Anisotropy of critical current density in c-axis-oriented MgB
2
thin films
Shashwati Sen, Ajay Singh, D. K. Aswal, S. K. Gupta,* J. V. Yakhmi, and V. C. Sahni
Technical Physics & Prototype Engineering Division, Bhabha Atomic Research Center, Mumbai 400 085, India
Eun-Mi Choi, Hyeong-Jin Kim, Kijoon H. P. Kim, Hyun-Sook Lee, W. N. Kang, and Sung-Ik Lee
National Creative Research Initiative Center for Superconductivity, Department of Physics,
Pohang University of Science and Technology, Pohang 790-784, Republic of Korea
Received 1 March 2002; published 6 June 2002
The critical current density ( J
c
) has been measured in c-axis oriented MgB
2
thin films as a function of
applied magnetic field H and angle ( ) between H and the ab plane. The measurements have been carried out
at various temperatures between 32 and 38 K. The field and angular dependence of J
c
indicates pinning by
point pinning centers and is in a good agreement with the predictions of anisotropic Ginzburg-Landau model.
Anisotropy parameter ( ) of 2.55 was determined from scaling behavior of J
c
.
DOI: 10.1103/PhysRevB.65.214521 PACS numbers: 74.60.Ge, 74.76.-w, 74.70.Ad
INTRODUCTION
Following the recent discovery of superconductivity in
MgB
2
with a critical temperature T
c
of 39 K, a large number
of studies have been carried out to establish fundamental
properties of this material so as to understand the mechanism
of superconductivity.
1–5
MgB
2
is found to have a hexagonal
crystal structure and band-structure calculations indicate that
quasi-2D two-dimensional boron planes are responsible for
superconductivity.
1
The material shows anisotropic super-
conducting properties and various measurements indicate an
upper critical field H
c 2 ab
(0) between 12 and 40 T and an
anisotropy ratio of 1.2–13.
2–4
Fluctuation conductivity
measurements made in thin films of MgB
2
show two-
dimensional nucleation of superconductivity.
1
Thin films of
MgB
2
show very high values of critical current density J
c
and films with c-axis oriented normal to the substrate show
magnetization J
c
of 1.610
7
A/cm
2
in zero field and 1
10
5
A/cm
2
in a field of 5 T at a temperature of 15 K.
5
While this shows the potential of MgB
2
for practical appli-
cations, measurement of critical current anisotropy to under-
stand flux-pinning mechanism has not been reported. Such a
study is of considerable importance for various applications
of the material and we report here results of such a study.
The study of current voltage ( I -V ) characteristics and
critical current I
c
of superconductors as a function of various
parameters, such as magnetic field H, temperature and angle
between field and crystal axis or current direction, has been
carried out in many conventional and high-temperature su-
perconductors. In many investigations made for conventional
isotropic superconductors, field and temperature dependence
of critical current density has been analyzed in terms of criti-
cal state model.
6,7
In terms of this model, the critical current
is determined by competition between Lorentz force due to
applied current and pinning forces on the vortices. For mag-
netic field H applied normal to the current direction, critical
current density J
c
is related to pinning force per unit volume
F
p
as F
p
=J
c
H . The dependence of J
c
on magnetic field and
temperature is seen to have similar behavior over a wide
range of microstructure, field, and temperatures and the scal-
ing behavior of J
c
and F
p
is generally given by
7,8
F
p
=J
c
H =A H
c 2
n
H / H
c 2
m
1 -H / H
c 2
l
. 1
High-temperature superconductors are highly anisotropic
and show a rich variety of interesting behavior. The critical
current has a strong dependence on the orientation of mag-
netic field with respect to crystal axis. Highly anisotropic
superconductor, Bi
2
Sr
2
CaCu
2
O
x
BSCCO displays a 2D su-
perconducting behavior where superconducting CuO
2
planes
are separated by non-superconducting or weakly supercon-
ducting intermediate layers. The material shows very high J
c
for H
ab plane compared to that for H
c axis. Measurements
as a function of angle show that J
c
is determined by the
component of magnetic field along the c axis. This arises
because the vortices parallel to the ab plane are strongly
pinned by weakly superconducting layers between CuO
2
planes. This is called intrinsic pinning and has been used to
explain angular dependence of J
c
.
9
Another high-
temperature superconductor, YBa
2
Cu
3
O
x
YBCO, has
lower anisotropy, and many of its physical properties can be
understood in terms of anisotropic Ginzburg-Landau GL
model. Blatter et al.
10
have shown that the anisotropic prop-
erties of superconductors with anisotropy parameter )
scale with reduced magnetic field
H , where
= sin
2
+
2
cos
2
2
is angle between H and the ab plane and =1/
=H
c 2c
/ H
c 2ab
.
Gupta et al.
11
have shown that I -V characteristics in
YBCO thin films scale with
H except at small angles (
10°) where the effect of intrinsic pinning has been ob-
served. Similarly, Braithwaite et al.
12
have found that critical
current scales with
H indicating agreement with aniso-
tropic GL model. Above scaling theory of Blatter et al.
10
does not give a functional dependence of J
c
with H and .
Watanabe et al.
8
have obtained such a functional dependence
using the conventional scaling law of Eq. 1, assuming that
the anisotropy in J
c
depends on the anisotropy of upper criti-
cal magnetic field H
c 2
( ).
8,13
This scaling behavior of J
c
is
given by
PHYSICAL REVIEW B, VOLUME 65, 214521
0163-1829/2002/6521/2145215/$20.00 ©2002 The American Physical Society 65 214521-1