Ac susceptibility measurements and extraction of inter- and intra-grain
superconductive transitions in polycrystalline RuSr2GdCu2O8 superconductor
M. M. Abu-Samreh1,4, R. M-L Kitaneh2, H. F. Braun3, and A. M. Saleh2,*
1 Physicsand Electronic Department, Faculty of Applied Sciences, Palestine Polytechnic University, Wadi-Alhariah, Hebron, West
Bank, Israel
2 Physics Department, College of Science and Technology, Al-Quds University, East Jerusalem, Abu-Dis, P O Box 20002, West
Bank, Israel.
3 Physikalisches Institut, Universitiit Bayreuth, 95440 Bayreuth, Germany
4 Permanent address: Physics Department, College of Science and Technology, Al-Quds University, East Jerusalem, Abu-Dis, P O
Box 20002, West Bank, Israel
A paper presented at the 2nd Physics Symposium
May 8-9, 2007
Organized by the Physics Department
An-Najah National University
Faculty of Science
Nabuls, Palestine
May 8-9, 2007
2ed Physics Symposium May 8-9, 2007, Organized by the Physics Department, An-Najah University, Faculty of Science, Nablus, Palestine
Abstract
•
•
Systematic measurements of the AC magnetic susceptibility of
polycrystalline RuSr2GdCu2O8 (Ru-1212) samples are reported for various
frequencies and magnetic field amplitudes. The study covered frequency
range from 22 Hz to 12.5 kHz and field amplitudes between 0.5 to 25
Gauss. Both of the susceptibility components χ', and χ'' are greatly
affected by frequency and applied field depending on the relevant range
under consideration.
In addition, the measured data of the susceptibility components were
employed to extract inter- and intra-grain superconductive transition
temperatures as well as the average transition temperature in magnetic
superconductor RuSr2GdCu2O8. The intra- and inter-granular
components of the granular susceptibility components were also
estimated. It was found that both of the intra- and inter-granular
transition temperatures increase by increasing field frequencies and
decrease by increasing the field amplitudes. This might be an indication
that the grains of RuSr2GdCu2O8 behave differently from a homogenous
bulk superconductor. The nature of curves indicated the presence of a
superconducting transition between grains, coupled by weak links with a
distribution of critical temperatures, and the superconducting transition
within the grains. The two transitions observed are linked to the typical
intra- and intergrain transitions of a granular superconductor. The weak
coupling between grains might be modeled in terms of Josephsonjunction arrays.
2ed Physics Symposium May 8-9, 2007, Organized by the Physics Department, An-Najah University, Faculty of Science, Nablus, Palestine
Introduction
The discovery of superconductivity (SC) (Tc=8– 46 K)
coexisting with spatially uniform ferromagnetism (FM)
(TCurie124-136 K) in the polycrystalline hybrid ruthenatecuprate material RuSr2GdCu2O8 (Ru-1212 Gd) had presented a
remarkable achievement in the study of competing magnetism
and SC and had opened an interesting and promising era for
new research topics in the field of superconductivity
The ACS technique was successfully employed to extract some
electronic and magnetic properties of Ru-1212Gd
polycrystalline superconductor such as its transition
temperature (TC), magnetization, critical current density (CCD),
JC(T), ordering parameters, penetration depth, and
conductivity
 It is well known that the fundamental complex ACS
(χac=χ΄-χ˝) has a clear physical meaning. The real
part of ACS,, corresponds to the dispersion of
magnetic into the medium that measures the
response of the system to the probing field, and
hence reflecting the supercurrent shielding effect in
the case of superconducting samples
2ed Physics Symposium May 8-9, 2007, Organized by the Physics Department, An-Najah University, Faculty of Science, Nablus, Palestine
•
Besides, the imaginary part, , corresponds to energy
dissipation that represents the bulk pinning hysteresis losses
of type-II superconductors that arises from the viscous flux
flow motion and hysteresis due to the pinning of flux vortices
• Several models have been proposed and developed to explore
the main features of χac(T) data and their dependencies on
ac field amplitudes, Hac, and frequencies [19-32]. The
simplest and oldest critical state models (CSMs) are the Bean
critical state model (BCSM) and Kim-Anderson model (KAM)
• In this work, the ACS data of Ru-1212 Gd polycrystalline
magnetic-superconductor were analyzed over the
temperature range (6–50 K) in order to investigate the
applicability of the ACS analytical models. In other words,
the main aim of the present paper is to check the general
agreement between the theoretical predictions ofand
relations with experimental data that may include additional
loss mechanisms like flow or flux-creep (FC).
