High intrinsic flux pinning strength of BaFe2-xCoxAs2 superconductor
K. Vinod, Shilpam Sharma, A. T. Satya, C. S. Sundar and A. Bharathi*
Condensed Matter Physics Division, Materials Science Group,
Indira Gandhi Centre for Atomic Research, Kalpakkam, India - 603102
Abstract
The field dependence of flux pinning potential, U0, for under-doped, optimally doped and
over-doped Ba(Fe,Co)2As2 single crystals has been investigated. U0 is determined using
the Thermally Activated Flux Flow (TAFF) model, for both H || ab and H || c
configurations. The observed power law dependencies of U0 versus H suggest that for
fields upto 12 T for H || ab and 7 T for H || c, individual flux pinning, and for fields
beyond 7 T for H || c, collective pinning becomes operative. A comparison of U0 for the
Ba(Fe,Co)2As2 system with some other superconductors is presented.
Keywords: Ba(Fe,Co)2As2 superconductor, pinning potential, critical current density.
PACS code: 74.70.Xa, 74.25.F-, 74.25.Ha
*
Corresponding author
A. Bharathi
Condensed Matter Physics Division,Materials Science Group,
Indira Gandhi Center for Atomic Research,
Kalpakkam, 603102 India.Tel: 91 44 27480081, Fax: 91 44 27480081
E-mail: bharathi@igcar.gov.in
1
High transition temperature (TC), large upper critical field (HC2), high
irreversibility fields (Hirr), large critical current density (JC), low anisotropy and good
inter-granular connectivity are essential characteristics of superconducting materials for
magnet applications. The two layer Ba arsenide (Ba122) superconductors, whose
fundamental properties have been extensively investigated due to the availability of good
quality single crystals, seem to possess large HC2, Hirr and JC along with low anisotropy. 14
The high JC of 105-106 A/cm2 [2,3] in seemingly defect free single crystals of doped
BaFe2As2 (Ba122) is surprising and elicits questions on the origin of flux pinning centres
in these materials. To answer this, real space visualization of the flux line lattice has been
carried out using magneto-optical imaging, scanning tunneling spectroscopy and
scanning SQUID microscopy, 5-7 all of which show the presence of a disordered vortex
lattice, suggesting strong bulk pinning of vortices in these materials.5-7 Based on
polarized-light imaging, x-ray diffraction and magnetic measurements, it was argued3
that the presence of twin boundaries enhance flux pinning in the optimally doped sample
giving rise to large JC. In agreement with these findings, SQUID microscopy images of
the vortex lines suggest that twin boundaries act as barriers for the motion of the flux
lines.8 This however is inconsistent with the observation of large JC in the overdoped
regime where twinning is absent. 7 In addition, since coherence length in the Ba122
arsenides is about few nanometers, the efficacy of micrometer sized twin boundaries
acting as good flux pinning centres seems questionable.
Apart from direct imaging techniques, study of flux dynamics viz., the study of
the variation in the magnitude flux pinning potential (U0), under magnetic field
can
provide valuable information on the nature of flux pinning. In addition, the magnitude of
2
U0 is an important factor that can affect JC and Hirr and in turn determine the
technological worth of a superconducting material. In the weak pinning regime,
phenomenological theories 9,10 exist that predict that the activation energy to move a
bundle of a two dimensional array of rigid fluxons is inversely proportional to the linear
power of flux density (U0 ∝ φ0/B). This gets modified in the presence of thermal
vibration of each fluxon, resulting in U0∝ φ0/B0.5. 9,10The presence of inter fluxon
interaction is seen to reduce the exponent even further.10 In the opposite limit of flux
pinning at individual fluxons, U0 depends weakly on the magnetic field.11
Experimentally, few investigations of the variation of U0 with magnetic field have been
carried out in single crystals of arsenide superconductors.12,13 Studies in (Ba,K)Fe2As2
single crystals in fields upto 13 T, indicate a large field independent U0,12 whereas similar
work carried out in superconducting oxy-arsenide single crystals indicate a smaller U0,
whose field dependence changes at 3 T, suggestive of a changeover in the nature of
pinning.13 In the Ba(Fe,Co)2As2 system the magnitude of flux pinning potential and its
variation with magnetic field has not yet been investigated systematically, although the
search for pinning centres responsible for flux pinning and its correlation to high JC has
been examined.3,8 Here we report on measurements of pinning potentials and their
magnetic field dependencies for three different concentrations in the superconducting
single crystals of BaFe2-xCoxAs2, to highlight the effects due to disorder. The Co
concentrations belong to the under-doped (x=0.082), close to optimum doped (x=0.117)
and over-doped (x=0.143) parts of the phase diagram. The BaFe2-xCoxAs2
superconducting single crystals were prepared by slow cooling without any flux as
described in ref [14].
