Angular dependence of pinning potential, upper critical field, and irreversibility field in underdoped BaFe1.9Co0.1As 2 single crystal

Article abstract of DOI:10.1063/1.3692582

Underdoped BaFe_1.9Co_0.1As₂ single crystal was studied by angular dependence of magneto-transport at fields up to 13 T over a wide range of temperature. Our results show that pinning potential, U _o, decreases slightly for 45 and remains constant for 45, while the upper critical field, H_c2, and the irreversibility field, H _irr, increase with . According to anisotropic Ginzburg-Landau theory, the anisotropy was determined by scaling the resistivity under different magnetic fields below the superconducting critical temperature, T_c. Anisotropy, , in the underdoped crystal is found to be temperature dependent and decreases from 2.1 to 1.8 for as T is reduced from 17 to 12.5 K.

Full text of DOI:10.1063/1.3692582

Angular dependence of pinning potential, upper critical field, and irreversibility field in
underdoped BaFe1.9Co0.1As2 single crystal
M. Shahbazi, X. L. Wang, S. R. Ghorbani, S. X. Dou, and K. Y. Choi
Citation: Applied Physics Letters 100, 102601 (2012); doi: 10.1063/1.3692582
View online: http://dx.doi.org/10.1063/1.3692582
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APPLIED PHYSICS LETTERS 100, 102601 (2012)
Angular dependence of pinning potential, upper critical field, and
irreversibility field in underdoped BaFe1.9Co0.1As2 single crystal
M. Shahbazi,1 X. L. Wang,1,a) S. R. Ghorbani,1,2 S. X. Dou,1 and K. Y. Choi3
1Institute for Superconducting and Electronic Materials, Faculty of Engineering, Australian Institute
for Innovative Materials, University of Wollongong, North Wollongong, NSW 2519, Australia
2Department of Physics, Sabzevar Tarbiat Moallem University, P.O. Box 397, Sabzevar, Iran
3Frontier Physics Research Division and Department of Physics and Astronomy, Seoul National University,
Seoul 151-747, South Korea
(Received 1 December 2011; accepted 19 February 2012; published online 7 March 2012)
Underdoped BaFe1.9Co0.1As2 single crystal was studied by angular dependence of
magneto-transport at fields up to 13 T over a wide range of temperature. Our results show that
pinning potential, Uo, decreases slightly for h ꢀ 45ꢁ and remains constant for h ꢂ 45ꢁ, while
the upper critical field, Hc2, and the irreversibility field, Hirr, increase with h. According to
anisotropic Ginzburg-Landau theory, the anisotropy was determined by scaling the resistivity
under different magnetic fields below the superconducting critical temperature, Tc. Anisotropy,
C, in the underdoped crystal is found to be temperature dependent and decreases from
C
V
2.1 to 1.8 for as T is reduced from 17 to 12.5 K. 2012 American Institute of Physics.
[http://dx.doi.org/10.1063/1.3692582]
The thermal activation behaviour of vortices in super-
conductors determines their magneto-transport properties,
which are critical for practical applications. In highly aniso-
tropic cuprates, a magnetic field perpendicular to the super-
conducting layers penetrates in the form of pancake vortices,
while a parallel field creates Josephson vortices.1 The inter-
action between pancake vortices and Josephson vortices cre-
ates vortex chains2 or Josephson vortices decorated by
pancake vortices3 when the magnetic field is tilted. The pin-
ning potential in cuprates is highly anisotropic and strongly
field dependent due to the strong thermally activated behav-
iour of two-dimensional (2D) pancake vortices.