2ed Physics Symposium May 8-9, 2007, Organized by the Physics Department, An-Najah University, Faculty of Science, Nablus, Palestine
Experimental
• Samples of Ru-1212 polycrystalline superconductor
were prepared following the two-step procedure
reported previously [1,2,8]. In the first step, Sr2116 was prepared from stoichiometric quantities
of RuO2, Gd2O3, and SrCO3. Then the mixed
powders were ground, calcined at 950 0C in air,
reground, milled, pressed into pellets and fired for
16 h at 1250 0C in air. In the second step, the
obtained Sr-2116 was mixed with CuO and the
mixture was ground, milled, pressed into pellets
and fired for 720 h at 1060 0C in flowing oxygen
atmosphere.
• The ACS measurements were performed by a
homemade susceptometer using a standard lock-in
amplifier technique. The measurements covered a
wide range of frequency (20-12500) Hz for different
field amplitudes that range between 0.5-25 G.
2ed Physics Symposium May 8-9, 2007, Organized by the Physics Department, An-Najah University, Faculty of Science, Nablus, Palestine
Results and discussion
1.00
0.98
c' (a.u)
0.96
22 Hz
100 Hz
500 Hz
1000 Hz
5000 Hz
0.94
0.92
0.90
0.88
0
10
20
30
40
c ' (a.u)
1.00
0.98
0.96
0.94
0.5 G
1.5 G
15 G
23 G
0.92
0.90
0.88
0
10
20
30
40
2ed Physics Symposium May 8-9, 2007, Organized by the Physics Department, An-Najah University, Faculty of Science, Nablus, Palestine
 This type of transition, which is characterized by a
steep drop in the χ' component of ACS, is known as the
intragrain transition.
In general, the intragrain
transition
corresponds
to
paramagneticsuperconductive (PM-SC) transition. Besides, this type
of dependence represents the transition from nearperfect screening to complete penetration of external.
ac magnetic field into the sample. Moreover, the linear
decrease of below the intra-grain temperature,,can be
interpreted on the basis of decreasing the JJ
penetration depth .
2ed Physics Symposium May 8-9, 2007, Organized by the Physics Department, An-Najah University, Faculty of Science, Nablus, Palestine
The temperature can be extracted from χ΄ dependencies on the frequencies of
the applied ac field using the crossing point of the two extrapolated linear
parts of above and below the transition (of the two straight lines of Fig. 2)
1.00
0.98
/
c (a.u)
0.96
0.94
TIntra
0.92
0.90
0
10
20
30
T (K)
40
50
60
2ed Physics Symposium May 8-9, 2007, Organized by the Physics Department, An-Najah University, Faculty of Science, Nablus, Palestine
A typical dependence of on ac field frequencies is shown in Fig. 3A. The measured
data showed almost a power-law behavior.
100
Tintra (K)

10
1
10
2
10
3
10
Frequency (Hz)
4
10
2ed Physics Symposium May 8-9, 2007, Organized by the Physics Department, An-Najah University, Faculty of Science, Nablus, Palestine
Additionally, the general behavior of curves shown in Fig. 3B, which
represents the dependence of on field amplitude, are quite different
from that expected for a bulk superconductor, i.e., from GinzburgLandau theory
30
25
20
Tintra (K)

15
10
5
0
0
5
10
15
B (G)
20
25
2ed Physics Symposium May 8-9, 2007, Organized by the Physics Department, An-Najah University, Faculty of Science, Nablus, Palestine
• Particularly, the uncommonly strong decrease of the
intragrain of at low field cannot be explained by
means of the bulk and homogeneous
superconductivity inside the grains. The observed
suppression rates for in Ru-1212 compound are an
indication of the intragrain superconductivity is
attributed to the phase-lock transition of nanoscale
JJA’s.
• Similarly, the peak of positive magnetoresistance
observed in Ru-1212 was quantitatively explained
under this assumption
2ed Physics Symposium May 8-9, 2007, Organized by the Physics Department, An-Najah University, Faculty of Science, Nablus, Palestine
More information about the intragrain superconducting state and its corresponding average transition
temperature, Tave, can be obtained from the temperature derivatives of χ΄curves, i.e. . The dependence of
on temperature between 10-50 K at different field frequencies and constant field amplitude of 0.5 G is
displayed in Fig. 4. The location of the average transition temperature, Tave, is generally represented by
the maximum of
versus temperature curves.
