dramatically decreases with the field (U0 (B)/U0 (0)
ranges from 1 down to 5.6 × 10−9 for fields lower than 5 T).
The parameters Tirr and α show a monotonic decrease with
724
10
the applied dc field. The trends for Tirr and α are shown
in figures 3(a) and 3(b), respectively. A signature of the fit
reliability is shown in figure 3(a) where the Tirr driven from
the fit is compared in the same picture with Tirr measured in
an independent way, by means of third-harmonic susceptibility
measurements [9]. The fitting parameter νo is about 10 kHz
and does not show a clear field dependence.
In figure 4(a) the values of ln(ν) against 1/T are reported
at different dc magnetic fields and the fitting curves are plotted
as broken curves. In figure 4(b) a selected fit shows a typical
trend in more detail. Thus the creep scenario is summarized
in figure 5, which shows the activation energy U (B, T ), as
evaluated through equation (2), using the field dependence of
the fitting parameters U0 (B), Tirr (B) and α(B).
4. Discussion and conclusions
Looking for the information driven from the procedure, we
stress the fact that the exponent α depends on field and it
approaches the value predicted by the Ginzburg–Landau theory
only at high dc fields (figure 3(b)). This means that a scaling
law as U/U0 (B) = f [T /Tirr (B)] to describe the system as a
whole can be considered only at very high applied fields. As
a consequence the dependence of U on T and B cannot be
considered separately.
Furthermore, the strong dependence of ln(ν) on 1/T
at lower fields could suggest a possible dependence of
the activation energy on the frequency. A straightforward
interpretation of this trend is that if the time window to observe
the creep is large (low frequency) the vortices are allowed
to make attempts to find out the deepest potential wells.
The probability to escape these wells is then very low. In
contrast, when the time window is narrow hopping towards a
shallow potential well is more likely. However, both (i) the
contrast between the structural granularity and the apparent
lack of magnetic granularity in MO images and (ii) the abovementioned modulated peak patterns, showing up just at low
field (lower than 0.5 T) as well as just in the same range where
the stronger dependence of α on field is exhibited, provide a
self-consistent set of experimental evidence to be considered.
Namely, all data point towards the setting up of further
Creep properties of MgB2 bulk
phenomena, interfering with the hopping-attempt-based
framework. We speculate that in this case the fact of using
different time windows also means observing the dynamics
of different interacting vortex lattices, the first consisting of
Josephson vortices and the second of Abrikosov vortices [10].
The hypothesis of a vortex lattice roughness driven by defects
due to texturing seems reasonable, if we also take into account
both optical and MO analysis [3]. No matter if there are ‘real’
strongly coupled Josephson junctions, the vortex roughness
involves a Josephson-like behaviour [11]. So we expect a
dynamics driven by a mixing up of a low-viscosity, highspeed Josephson vortex lattice and a low-speed, high-viscosity
Abrikosov vortex lattice, with different phase diagrams. In this
sense MgB2 looks like an extremely interesting material, both
from fundamental and application points of view.
Acknowledgment
We acknowledge the support of the Italian Space Agency under
ARS/99/16 project.
References
[1] Larbalestier D C et al 2001 Nature 410 187
[2] Gozzelino L, Laviano F, Botta D, Chiodoni A, Gerbaldo R,
Ghigo G, Mezzetti E, Giunchi G, Ceresara S and
Ripamonti G 2001 Phil. Mag. B at press
(Preprint cond-mat/0104069)
[3] Gerbaldo R, Ghigo G, Gozzelino L, Giunchi G, Laviano F and
Mezzetti E 2001 Eur. Phys. Lett. submitted
[4] Cai X Y, Gurevich A, I-Fei Tsu, Kaiser D L, Babcock S E and
Larbalestier D C 1998 Phys. Rev. B 57 10 951
[5] Edison S.p.A. patent pending
[6] Palstra T T M, Batlogg B, van Dover R B, Schneemeyer L F
and Waszczak J V 1990 Phys. Rev. B 41 6621
[7] Fabrega L, Fontcuberta J, Piñol S, van der Beek C J and
Kes P H 1993 Phys. Rev. B 47 15 250
[8] Qin M J, Wang X L, Liu H K and Dou S X 2001 Preprint
cond-mat/0104112 and references therein
[9] Mezzetti E, Gerbaldo R, Ghigo G, Gozzelino L and Gherardi L
1999 Phys. Rev. B 59 3890
[10] Gurevich A and Cooley A D 1994 Phys. Rev. B 50 13 563
[11] Koshelev A E 1999 Phys. Rev. Lett. 83 187
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