Iron based superconductors4 exhibit relatively high tran-
sition temperature, Tc, very high upper critical field,5 Hc2,
and relatively low anisotropy.6–9 Among pnictide supercon-
ductors, Ba-122 compounds have typical 2D layered crystal
structure. However, they show nearly isotropic superconduc-
tivity6 and very high intrinsic pinning potential, which is
weakly field dependent.10 These unique futures make the
122 superconductors more favourable for practical applica-
tion than other pnictide superconductors.
angle and field. So far, there has been no report on the angu-
lar dependence of these parameters in any pnictide supercon-
ductors. In this letter, we report the angular dependence of
the upper critical field, the irreversibility field, and the pin-
ning potential of underdoped BaFe1.9Co0.1As2 single crystal
by measuring magneto-transport at different magnetic fields
and angles. Furthermore, by scaling the angular dependence
of the resistance, based on the anisotropic Ginzburg-Landau
(GL) theory, the anisotropy value (C) was determined for
different temperatures. Our results show that the pinning
potential, Uo, is strongly angle dependent for h ꢀ 45ꢁ and
almost angle independent for h ꢂ 45ꢁ, while both Hc2 and
H
irr increase monotonically with increasing angle.
The single crystal of BaFe1.9Co0.1As2 was grown using
the high temperature self-flux method. FeAs and CoAs were
prepared by placing a mixture of As powder and Fe/Co pow-
der in a quartz tube and reacting it at 600 ꢁC for 10 h after it
had been heated to 600 ꢁC for 17 h. A mixture of FeAs/CoAs
and Ba pieces was then placed in an alumina crucible. The
whole assembly was sealed in a large quartz tube and heated
to 1180 ꢁC for 15 h, which was followed by a reaction at
1180 ꢁC for 10 h.16 The as-grown single crystal was cleaved
and cut into a rectangular shape for measurements. The
transport properties were measured over a wide range of
temperature and magnetic fields up to 13 T with applied cur-
rent of 5 mA, using a physical properties measurement sys-
tem (PPMS, quantum design). The current was applied in the
ab plane. The angular dependence of the resistivity was
measured using the 13 T PPMS, with the angle, h, varied
from 0ꢁ to 180ꢁ, where h ¼ 0ꢁ corresponded to the configura-
tion of H//c and h ¼ 90ꢁ to H//ab, respectively.
Thermally activated flux flow has been studied in
11
NdFeAsO0.7F0.3
,
Ba0.72K0.28Fe2As2,10 BaFe1.9Ni0.1As2,12
and Tl0.58Rb0.42Fe1.72Se2 (Ref. 13) single crystals for H//ab
and H//c. Very recently, studies of the angular dependence
of the transport critical current density, Jc, have indicated
that the Jc decreases monotonically with angle, h, for
h < 90ꢁ, where h is defined as the angle between the mag-
netic field and the c-axis. The ratio of Jc(H//ab)/Jc(H//
c) ¼ 7.5 or 1.8 at H ¼ 1 T and T ¼ 4.2 K for La-1111 (Ref.
14) and Co-122 (Ref. 15) thin film, respectively. It should be
noted that the determination of the angular dependence of
the pinning potential, Hc2, and the irreversibility field, Hirr,
are important for understanding how Jc changes with both
The temperature dependence of the in-plane resistivity
of the underdoped BaFe1.9Co0.1As2 single crystal is shown in
Fig. 1. The resistivity decreases with decreasing temperature
from 300 K to 50 K, supporting metallic behaviour of this
compound. The resistivity increases with further decreasing
temperature and shows an anomaly at 49 K due to a
a)Author to whom correspondence should be addressed. Electronic mail:
xiaolin@uow.edu.au.
C
V
0003-6951/2012/100(10)/102601/4/$30.00
100, 102601-1
2012 American Institute of Physics
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102601-2
Shahbazi et al.
Appl. Phys. Lett. 100, 102601 (2012)
FIG. 3. (Color online) (a) Temperature dependence of resistance at different
magnetic fields for h ¼ 45ꢁ where h is the angles between the applied mag-
netic field and the c-axis. (b) Arrhenius plots of the resistivity at the same
angles in underdoped BaFe1.9Co0.1As2 single crystal.
able compared to estimating the anisotropy using the ratio of
H
c2 in the ab plane to that along the c-axis.
