. . . . . . . .
J
Physics C 185-189 (1991) 1527-1:528 North-Holland
ANOMALOUS MAGNETIC PROPERTIES OF WEAK-LINKS-BEARING S~ERCONDUCTORS Sergei
SERGEENKOV
Joint I n s t i t u t e
for Nuclear
Research,
Dubna 1 4 1 9 8 0 ,
USSR
A possible scenario for dislocation-induced intragrain weak l i n k s g e n e r a t i o n i s p r o p o s e d . The t h e o r y p r e d i c t s a reentrant-like behavior of the critical current density versus magnetic field due to the sample deoxygenation. A qualitative agreement with high-T c single crystals anomalies is discussed. P r o b a b l y , t h e r e a r e a l r e a d y no d o u b t s that, due t o small coherence length, practically any defects (imperfections)
We a r e i n t e r e s t e d in a concord between a finite dislocation density p(x) inside the crystal and an appearance of the
in high-T c single crystals may contrib-
Josephson supercurrent J s [ P ( x ) ] . The k e y p o i n t of t h e p r e s e n t t h e o r y i s t h e a s s o ciation of the (SIS-type) weak l i n k s j u n c t i o n s w i t h t w o phases r e s u l t i n g from the dislocations paths through the crystal. Supposing, for simplicity, the twinning boundaries a s t h e weak l i n k s sources, we are able to use for their treatment the dislocation theory of elastic twinning 5. If, for instance, a
to both the weak-links properties and the flux pinning 1-4. In a recent pa-
ute
per of Daeumling et
a l . 3,
for
instance,
a rather intriguing correlation between defect pinning, intragrain weak links, and oxygen deficiency i n YBa2Cu307_ ~ single crystals is discussed. In this paper a possible scenario of the intragrain weak links generation via dislocation mechanism is proposed, and their influence on the Josephson critical
current
density
vs.
magnetic
field
us
consider
Josephson contacts
the
model
of
magnetic
small
with length L~Aj,
is the Josephson penetration depth, strong
field
such
that
Aj
in a
(second)
thickness. critical
In
junction, this
current
pedbythe
t is insulator
case
density
the
maximum
through
the
field WO ) is stop-
etc,
then
density distribution law 5:
the
dislocation
is governed by the
p(x) = PO[ L~x } I/2
(3)
Here L = 2b/~ 0 is the twinning length, b is the total Burgers vector.
Integrating
Eq.(2) with the dislocation density (3) over o(x), and averaging over random junction size d, one obtains for the maximum critical current density
contact is : Js(X) = Jcsin#[p(x)], (I) where the variation of the superconduc--
Js(H ) = jc/(I+H2/H~)
(2)
,
:
(4)
where
ring phase obeys the law : 2~d dp -I d# dp - ~0-''H(~-~)
external
crystalline grain boundaries,
H
#O/2ffAjd, where d=ALI+AL2+t, ALl(2 ) is the London penetration depth of the first
homogeneous interfaces
is discussed as well. Let
freely growing twinning boundary (in the
Hp
~0 2ndoAp
0921-4534D1/$(73.50 © 1991 - Elsevier Science Publishers B.V. All fights reserved.
4b 2 [02+ 462 ] - 1
Ap
S. $ergeenkov / Weak4inks-bearingsuperconductors
1528 As
is seen,
describes
Eq.(4),
at
an ordinary
least
1.00
formally,
decreasing
of the
critical current density with H, but ac-
zO.80
tually this
a
the
is not the case
implicit dependence
of
of a character-
istic "penetration
depth"
ternal
sources
affecting
cation
(via the
~0
in v i e w
Ap on the ex-
twinning
the
dislo-
length
L,
see
Eq.(3)). To prove this statement,
let us
define the form of these sources.
First
of a11, the
if the dislocation
boundary
rent
of
magnetic
line
two phases
lies on
with
susceptibilities
Eo.6o o0.40
~
diffe(~I
0.20
0.00
0.00
and
1.00
2.00
MAGNETIC
FIELD
3.00
X2), then such a dislocation will be influenced,
in nonzero magnetic
field,
by
a force : fm = ~ ( ~ 1 - ~ 2 )H2 " Here a is an interplane
(5) distance. The
FIGURE I N o r m a l i z e d critical current density (4) versus reduced m a g n e t i c field h=H/Ho :
I)
6=0, 2) 6=0.01, 3) 6=0.05.
force (5) will be equalized by the force of a dry friction
(which is always
sent inside crystal),
pre-
and by the osmotic
overcomes this barrier
(existing only
for
becomes
6#0),
the
pinning
force fo due to an excess nonequilibrium
fective,
concentration of vacancies cac 0 (or oxy-
the critical current
gen deficiency 6=c/c0-I ) :
a=10~, (6)
I n accordance w i t h E q s . ( 4 ) - ( 6 ) , inal
oxygen d e f i c i e n c y
t h e nom-
~aO l e a d s t o
appearance of an effective field H*(6) = ~(T)[log(l+6)] 1/2,
the
b=10nm,
:
field
H*(0.05)~4T,
the
fields
Taking
and supposing that ~ 2 ~ I ,
for T=70K and 6=0.05,
a rough estimate
nomena in (7)
is observed.
tains to
ef-
and a rather smooth fall-off of
X2=-I/4~,
kBT f0 = .........b 2 1 o g ( t + 6 ) .
less
where
one
of the effective
which
is very
the anomalous
YBa2Cu307_6
ob-
single
close phe-
crystals
have been observed 3.
where
f 2 BT I/2 z(T) = taa---~-~-~ } When t h e
applied
REFERENCES •
magnetic
field
reaches
I. G. Deutscher and K.A. MUller, Rev. Lett. 59 (i987) 1745.
Phys.
the effective one H*(6), the moving dislocation is blocked, enhancement as
a
of
result,
the to
thus leading to the pinning
the
forces
recovery
2. J.R. Clem, Physica 162-164C (1989) 1137.
and,
of
the
3. M. Daeumling, Larbalestier,
J.M. Seuntjens and D.C. Nature 346 (1990) 332.
critical current density (see Fig, l). It is
seen
H=H*(6),
that
at
the
the additional
points, peaks
where
4. R.L. Peterson and J.W. Ekin, Phys. Rev. 37B (1988) 9848.
are gene-
rated in agreement with the observations of Daeumling et al. 3 When magnetic field
5. L.D. Landau and E.M. Lifshitz, Theory of Elasticity (Pergamon, New York, 1960).