3
-6
-8
H || ab
H || c
x = 0.082
x = 0.082
-4
1T
2T
3T
4T
5T
6T
7T
8T
9T
10 T
11 T
12 T
ln (R)
ln (R)
-4
-6
-8
TAFF
region
-10
-10
0.06
0.08
0.10
-1
0.06
0.08
0.10
-1
1/T (K )
1/T (K )
FIG 1: (Color online) Arrhenius plot for the BaFe2-xCoxAs2 (x = 0.082) crystal for H || ab
and H || c directions. TAFF region occurs below the dashed line. The slope of the curve in
this region is used to determine U0.
In the thermally activated flux flow (TAFF) model, the temperature and field
dependent resistance is described by R(T,H) =R0exp[-U0/kBT], where R0 is a fitting
parameter, kB is the Boltzmann constant and U0 is activation energy (pinning potential)
for vortex bundle hopping.15 Our measurements employ a ~2ma current on crystals with
typical dimension of ~ 1 mm x 1 mm x 0.2 mm. This implies that the transport current
density is much smaller than JCKBT/U0, ensuring the
necessary condition for the
applicability of the TAFF model.15,16 U0 versus magnetic field, parallel to the ab plane (H
|| ab) and parallel to the c axis (H || c) were obtained for two set of crystals (S1 and S2),
for each Co composition. Fig.1 shows ln (R) vs 1/T for one of the samples with Co
fraction of x = 0.082, measured with H || ab and H || c directions. The observation of
linear dependence close to the downset of the superconducting transitions, below the
4
dashed line indicated in Fig.1, viz., for R(T) < 0.1Rn, where Rn is the normal state
resistance, indicates that TAFF dominates the resistivity behaviour at these temperatures.
From measurements of the slope of each of these curves [U0 = -d(ln R)/d(1/T)], U0 at the
particular applied field is obtained.
S1
S2
x = 0.082
x = 0.117 1000
x = 0.143
U0 (meV)
1000
100
100
(b) H || c
(a) H || ab
1
10
μ0H (T)
1
μ0H (T)
10
FIG 2 : (Color online) Pinning potential, U0 obtained from R(T,H), for the x = 0.082, x =
0.117 and x = 0.143 BaFe2-xCoxAs2 samples for (a) H || ab and (b) H ||c directions. The
open and filled symbols correspond to measurements on two crystals (S1 & S2), for each
composition. Solid lines shows fit with U0 ∝ H-n, and the fit shows change in the
exponent ‘n’ at higher fields for the H || c direction.
The U0 values in the three Co substituted samples, for H || ab and H ||c, are
compared in Fig. 2. The agreement of the U0 in two sets of samples for each composition
testifies the reliability of the data. It is clear from Fig. 2 that U0 is the highest for the
optimally doped sample. Further, it is notable that for the optimally and over doped Co
concentrations the value of U0 is higher for the H || ab direction as compared to the H || c
5
direction. Whereas, for the under doped composition, U0 for H || c direction is slightly
higher compared to that in the H || ab direction at lower fields. The larger value of U0 for
H || ab compared to that for H || c observed in the optimum and overdoped samples, could
arise on account of the larger HC2 along the H || ab direction (since U0 depends on the
superconducting condensation energy.9) The variation in the magnitude of U0 versus Co
concentrations at a given field shown in Fig. 2 seems to be consistent with the JC
variation observed with Co concentration.3
Table 1 : Value of the exponent ‘n’ for U0 ∝ H-n, for the three Co , for H || ab and H || c
directions.
Value of the exponent ‘n’
Sample
H || ab
H || c
H<7T
H>7T
x = 0.082
0.22 ± 0.02
0.34 ± 0.04
1.19 ± 0.07
x = 0.117
0.27 ± 0.02
0.36 ± 0.04
0.88 ± 0.19
x = 0.143
0.28 ± 0.03
0.29 ± 0.03
0.65 ± 0.09
It is evident from the Fig. 2 that U0 fits to a single power law for H || ab and is
proportional to H-n with n ~ 0.25 (see table.1). However, for the H || c direction U0
shows a faster variation with H, with different power-law behaviours, in two field ranges.