The nature of curves indicate the presence of a
superconducting transition between grains coupled by weak links, with a distribution of critical
temperatures, TC, and the superconducting transition within the grains. The superconducting transition is
generally connected with a magnetic phase transition.
1.2
1.0
12500 Hz
5000 Hz
100 Hz
H = 0.5 G
0.8
Intergranular
transition
dc' / dT

Intragranular
transition
0.6
0.4
DT
0.2
0.0
10
15
20
25
T (K)
30
35
40
2ed Physics Symposium May 8-9, 2007, Organized by the Physics Department, An-Najah University, Faculty of Science, Nablus, Palestine
•
•
•
The peak positions of plots in Fig. 4 occurred around T ~
27.8 K, 25.4 K, 22 K for f = 12.5 kHz, 5 kHz, and 100 Hz,
respectively. The obtained values of Tave were found to
range from 22 to 30 K. The low frequency values were
found to be in a good agreement with the values obtained
from the specific heat measurements.
Typical log-log plot of the frequency dependence of Tave
is exhibited in Fig. 5. Clearly, the general behavior of the
log-log dependence on Tave is almost linear. It should be
pointed out that Tave was defined as the intragrain
transition temperature based on both the size and the ac
field amplitude dependencies of the measured ACS in the
same sample.
The outcome of this study had shown that Tintra and Tave
exhibited the same field dependence, but the obtained
values of Tintra are higher than Tave by almost 2 K. This
is a clear indication that the two transition temperatures
are different and the samples might possess a weakcoupling limit similar to that between JJA’s.
2ed Physics Symposium May 8-9, 2007, Organized by the Physics Department, An-Najah University, Faculty of Science, Nablus, Palestine
•
The temperature transition width, ΔT, between points on curve had been chosen to
represent half of the maximum value of the first derivative and thus it can be considered
as a good quantitative measure of the transition width. At fixed field amplitude, this width
depends on the frequency where it decreases by increasing the frequency. In the present
data ΔT = 12 K at 100 Hz while at 12.5 kHz the width, ΔT, is about 9.6 K.
•
Tintra (K)
100
10
1
10
2
10
3
10
Frequency (Hz)
4
10
2ed Physics Symposium May 8-9, 2007, Organized by the Physics Department, An-Najah University, Faculty of Science, Nablus, Palestine
 The imaginary part of the ACS, , dependence
on
temperatures
at
different
field
frequencies and constant field amplitude (0.5
G) is exhibited in Fig. 6A, while Fig. 6B
displayed the dependence of χ˝(T) on field
amplitudes at 1 K Hz. Generally, a peak
around a certain temperature, known as the
inter-grain
transition
temperature,,
is
characterized by most of χ˝(T) curves. The
observed peak in χ˝(T) curve represents the
losses to the shielding current flowing in
between individual grains .
The can be
simply extracted from χ˝ dependencies on
field amplitudes and frequencies. The intergrain transition for Ru-1212 was found to
occur within 8 - 30 K. This relatively weak
intergrain
coupling
may
partially
be
attributed to heat treatment conditions.
2ed Physics Symposium May 8-9, 2007, Organized by the Physics Department, An-Najah University, Faculty of Science, Nablus, Palestine
1.0
c''(a.u)
0.8
0.6
22 Hz
100 Hz
500 Hz
1000 Hz
2000 Hz
5000 Hz
0.4
0.2
0.0
0
10
20
30
40
1.1
0.5 G
1.5 G
4.0 G
10 G
c" (a.u)
1.0
0.9
0.8
0.7
0.6
0
10
20
T(K)
30
40
2ed Physics Symposium May 8-9, 2007, Organized by the Physics Department, An-Najah University, Faculty of Science, Nablus, Palestine
The dependencies of on field frequencies at of 0.5 G and its dependence on field amplitudes at 1 KHz are
displayed in Figs. 7A and 7B, respectively. The dependencies of on frequencies and field amplitudes are
similar to those of. The results had shown that by increasing the frequency is increased, while it is
Tinter (K)
decreased by increasing field amplitude. The frequency
10
2
10
1
10
0
10
1
10
2
f (Hz)
10
3
10
4
24
Tinter(K)
18
12
6
0
0
5
10
H (G)
15
20
2ed Physics Symposium May 8-9, 2007, Organized by the Physics Department, An-Najah University, Faculty of Science, Nablus, Palestine
•
•
•
According to explanation of the FC model by Tinkham and Müller, when
the frequency is increased, the intergranular vortices have less time to
relax and then penetrate the superconductor during each cycle. In order
to reach full flux penetration, the effective intergranular pinning force
density must be weakened. Since the pinning force density is weakened
by increasing temperature, the, must increase with increasing frequency.
