Several experimental studies have been reported as evidence of Josephson coupling between the superconducting layers in the highly anisotropic oxide such as the Bi2Sr2CaCu2O8 and Tl2Ba2CuO6 systems. These include the large penetration depth of 100 mu m measured, ac and dc Josephson effects. Recently two critical temperatures corresponding to Josephson coupling in between the layers and the Berezinskii-Kosterlitz-Thouless transition in the ab-plane have been directly observed in the transport measurements. If the field is applied parallel to the superconducting layers, the magnetic excitation is not the conventional Abrikosov vortices, but the Josephson vortices which extend lambda(sub ab) in the c-axis direction and lambda(sub J) = gamma s in the plane (s is the interlayer distance, gamma is the anisotropy constant). Because of the weak screening effect associated with the Josephson vortices, there have been predictions of magnetic transparent states at magnetic field above a characteristic field H(sub J), a behavior distinctively different from that of the type-II superconductors. In this paper, we report an experimental result which illustrates a transition from the Meissner state to the magnetic transparent state in single crystal of Nd(1.85)Ce(0.15)CuO(4-y). Magnetization has been measured as a function of temperature and field in the magnetic field parallel or close to ab-plane geometry. For a fixed magnetic field, the magnetization shows a two-step transition in M(T); for a fixed temperature, the magnetization shows an abrupt change to almost zero value above a characteristic field H(sub J), an indication of magnetic transparent state. The data of magnetization as a function of field clearly deviates from the behavior predicted by the Abrikosov theory for type-II superconductors. Instead, the data fit well into the picture of Josephson decoupling between the CuO2 layers

Zuo, F.

English

NASA Technical Reports Server

Transparent Magnetic State in Single Crystal
Nd1.ssCe0.15CuO4-y Superconductors
F. Zuo
Physics Department, University of Miami
Corm Gables, FL 33124
Several experimental studies have been reported as evidence of Josephson cou-
pling between the superconducting layers in the highly anisotropic oxide such as the
Bi2Sr2CaCu_Os and T12Ba2CuO6 systems[i-8]. These include the large penetration
depth of 100 /zm measured[l], ac and dc Josephson effects[3]. Recently two criti-
cal temperatures corresponding to Josephson coupling in between the layers and the
Berezinskii-Kosterlitz-Thouless transition in the ab-plane have been directly observed
in the transport measurements[7]. If the field is applied parallel to the superconduct-
ing layers, the magnetic excitation is not the conventional Abrikosov vortices, but
the Josephson vortices which extend Aabin the c-axis direction and A3 = 7s in the
plane (s is the interlayer distance, 3' is the anisotropy constant). Because of the weak
screening effect associated with the Josephson vortices, there have been predictions
of magnetic transparent states at magnetic field above a characteristic field I-Ij, a
behavior distinctively different from that of the type-II superconductors.
In this paper, we report an experimental result which illustrates a transi-
tion from the Meissner state to the magnetic transparent state in single crystal of
Ndl.ssCe0.15CuO4-u • Magnetization has been measured as a function of temperature
and field in the magnetic field parallel or close to ab-plane geometry. For a fixed
magnetic field, the magnetization shows a two-step transition in M(T); for a fixed
temperature, the magnetization shows an abrupt change to almost zero value above
a characteristic field H j, an indication of magnetic transparent state. The data of
magnetization as a function of field clearly deviates from the behavior predicted by
the Abrikosov theory for type-II superconductors. Instead, the data fit well into the
picture of Josephson decoupling between the CuO2 layers[8].
Single crystals of Ndl.ssCe0.1_CuO4_y are grown using a directional solidifica-
tion technique[9]. Four crystals are used in the measurement with average dimensions
250
https://ntrs.nasa.gov/search.jsp?R=19960000257 2020-06-16T07:04:47+00:00Z
of 1x 1× 0.02mm. Extensive measurements were made on two samples A and B with
Tc of 22.5K and 21K, respectively. Typical magnetic transition widths measured
at 1G with zero-field cooling are about 1-2K. Measurements are performed using a
Quantum Design magnetometer with low field options. After degaussing and magnet
resetting (quenching) the remanent field is typically 5-10raG. All measurements were
done with the sample zero-field cooled to a temperature below To. Magnetizations in
both directions H 11ab and HI ab were measured. For samples with ab-plane aligned
parallel to the field, mlsalignment of a few degrees were often observed.
