Physica C 332 Ž2000. 27–34
www.elsevier.nlrlocaterphysc
Vortex lattice matching effects and 1rf-noise reduction in HTS
films and devices equipped with regular arrays of artificial defects
)
R. Wordenweber
, A.M. Castellanos, P. Selders
¨
Institut f ur
D-52425 Julich,
Germany
¨ Schicht- und Ionentechnik, Forschungszentrum Julich,
¨
¨
Abstract
In this contribution, we report Ži. on the observation of commensurability effects between regular arrays of artificial
defects and the vortex lattice in high-temperature superconductor ŽHTS. films and Žii. on the reduction of low-frequency 1rf
noise in high-Tc superconducting quantum interference devices ŽSQUIDs. caused by these regular arrays of artificial defects.
Arrays of submicrometer holes Žantidots. with periodicity down to 0.5 mm were patterned into YBCO thin films without
deterioration of superconducting properties. Commensurability effects between the antidot and vortex lattice were observed
via resistive and inductive measurements, which clearly prove the presence of an attractive interaction between vortices and
antidots and the existence of multiquanta vortices. Consequently, the attractive interaction between antidots and vortices was
used to reduce the vortex motion in superconducting devices, thus leading to a strong reduction of 1rf noise. For a proof of
the principle, YBCO films with antidot lattices Ž5 mm spacing. were mounted in flip-chip configuration onto bicrystal
rf-SQUIDs. Commensurability between vortex lattice in film, fluxons in the bicrystal boundary and the antidot array was
observed in the form of a strong reduction and increase of the 1rf noise at discrete magnetic inductions, which are predicted
by simple geometric considerations. The transfer of this very promising technology for 1rf noise reduction to standard HTS
SQUIDs used in applications Že.g., NDE, MGC. is presently under way. q 2000 Elsevier Science B.V. All rights reserved.
Keywords: Vortex lattice; Antidot; Noise reduction; SQUID; Applications of high-Tc superconductor
1. Introduction
The application of high-temperature superconductors ŽHTS. to highly sensitive cryogenic active devices strongly depends on the reduction of noise. In
particular, low-frequency 1rf noise due to unwanted
flux motion in the superconducting material w1x
Žfluctuations of the contact properties w2,3x can be
eliminated via ac bias w4x. represents a serious limitation for the application of superconducting quantum
interference devices ŽSQUIDs. in unshielded envi)
Corresponding author. Tel.: q49-2461-61-2365; fax: q492461-61-2940.
ronment. Various remedies have been suggested and
tested in the past: Ži. Flux entry into the superconductor has been avoided by reduction of the superconductor line width w5,6x or implementation of a
flux-dam w7–9x. Žii. Methods of moving vortices into
pinning sites or out of the superconducting film have
been developed w10,11x. