PHYSICAL REVIEW B 83, 134514 (2011)
Critical current densities in ultrathin Ba(Fe,Co)
2
As
2
microbridges
D. Rall,
1,2,*
K. Il’in,
2
K. Iida,
3
S. Haindl,
3
F. Kurth,
3
T. Thersleff,
3
L. Schultz,
3
B. Holzapfel,
3
and M. Siegel
2
1
Lichttechnisches Institut (LTI), Karlsruher Institut f¨ ur Technologie, Engesserstrasse 13, D-76131 Karlsruhe, Germany
2
Institut f ¨ ur Mikro- und Nanoelektronische Systeme (IMS), Karlsruher Institut f¨ ur Technologie, Hertzstrasse 16, D-76187 Karlsruhe, Germany
3
Institute for Metallic Materials (IMW), IFW Dresden, P.O. Box 270116, D-01171 Dresden, Germany
(Received 8 December 2010; published 18 April 2011)
The critical current density, j
C
, in Ba(Fe,Co)
2
As
2
thin-film microbridges was evaluated from current-voltage
characteristics measured using a standard four-probe technique. The 90-nm-thick films were deposited by pulsed
laser deposition on heated (La,Sr)(Al,Ta)O
3
substrates and patterned by means of photolithography and ion-
milling techniques. The resulting microbridges show a good long-term stability and only minor degradation of
the superconducting properties with respect to as-deposited films. The self-field j
C
at T = 4.2 K reaches a value
of about 3 MA/cm
2
. The temperature dependence of j
C
is described by (1 − T/T
C
)
1.5
, which is identical to
the Ginzburg-Landau theory for the depairing critical current, in the wide temperature range 0.4 <T/T
C
< 1.
Expulsion of the magnetic vortices is considered to be the mechanism responsible for overcoming Likharev’s
limit, where the width of the microbridge must be smaller than 4.4ξ
GL
(T ) to observe the depairing critical current.
DOI: 10.1103/PhysRevB.83.134514 PACS number(s): 74.25.Sv, 74.25.F−, 74.70.Xa, 74.78.−w
I. INTRODUCTION
Superconducting thin films offer a unique opportunity to
study mesoscopic phenomena arising from a reduction in
dimensionality since quasi-two-dimensional or even quasi-
one-dimensional experimental situations can be achieved by
thin-film structures with decreasing thickness. Low dimen-
sionality becomes crucial whenever the geometrical size of
the studied structure is comparable or even smaller than the
characteristic lengths, such as the magnetic-field penetration
depth, λ, and the coherence length, ξ . In addition, mesoscopic
effects introduce a powerful way to tailor the wide variety of
superconducting thin-film applications in the field of cryogenic
quantum electronics.
The recent discovery of the iron-based superconductors
1
provides a new set of challenges for the field of supercon-
ducting thin-film growth, as researchers seek to understand the
fundamental properties of this system as well as assess the suit-
ability of these materials for the development of devices and
applications. One of the iron-based superconducting families
discovered to date
2,3
is BaFe
2
As
2
, which was dubbed the 122-
family. Bulk samples with hole-doping [(Ba
1−x
K
x
)Fe
2
As
2
]
show superconducting transition temperatures of up to T
C
≈
38 K,
2
with electron doping [Ba(Fe
1−x
Co
x
)
2
As
2
] up to
22 K.
4
As all iron-based superconductors, the 122-family
also possesses the FePn tetrahedron within its layer, where
Pn is pnicogen or chalcogen. For general application pur-
poses, the 122-family seems to be the most suitable among
the iron-based superconductors because of their rather high
critical temperature and upper critical field B
C2
45 T,
5
low
electronic anisotropy, reduced thermal fluctuations, and an
apparently strong pinning of magnetic vortices.
6
Additionally,
preparations of thin films made from the 122-family are easier
than those from the F-doped LnFeAsO compounds (Ln being
a rare-earth element). Furthermore, Ba-122 is more stable
against exposure to moisture than Sr-122.
7
Concerning devices, one of the crucial parameters of
superconducting thin films is the critical current density, j
C
,
which determines the current-carrying ability of the final
device fabricated from these films. There are two main
mechanisms for the generation of the critical state caused by
an applied transport current across a microbridge. The first
mechanism is the depairing of Cooper pairs. This mechanism
determines the ultimate limit of j
C
. The second mechanism
is typical for thin films made from type-II superconductors
in which magnetic vortices penetrate into the thin films. In
this case, the critical current is determined by competition
between the pinning force attracting the vortex to a pinning
site (e.g., defects of the crystalline microstructure of thin film)
and the Lorentz force acting on this vortex in the presence
of the externally applied transport current. Typical operation
conditions of superconducting thin-film devices exclude ex-
ternally applied magnetic fields or even special efforts are
undertaken for absolute shielding of the devices against any
sources of magnetic fields, including the Earth’s magnetic
field. Therefore, in low- as well as in high-T
C
superconducting
devices, one has to deal only with depinning of so called self-
generated magnetic vortices, the vortices caused by penetration
of the magnetic field generated by the applied transport
current. According to Likharev,
8
magnetic vortices do not
penetrate into superconducting bridges with a width W smaller
than 4.4ξ
GL
(T ), where ξ
GL
(T ) is the temperature-dependent
Ginzburg-Landau coherence length. At temperatures in the
vicinity of T
C
, the coherence length diverges, thus realizing
conditions for the observation of the depairing critical current.
At low temperatures, where the condition W< 4.4ξ
GL
(T ) is
not satisfied anymore, penetration, depinning, and movement
of magnetic vortices can significantly reduce j
C
.
A number of experimental studies on the behavior of critical
currents in the iron-based superconductors—particularly in
Ba(Fe,Co)
2
As
2
thin films and single crystals—have been
conducted.
9
Numerous techniques have been applied for this.
First, nondestructive measurements of the magnetization allow
one to estimate the critical current density on the basis
of Bean’s critical state model.
10,11
Second, magneto-optical
imaging can be used to study the structure of the critical state
by analyzing the spatial distribution of the magnetic induction
on the sample.
12
Third, the study of the time-dependent
134514-1 1098-0121/2011/83(13)/134514(6) ©2011 American Physical Society