The exponent for the H || c, is n=0.29-0.36 at lower fields and changes to n=0.65-1.19
beyond ~ 7 T, for all the three Co concentrations (see table.1). It is clear from table.1 that
for H || c and for magnetic fields >7 T, the field exponent is close to 1 for the lowest
concentration of Co. The observation of an exponent of n~1 implies that weak pinning of
6
flux bundles 9,10 dominates the magnetic field dependence for H || c, for the lowest Co
concentration. The exponent in this field regime shows a clear decrease with increase in
Co concentration, viz., the high field exponent reduces from 1 to 0.65. Since more
disorder is introduced due to Co addition, it is likely that flux pinning from individual
pinning centres starts competing with bulk pinning, leading to the reduction of the
exponent. For H || c upto 7 T, the field exponent of U0 is even more reduced with n ~
0.33-0.29, as compared to that in fields >7 T, implying again that individual pinning
from disorder dominates in this regime. This is understandable, since inter-fluxon
interactions would reduce with decrease in flux density at lower fields and individual
pinning of flux lines would start to dominate. Along the H || ab direction the field
exponent is ~0.25 upto fields of 12 T, which again is closer to the exponent expected for
individual flux pinning rather than for bulk pinning.
The results of table.1 suggest that the field exponent of U0 depends on the
interplay between robustness of superconducting order, individual flux pinning strength
and bulk flux pinning strength. At low flux density and in the presence of a robust
superconducting order, individual flux pinning dominates and U0 is weakly dependent on
H. 9,10 At higher field density inter fluxon interactions start playing a role and U0 is
determined by collective behavior of fluxons and the field exponent becomes larger
although,
moderated by the degree of disorder. This is brought out nicely from the U0
behaviour seen for H⎟⎟ c and at fields greater than 7 T, where a gradual decrease in ‘n’ is
clearly seen with increase in Co concentration. These results point out that the currently
available flux pinning models are inadequate to understand the behaviour of field
7
exponent of U0 and models that include the effect of disorder on bulk flux pinning
exponent need to be formulated.
4
10
4
U0 (meV)
H || c
H || ab
Ba(Fe,Ni)2As2 [17]
NdFeAsOF [18]
Bi-2212 [15]
MgB2 [19]
Ba(Fe,Co)2As2
(present work, x=0.117)
(Ba,K)Fe2As2 [12]
3
10
10
2
3
10
2
10
10
1
10
μ0 H (T)
1
μ0 H (T)
10
FIG 3: (Color online) Field dependence of U0 for different types of superconductors
compared with optimum doped Ba(Fe,Co)2As2 sample. Data for other superconductors
are taken from literature.12,15,17-19
A comparison of the U0 (H) obtained from the Co doped Ba122 samples with that
observed in other FeAs based superconductors is shown in Fig. 3. It is evident from the
Fig. 3a that U0 in the optimally doped sample, viz., x=0.117 from the present set of
measurements has the highest pinning potential for H || ab direction. The figure also
suggests that other Ba122 superconductors viz., (Ba,K)Fe2As212 and Ba(Fe,Ni)2As217 have
large U0 which are weakly dependent on field. In comparison the U0 values of the oxyarsenide are smaller. The U0 variation for H || c for the MgB2 thin film is strongly
dependent on field, although the low field U0 value is comparable to that in the Ba122
8
compounds. In the HTS compound Bi2122, on the other hand the U0 values are much
smaller ascompared to that seen in the Ba122 compounds.
From the present study and flux imaging studies, it is compelling to suggest the
large intrinsic pinning seen in the Co doped Ba122 arises due to the strong disorder
induced by Co atoms. Recent band structure calculations 20 have suggested that all the
extra electrons from the Co atom in the Fe sublattice tend to be confined to its muffin tin
radius, resulting in a strong disorder around the dopant atom. The Co atom also induces
an additional moment of 0.5 μB/cell creating magnetic disorder, which due to magnetic
exchange interaction with neighbouring Fe spreads to sizes larger than four unit cells.21
The latter could result in the alteration of the superconducting order parameter around the
substituting Co atom and being magnetic in nature could give rise to strong pinning.
This is consistent with recent bitter decoration studies, which suggest that strong flux
pinning could arise due of nano-scale spatial in-homogeneities in the superfluid density
intrinsically, present in all arsenide superconductors.22
In summary, the flux pinning potential of Co doped BaFe2As2 superconductor has
been investigated form magneto-resistance measurements. The Ba(Fe,Co)2As2
superconductor has very high intrinsic pinning potential that is field independent. This
could result in large field independent JC observed in these systems. Further systematic
investigations of the pinning potentials for other substitutions in BaFe2As2, correlated
with local electron/spin density calculations may help clarify the intrigue of high intrinsic
pinning strength observed in the Ba122 arsenide superconductors.
Vinod K acknowledges Department of Atomic Energy (DAE), India for the K.S.
Krishnan Research Associateship.
9
1.