Shown in Figure l(a) and (b) are plots of magnetization of sample A as
a function of temperature in field parallel to c-axls and ab-plane, respectively. In
Figure l(a), the transition temperature Tc is about 22.5K and M(T) is almost fiat
for T below 20K. The transition width is less than 2K in the applied field of 1G,
an indication of high crystal quality. The magnetization in the field close to ab-
plane direction is clearly different from that of field parallel to c-axis direction. For
an applied field of 10G, there are two apparent transitions. The high temperature
transition corresponds to the same Tc as from Figure l(a), the lower transition starts
around 12K and magnetization saturates above 16K.
0 ' ' ' _ T,__
i -1 H--1G \\C zfe /_o -2 (a)
--5 I I I I I
5 10 15 20 25
I I I I I
0.0 H=IO G H\\ ab zfc
7o-0.5_,..,
-1.0
I I I I I
5 10 15 20 25
T(K)
Fig. 1 Temperature dependence of
magnetization in field parallel to c-
axis (a) and ab-plane (b).
Shown in Figure 2 is an overlay of magnetization as a function of tempera-
ture of sample A at different applied field H=30G, 40G, 50G and 60G. Again, two
25!
regimes are dearly distinguishable. In the low temperature regime, the magnetiza-
tion is nonlinear with the applied field. At the lowest temperature measured (5-6K),
magnetization increases in magnitude from 30G to 40G, then decreases at 50G and fol-
lowed by further increase at H=60G. The magnetization of H=50G and 60G crossover
at higher temperature (,-_ 8K). In the high temperature regime, the magnetization
is relatively flat with respect to temperature. The magnitude of M is quasi-linear
with field H. With further increases in temperature the sample becomes normal with
paramagnetic susceptibility above To. The transition width increases with increasing
field.
I I I I I
0
-2 l,f t . H=3OG
// / • H=4OG
-3 i i i n t
5 10 15 20 25
T(K)
Fig. 2 Temperature dependence of
magnetization at different fields
H=30G, 40G, 50G and 60G with the
field parallel to ab-plane.
The nonlinear field dependence of M observed at low temperature is in contrast
with magnetization in the c-axis direction. To understand this anomalous behavior,
we have performed detailed magnetization as a function of field at fixed temperatures.
For these measurements, the sample is zero-field cooled to a set temperature and M
is measured with the magnet set in the non-overshot, persistent mode. Plotted in
Figure 3 is a typical magnetization as a function of field for a second sample B of
Tc=21K.
Two linear regimes are observed. In the first regime, M is linear in H (<65G),
then followed by an abrupt increase in M at a critical field (H.r=fSG); in the second
regime (H>100G) M is again linear in H. For intermediate field 65G < H < 100G,
additional, smaller jumps are typically observed. In the H-descending direction, M is
252
linear all the way to zero field with the same slope defined in the second regime. This
characteristic dependence has been observed in Bi2Sr2CaCu20s single crystal[61 where
detailed angular dependence were performed to confirm the fact that the M(H) in the
second regime is the contribution of M± (parallel to c-axis) due to mlsalignment. We
have also checked it by varying the sample orientation slightly, and we found the slope
of M(H) changes accordingly in the second regime. Typical n_salignment is about
2-6 degrees.
I I I I I I I I I I
o T-IOK
0
o T=IOK 0
°
-2 _ -1
(a) H,=aSG (b)
--3 I I I I --2 I I I I I
O 50 1O0 150 200 0 50 1O0 150 200
H(G) H(G)
Fig. 3 Magnetization as a function Fig. 4 The corrected magnetization
of applied field at T=10K for sam- as a function of applied field. The
ple B. dashed and dotted line are theoreti-
cal fits.
The measured magnetic moment M can be written as M = 3/11cos O+M_Lsin O)
with MII = (VII cos0/4rr)/(1 - Nab) and M± = (VII sin 0/4or)/(1 - Arc),where V is
the volume of the sample, 8 is the angle between the ab-plane and the applied field,
and Nab and Arcare the demagnetization factors for field along the ab-plane and
c-axis, respectively. For sample B, we obtained 1/(1 - Arc) ,,_ 110 using the suscep-
tibilities measured on both directions. Shown in Figure 4 is a plot of magnetization
along the ab-plane after subtracting the contribution of M±. The M± contribution
is obtained by measuring the slope X, of the second linear regime or the slope of the
descending branch. The corrected magnetization is given by M = M - X2II. From
the corrected magnetization and X2 one can calculate the misalignment angle to be
around 3.3 degrees. The corrected magnetization, again, shows a sharp transition in
M at H=65G, followedby a plateau and then M goes to zero quickly starting at about
H=85G. The jump in M at Hj at T=10K is about 80% of full Meissner value. The
dashed and dotted lines are models to be discussed later. On the descending branch
253
of the magnetization, M is essentially zero, independent of the field value.
i I I I I I I I I
x\\ab
800
3 0o h
• lox NI I 201
[] 16K "t_ \
f-T
-2, , , , , 0 , o ; '00 50 100 150 200 0 5 1 1 2 25
H(G) T(K)
Fig. 5 An overlay of magnetiza- Fig. 6 The first critical field as a
tion as a function of field at differ- function of temperature.
ent temperatures T=8K, 10K, 14K
and 16K.