It appears from Fig. 7B that decreases steeply with an initial slope of ~ 8
K/G by increasing ac field amplitude. It should be pointed out here that
the maximum loss always takes place when the magnetic flux lines just
penetrate to the center of the sample. As the driving field amplitude
increases, larger screening currents are required to shield the applied
field and consequently decreasing This fraction of available links
diminishes as the external field is increased leading to sharper
transitions. Such type of behavior is typical for a granular
superconductor with weak intergranular JJA’s coupling. This is an
indication that Ru-1212 exhibits a strong intragrain granularity effects.
Granularity of Ru-1212 have been previously reported in the temperature
dependence of the resistivity measurement, which is more sensitive to
weak links across the grain boundaries, and it was attributed to either
structural defects or possible phase separation [7,12,17,30-31].
Accordingly, a JJAs model should be invoked to interpret the present
data.
An attempt has been made to fit the dependence of and on frequency
and field amplitudes. The dependence of both temperatures on angular
frequency, ω = 2πf, is found to fit an empirical equation of the form:

Ti  Tf 
 o



n
(1)
2ed Physics Symposium May 8-9, 2007, Organized by the Physics Department, An-Najah University, Faculty of Science, Nablus, Palestine
• The experimental inter-granular matrix susceptibility
could be extracted from the measured susceptibility
components and using the following equations [32-34]:
•
Here is effective volume fraction of superconducting
grains excluding a shell of thickness of order of the
London penetration depth and are the intragrain
susceptibility components. The values were estimated
using the method introduced by Ravi. The estimated
values of at T = 22, 24, 28 K are 0.31, 0.33, 0.34,
respectively. As it could be noted the fraction of
susceptibility χ′g or χ′i will depend mostly on the quality
of the sample; that is the grain size and grain contribution.
The average of the volume fraction of the grains fg in this
study is taken as 0.33. Using the value in eq. (3), the
experimental values were determined. Accordingly, the
ACS components can be rewritten as the summation of
granular susceptibility components: . Therefore, the ACS
component is divided as 1:2 between the granular ACS
components (the intra- and the inter-). The granular ACS
components of the investigated samples are displayed in
Fig. 8.
2ed Physics Symposium May 8-9, 2007, Organized by the Physics Department, An-Najah University, Faculty of Science, Nablus, Palestine
102
1.1
A
1.0
100
0.8
96
0.7
H = 3.88 G
f = 100 Hz
94
c" (a. u)
c' (a. u)
0.9
98
0.6
92
0
10
20
65
30
c'i
60
40
0.5
50
7.5
B
c"i
c' (a. u)
55
c" (a. u.)
6.0
H = 3.88 G
f = 100 Hz
50
4.5
c"g
45
40
3.0
c'g
35
30
1.5
0
10
20
30
T (K)
40
50
2ed Physics Symposium May 8-9, 2007, Organized by the Physics Department, An-Najah University, Faculty of Science, Nablus, Palestine
•
•
•
. Conclusion
The inter-, intra-transition temperatures are determined for the
magnetic Ru-1212 polycrystalline superconductor from ACS
measurements as function of temperature, frequency and field
amplitude. The inter- and intra-transition temperatures were
found to decrease with increasing field amplitudes and to
increase by increasing the field frequencies. This sort of
behavior is explained by assuming that the intragrain
superconductivity is due to a phase-lock transition of a
nanoscale JJA’s. The intra- and inter-grain transitions are
attributed to the paramagnetic-superconductive (PM-SC)
transition.
The nature of the temperature derivative of the real part of the
ACS curves indicated the presence of a superconducting
transition between grains, coupled by JJA’s weak links with a
distribution of critical temperatures, and the superconducting
transition within the grains. The observed suppression rates of
the transition temperatures in Ru-1212 magnetic
superconductor compound are in compatible of the nanoscale
JJA’s. This means that the ruthenate-cuprate grains were
actually JJA’s, in agreement with the phase separation model
[30]. Generally, the overall behavior of is very different from
what might be expected for a bulk superconductor, i.e., from
Ginzburg-Landau theory.
2ed Physics Symposium May 8-9, 2007, Organized by the Physics Department, An-Najah University, Faculty of Science, Nablus, Palestine
• Thank You For Your Attendence