D. C. Johnston, Advances in Physics 59, 803 (2010).
2.
D. L. Sun, Y. Liu, and C. T. Lin, Phys. Rev. B 80, 144515 (2009)
3.
R. Prozorov, M. A. Tanatar, N. Ni, A. Kreyssig, S. Nandi, S. L. Bud’ko, A. I.
Goldman, and P. C. Canfield, Phys. Rev. B 80, 174517 (2009).
4.
M. Kano, Y. Kohama, D. Graf, F. Balakirev, A. S. Sefat, M. A. Mcguire, B. C.
Sales, D. Mandrus, and S. W. Tozer, J. Phys. Soc. Jpn. 78, 084719 (2009).
5.
M. R. Eskildsen, L. Ya Vinnikov, T. D. Blasius, I. S. Veshchunov, T. M. Artemova,
J. M. Densmore, C. D. Dewhurst, N. Ni, A. Kreyssig, S. L. Bud'ko, P. C. Canfield,
and A. I. Goldman, Phys. Rev. B 79, 100501 (2009).
6.
R. Kopeliansky, A. Shaulov, B. Ya Shapiro, Y. Yeshurun, B. Rosenstein, J. J. Tu, L.
J. Li, G. H. Cao, and Z. A. Xu, Phys. Rev. B 81, 092504 (2010).
7.
D. S. Inosov, T. Shapoval, V. Neu, U. Wolff, J. S. White, S. Haindl, J. T. Park, D. L.
Sun, C. T. Lin, E. M. Forgan, M. S. Viazovska, J. H. Kim, M. Laver, K. Nenkov, O.
Khvostikova, S. Kühnemann, and V. Hinkov, Phys. Rev. B 81, 014513 (2010).
8.
B. Kalisky, J. R. Kirtley, J. G. Analytis, J.-H. Chu, I. R. Fisher, and K. A. Moler
Phys. Rev. B 83, 064511 (2011).
9.
M. Tinkham, Phys. Rev. Lett. 61, 1658 (1988).
10.
Y. Yeshurun, and A. P. Malozemoff, Phys. Rev. Lett. 60, 2202 (1988).
11.
G. Blatter, M. V. Feigel’man, V. B. Geshkenbein, A. I. Larkin, and V. M. Vinokur,
Rev. Mod. Phys. 66, 1125 (1994).
12.
X. L. Wang, S. R. Ghorbani, S. I. Lee, S. X. Dou, C. T. Lin, T. H. Johansen, K. H.
Muller, Z. X. Cheng, G. Peleckis, M. Shabazi, A. J. Qviller, V. V. Yurchenko, G. L.
Sun, and D. L. Sun, Phys. Rev. B 82, 024525 (2010).
10
13.
H. S. Lee, M. Bartkowiak, J. S. Kim, and H. J. Lee, Phys. Rev. B 82, 104523 (2010).
14.
K. Vinod, A. T. Satya, Shilpam Sharma, C. S. Sundar and A. Bharathi, Phys. Rev. B
84, 012502 (2011).
15.
T. T. M. Palstra, B. Batlogg, R. B. van Dover, L. F. Schneemeyer, and J. V.
Waszczak, Phys. Rev. B 41, 6621 (1990).
16.
V. Geshkenbein, A. Larkin, M. Feigel'man, and V. Vinokur, Physica C 162-164,
239 (1989).
17.
M. Shahbazi, X. L. Wang, Z. W. Lin, J. G. Zhu, S. X. Dou, and K. Y. Choi, J. Appl.
Phys. 109, 07E151 (2011).
18.
J. Jaroszynski, F. Hunte, L. Balicas, Y. jung Jo, I. Raicevic, A. Gurevich, D. C.
Larbalestier, F. F. Balakirev, L. Fang, P. Cheng, Y. Jia, and H. H. Wen, Phys. Rev.
B 78, 174523 (2008).
19.
A. Sidorenko, V. Zdravkov, V. Ryazanov, S. Horn, S. Klimm, R. Tidecks, A.
Wixforth, Th. Koch, and Th. Schimmel, Phil. Mag. 85, 1783 (2005).
20.
H. Wadati, I. Elfimov, and G. A. Sawatzky, Phys. Rev. Lett. 105, 157004 (2010).
21.
F. Kemper, C. Cao, P. J. Hirschfeld, and H.-P. Cheng, Phys. Rev. B 80, 104511
(2009).
22.
S. Demirdis and C.J. van der Beek, Y. Fasano, N.R. Cejas Bolecek, H. Pastoriza, D.
Colson and F. Rullier-Albenque, cond-mat.arXiv:1106.6065v1
11