Plotted in Figure 5 is an overlay of magnetization (after subtraction) as a
function of field at T = 8, 10, 14, and 16K. The overall features of M at different
T are similar, but some differences are observed. For T=8K, the first transition
occurs at H=70G, followed by a second transition at about H=82G. The plateau seen
in M at T = 10K clearly becomes a sharp transition. At T=14K, there are three
transitions in M(H), with the largest jump in M occurring at the second transition.
The transition is continuous at T=16K. We define the critical field Ha to be field value
at the first jump. As is clear from the data, the critical field decreases with increasing
temperatures, and the increase in M at Hj becomes more gradual. For T>15K, no
abrupt changes are observed, the shapes of M(H) are similar to the reported data on
Bi2SrzCaCu2Os .
Figure 6 is a plot of the first critical field as a function of temperature. For
temperature below 12K, the critical field Hj is almost constant around 70G, while
Ha decreases sharply for T greater than 12K.
To study the effect of transition temperature on the critical field Ha, we have
performed similar measurements on several Ndl.ssCe0.1_CuO4-v crystals. Shown in
Figure 7 is an overlay of magnetization as a function of field at different temperatures
for sample A. Again the abrupt changes are observed in the M(H) at the critical field.
254
At T=5K, several steps are in fact observed with the first critical field around 35G. At
higher temperatures, the similar features to that of Figure 5 are observed, except the
critical field is much smaller than that of sample B. The magnetization in descending
branch of the hysteresis loop is also zero after correction.
The direct measurement of M(H) is consistent with the results of magnetization
as a function of temperature. In Figure 2, the nonlinear field dependence of M seen
at low temperature is a direct reflection of abrupt change in M at Hj _ 35G. The
crossover between the 50G and 60G data at low temperature indicates the relative
contributions due to the jump and M±. The quasi-linear M on H demonstrates the
fact that at high temperatures the main contribution is from M± when the sample is
misaligned.
' ' H\\ab .... ' = '
o 40
20
\T
,= I2K I 10 "_\
= I4K /
, i o I I I I
--3 i i I i i
0 50 100 150 200 5 10 15 20 25
H(G) T(K)
Fig. ? An overlay of corrected Fig. 8 The first critical field as a
magnetization as a function of function of temperature for sample
temperatures T=SK, 10K, 12K,and A.
14K for sample A.
Plotted in Figure 8 is the temperature dependence of the first critical field. The
temperature dependence is also similar to that of sample B, i.e. Ha saturates at low
T and decreases sharply at high T. Notice the saturation value of Hj is considerably
smaller than that of sample B.
The abrupt change in the magnetization at the critical field is clearly different
from that of conventional type-II superconductors. The magnetization of conventional
type-II superconductors can be well described by the Abrikosov's theory[10]. At field
255
slightly larger than the lower critical field Hcz, the magnetization is obtained by
neglecting interaction between vortex lines 4_rM = _{ln[4._2_L_,_)]} -2 - H. In
the case of high Tc cuprate, the very large value of the Ginzburg-Landau parameter
i¢ renders the use of this result to magnetic field very close to He1 (Hcz < H <
He1+10G). For intermediate fields, the magnetization is given by 4_'M = ---cl a_(x/O
where/3'=0.231, and l is the lattice constant given by B = 2dpo/v/3l2 for a triangular
lattice[10]. Assuming _€= _/_ _-,20 and Hcl=65G, the equilibrium magnetization
can be calculated numerically as a function of field. The result is shown as the dotted
line in Figure 4. The jump in M(H) clearly rejects the use of this model.
As suggested by the zero magnetization in the descending branch of the hys-
teresis loop, the entrance field is determined by Bean-Livingston surface barriers[11].
In the presence of surface barriers, the penetration field is not the lower critical field
HCz,but comparable to the thermodynamic critical field He. The surface barrier is
a result of attractive interaction between an image vortex with the entering vortex.