FIG. 1. (Color online) Temperature dependence of the in-plane resistivity of
BaFe1.9Co0.1As2. The inset shows an enlargement of the region with
T ꢀ 35 K and a schematic diagram of the sample.
The results of magneto-transport measurements at
h ¼ 45ꢁ is shown in Fig. 3(a) where h is the angles between
the applied magnetic field and the c-axis. According to the
thermally activated flux flow model, the resistance can be
described as
magnetic/structural phase transition.17 The Tc
and Tc(0)
onset
were determined to be 17.4 and 15.2 K, respectively.
The angular dependence of the resistance at T ¼ 17 K is
shown in Figure 2(a). All the curves show a symmetric dip-
like structure, with a minimum at 90ꢁ and maximum resist-
ance at 0ꢁ and 180ꢁ. The normal state resistance decreases
with decreasing magnetic field and temperature, due to the
enhancement of the superconducting state. The angular de-
pendence of resistance is not very sharp with varying field
and temperature, possibly due to the moderate anisotropy of
the BaFe1.9Co0.1As2 sample, which has also been reported in
Nd-1111 single crystals.18 Similar behaviour observed at
T ¼ 15 and 12.5 K.
ꢀ
ꢁ
JHVL
T
R ¼ ð2t0LH=JÞsinh
ejc0HVL=T
;
(1)
where v0 is the attempt frequency for flux bundle hopping, L
is the hopping distance, J is the applied current density, Jc0 is
the critical current density at 0 T, and V is the bundle vol-
ume.21 If JHVL/T ꢃ 1, Eq. (1) can be written as
R ¼ ð2RcU=TÞeꢄU=T
;
(2)
where U ¼ Jc0HVL is the thermally activated energy and the
critical resistance, Rc ¼ v0LH/Jc0. Assuming that 2RcU/T is a
temperature independent constant, defined as R0 and
U ¼ Uo(1-T/Tc) then Eq. (2) can be simplified as the Arrhe-
nius equation
In layered superconductors, the variation in the super-
conducting order parameter, w, can be described by ðW/ðz
when the order parameter is quasi-continuous across the
neighbouring layers. Therefore, the anisotropic Ginzburg-
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
2
ab
Landau approximation, H = sin h þ C cos2h, can be used
c2
to estimate the anisotropy values for our sample. The angular
ln RðT; HÞ ¼ ln R0 ꢄ U0=T;
dependence of the resistance can be scaled as R ¼ R (0)f(H/
c2
19
). Then, the resistance measured under different mag-
GL
Therefore, the activation energy, Uo(B), is the slope of the
lower part of the curve in the Arrhenius plot.
H
netic fields should collapse into one curve at a certain tem-
perature if the C parameter is properly scaled. The results of
this scaling at T ¼ 17 K is shown in Figure 2(b). The esti-
mated anisotropy value, is 1.8 for T ¼ 12.5 K, 1.9 for
T ¼ 15 K, and 2.1 for T ¼ 17 K. The obtained anisotropy val-
ues are very close to the reported value of 2 at T ¼ Tc for
BaFe2-xCoxAs2 single crystals.20 The anisotropy values
which are obtained from this rescaling analysis are more reli-
In order to study the flux motion in BaFe1.9Co0.1As2
single crystal, we plot the electrical resistance as a function of
1/T at different magnetic fields up to 7 T and different angles
between the applied magnetic field and the c-axis. Fig. 3(b)
shows the Arrhenius plot of the resistance for h ¼ 45ꢁ. The lin-
ear dependence of ln R on 1/T in the lower part of the curves
indicates that this part can be described by the thermally
FIG. 2. (Color online) (a) The angular
dependence of the magnetoresistance at
T ¼ 17 K. (b) Scaling of the resistance as
a
function of H(sin2h þ C2cos2h)1/2
based on GL theory at T ¼ 17 K.
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102601-3
Shahbazi et al.
