Two-stage crossover from thermal to quantum flux creep of dilute vortex ensembles in various
high-T
c
superconducting thin films
Johan J. A
˚
kerman
Department of Materials Science-Tmfy-MSE, Royal Institute of Technology, S-100 44 Stockholm, Sweden
and Physics Department, University of California—San Diego, 9500 Gilman Drive, La Jolla, California 92093-0319
E. L. Venturini and M. P. Siegal
Sandia National Laboratories, Albuquerque, New Mexico 87185-1421
S. H. Yun and U. O. Karlsson
Department of Materials Physics, Royal Institute of Technology, S-100 44 Stockholm, Sweden
K. V. Rao
Department of Materials Science-Tmfy-MSE, Royal Institute of Technology, S-100 44 Stockholm, Sweden
Received 20 February 2001; published 8 August 2001
The thermal-to-quantum flux creep crossover at low vortex densities has been studied in YBa
2
Cu
3
O
7
,
TlBa
2
CaCu
2
O
7-
, and HgBa
2
CaCu
2
O
6+
thin films using ac susceptibility. The crossover temperatures T
cr
are
10–11, 17, and 30 K, respectively. Both thermal and quantum flux creep is suppressed as the vortex density is
decreased. We observe a two-stage nature in the crossover behavior which appears to be a general property of
all the three materials studied.
DOI: 10.1103/PhysRevB.64.094509 PACS numbers: 74.60.Ge, 74.76.Bz
I. INTRODUCTION
Magnetic vortices in type-II superconductors are one of
the few systems in which macroscopic quantum tunneling
can occur. This intriguing phenomenon was first reported in
high-T
c
superconductors HTS,
1
and although subsequently
observed in conventional superconductors,
2–4
its study has
mostly focused on optimally doped Y-123,
5–11
oxygen-
deficient Y-123,
12,13
and other HTS materials such as
Y
1 -x
Pr
x
Ba
2
Cu
3
O
7
,
14
YBa
2
Cu
3
O
8
,
11
Bi
2
Sr
2
CaCu
2
O
8
, and
Bi
2
Sr
2
Ca
2
Cu
3
O
10
,
15–17
Tl
2
Ba
2
CaCu
2
O
8
,
18–20
Tl
2
Ba
2
Ca
2
Cu
3
O
10
,
21
Hg
0.8
Tl
0.2
Ba
2
CaCu
3
O
8
,
22
and
YBa
2
Cu
3
O
7
/PrBa
2
Cu
3
O
7
multilayers.
23,24
However, to the
best of our knowledge, quantum creep has previously not
been studied in either TlBa
2
CaCu
2
O
7 -
Tl-1212 or
HgBa
2
CaCu
2
O
6 +
Hg-1212, which are two of the materials
investigated in this work. These material systems are of par-
ticularly high technological importance due to their high
critical temperature, high critical current density, and moder-
ate anisotropy.
25,26
The low-temperature flux creep behavior can be very dif-
ferent for single crystals and thin films of the same
material.
27
The crossover temperature T
cr
, below which
quantum creep effects can be observed, is generally higher
for thin films. Theory also predicts a higher T
cr
in the case of
single-vortex creep low fields compared to creep of flux
bundles, since the tunneling probability decreases with the
size of the tunneling object.
28
Thin films generally also show
a strong suppression of quantum creep with decreasing field,
whereas a similar anomaly is not observed for single crystals.
This difference has been ascribed to differing characteristic
pinning sites of thin films and single crystals. In particular it
has been argued that the suppression of quantum creep as
B →0 is due to the presence of a limited number of strong
pinning sites that dominate the pinning at low vortex densi-
ties. Hence, we expect both an increase in T
cr
and a decrease
in overall creep in our thin film samples with highly dilute
vortex ensembles.
In this work we determine the thermal-to-quantum cross-
over temperatures for Y-123, Tl- and Hg-1212 thin films at
very low fields 7–140 Oe. While we find T
cr
=10– 11 K for
Y-123 thin films, in good agreement with previously pub-
lished high-field values, T
cr
is found to be as high as 17 and
30 K for Tl- and Hg-1212 thin films respectively. Further-
more, the crossover seems to proceed in two distinct steps,
and consequently a second temperature T
cr
* can be defined
for all three materials. We also find that quantum creep is
suppressed down to the lowest accessible fields.
II. THERMAL AND QUANTUM CREEP
The theory of collective flux creep
29,30
CFC predicts a
nonlinear current dependence of the flux creep activation en-
ergy,
U J
c
=
U
0
J
c 0
J
c
-1
, 1
where J
c 0
is the original critical current density before flux
creep sets in, J
c
is the measured decaying critical current
density and is an exponent describing the degree of non-
linearity, with values between 1/7 and 5/2 depending on the
actual collective flux creep regime. The concept of a
temperature- and field-dependent exponent has been suc-
cessfully applied in the analysis of flux creep in Y-123.
31–35
It is also well known that a simpler, logarithmic current
dependence,
36
U ( J
c
) =U
0
ln(J
c0
/J
c
), which formally corre-
sponds to =0, is often a very good description of experi-
PHYSICAL REVIEW B, VOLUME 64, 094509
0163-1829/2001/649/0945095/$20.00 ©2001 The American Physical Society 64 094509-1