Strong evidence has been found in the field parallel to the c-axis direction in high
quality single crystal materials[12, 13, 14] The magnetization for field greater than
the penetration field Hv and assuming no bulk pinning, has been discussed in several
recent articles[12, 15]. By modeling an Abrikosov lattice in the bulk of the sample
and vortex-free zone near the surface due to surface barriers, the magnetization is
derived and given by -4_'M = H - _/H 2- Hi. The result is plotted as the dashed
line in Figure 4. Again, the model deviates from the magnetization data. It is to be
.noted that the expression above is derived for conventional type-II superconductors,
where the flux lattice is the Abrikosov lattice.
The abrupt change occurred at Hj strongly indicates the inadequacy of the
use of Abrikosov's theory in the magnetization of Ndl.ssCe0.zsCuO4__ crystals in the
H [I ab direction. Since the M±(H) clearly exhibits the Meissner effect in the per-
pendicular direction, the jump in MII(H) shows directly magnetic decoupling between
superconducting layers at the critical field Hj.
For weakly Josephson coupled layered superconductors, the critical current in
the c-axis direction, which provides magnetic screening when field is in the ab-plane,
is determined by the coupling strength. For small applied field, complete screening of
external field is possible. At the critical field, the Josephson coupling breaks down,
magnetic field penetrates into the sample. If the layers are effectively decoupled, a
transparent magnetic state is expected, due to the fact that the 2D superconducting
layers can not support screening current by themselves.
The jump in MII(H) can also be qualitatively understood from the field de-
pendence of critical current of a single Josephson junction: J_(H) = dosin(_)/(_)
256
where J_(H) is the field dependent critical current, Jo is the maximum zero field
critical current, and € is the magnetic flux through the junction. The critical current
is almost zero when there is a finite number of Josephson vortices threading through
the junction. Assume the magnetization is proportional to the critical current, M
should become zero as Josephson vortices penetrate into the junction. For stacked
layers with Josephson coupling, the field dependence of Jc should not be the same as
that of single Josephson junction, rather one expects a stronger reduction in Jc(H)
with increasing H. In this picture, the experimentally observed smaller jumps in the
magnetization data thus would indicate the presence of superconducting layers with
different Josephson couplings.
To describe the vortex state of the Josephson coupled superconducting stacks
quantitatively, one has to solve the coupled Lawrence-Doniach equations[16]. In the
case where the applied field is tilted to the superconducting layers, several theoretical
models are proposed. Recently it has been shown that there are two distinct vortex
structures depending on the anisotropy constant 7 = .kj/s, where Aj is the Josephson
penetration depth and s is the separation between the superconducting layers. If
,kj < Aab,the theory suggests a tilted vortex line structure, where different segments
of vortex lines parallel to the ab-planes are connected by pancakes residing in the ab-
planes[17, 18]. If Aj > Aab,the model predicts that coexisting sets of perpendicular
and parallel vortices should exist when the field is applied dose to the ab-plane. The
Abrikosov vortices are due to Ha_,and Josephson vortices are due to HII. The vortices
due to HII and Ha_act independently of each other. The complete Meissner effect is
possible only if HII < H_ and Ha_ < H_. For HII > H_, HII penetrates into the
layers between the CuO2 planes almost completely, creating the so called magnetic
transparent state[18, 19, 20].
The experimental results clearly demonstrate the complete Meissner state for
H < Hj. The linear field dependence of M in the descending branch and the overlap-
ping M(H) at high field indicate H± < H_. For H > Hj, there are only Josephson
vortices parallel to the ab-plane and M± is still in the Meissner state. The jump
in M(H) for H > Hj indicates the transition to the magnetic transparent state in
Josephson coupled layered superconductors.
The difference in magnetic transition around the critical field between the
Nd1.ssCe0.15CuO4-u and the Bi2Sr_CaCu2Os , TI_Ba2CuO6 crystals is not dear. One
possibility is that the Bi_Sr2CaCu_Os , T12Ba2Cu06 crystals studied are very thick[6,
21]. A broad distribution in the coupling strength will smear out the transition. This
picture is supported by a recent report which shows a similar abrupt change in M(H)
in another TI_Ba2CuOs crystal[22].
In summary, we have presented an experimental measurement of an abrupt
257
Josephson decoupling between the Cu02 planes at the critical field Hj parallel to
ab-planes. The abrupt increase in M(H) at Hj is incompatible with the conventional
Abrikosov theory. For field Hi[ > H j, the magnetic field has a complete penetra-
tion in between the superconducting layers-a magnetic transparent state. A more
detailed study of H.r as a function of Tc will help to elucidate the mechanism of
superconductivity in the layered superconductors.
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Transparent magnetic state in single crystal Nd(1.85)Ce(0.15)CuO(4-y) superconductors

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