Appl. Phys. Lett. 100, 102601 (2012)
FIG. 4. (a) (Color online) Field depend-
ence of Uo for BaFe1.9Co0.1As2 single
crystal. (b) Angular dependence of pin-
ning potential for different magnetic
fields.
activated flux flow model.11 Similar measurements were per-
formed for several other angles, from 0ꢁ up to 90ꢁ, and Uo(B)
was calculated from the corresponding Arrhenius plots.
orthorhombic could act as barriers to vortex motion, result-
ing in the higher Uo value for H//c (Refs. 23 and 24) com-
pared to that for H//ab.
Fig. 4(a) shows the magnetic field dependence of Uo for
H//c and H//ab in underdoped BaFe1.9Co0.1As2 single crystal.
The best fit of the experimental data yields pinning potential
values ranging from Uo/kB ¼ 2900 K to 1900 K, where kB is
the Boltzmann constant, for H//c and H//ab, respectively, at
the low magnetic field of 0.1 T. These values are comparable
to the reported values of Uo ¼ 3000-4000 K for NdFeA-
sO0.82F0.18 single crystals.11 For comparison, we also
included the Uo for Bi-2212 single crystal in Fig. 4(a). The
Uo value for underdoped BaFe1.9Co0.1As2 is three times
higher than for Bi-2212 single crystal.22 However, this value
is lower than the reported value of 9100 K for Ba0.72K0.28
Fe2As2 single crystal10 for H//ab. The Uo value for our
underdoped BaFe1.9Co0.1As2 crystal with H//c exhibits a
weak power-law dependence (Uo ! Hꢄ0.15) for H < 3 T,
where single vortex pinning dominates, followed by a
power-law decrease with Uo ! Hꢄ0.81, indicating collective
pinning at higher fields, H > 3 T. The pinning potential val-
ues decrease when the sample is rotated from H//c to H//ab.
It should be noted that the Uo decreases slightly for
0 < h ꢀ 45ꢁ, and then remains constant for h ꢂ 45ꢁ
(Fig. 4(b)). Possibly, twin boundaries which can form below
the temperature of the structural transition from tetragonal to
The critical current density, Jc, vs. magnetic field is shown
in Fig. 5(a). Jc was calculated from the magnetic hysteresis
data at T ¼ 2 and 4.2 K by using the extended Bean model
Jc ¼ 20 ꢅ DM=V=ðað1 ꢄ a=3bÞÞ with a < b;
where a and b are the sample dimensions, V is the sample
volume, and DM is the height of the magnetization loop. The
Jc is as high as 1.7 ꢅ 105 and 1.5 ꢅ 105 A/cm2 at T ¼ 2 and
4.2 K in zero magnetic fields, respectively. The Jc decreases
with increasing magnetic field up to 1 T and after that
become nearly field independent which is related to rela-
tively high pinning potential and weakly anisotropic property
in BaFe1.9Co0.1As2 single crystal.
The upper critical field, Hc2, is characterized as the field
at which the resistivity becomes 90% of the normal state re-
sistivity; while the irreversibility field, Hirr, is defined by
10% of the normal state resistivity. Figure 5(b) shows Hc2
and Hirr as functions of temperature for different angles
between the field and the c-axis. From Fig. 5(c), the Hc2 and
Hirr follow the same trend with angle for h > 45ꢁ.The esti-
mated slopes dHc2ab/dT and dHirrab/dT are 4.8 and 3.79 T/K
for H//ab. The dHc2ab/dT is in good agreement with the
reported value of dHc2ab/dT ¼ 4.9 T/K.20 The slopes decrease
as the sample is rotated from 0ꢁ to 90ꢁ (Fig. 5(d)), which is
similar to the trend of Uo with angle.
In summary, we have investigated the angular depend-
ence of Uo, Hc2, and Hirr for underdoped BaFe1.9Co0.1As2
single crystal. Uo decreases while Hc2 and Hirr increase with
angle from H//c to H//ab. The anisotropy parameter
decreased from 2.1 to 1.8 as T decreased from 17 to 12.5 K,
using the anisotropic GL theory.
This work is supported by the Australian Research
Council (ARC) through Discovery Projects DP 1094073 and
DP0558753.
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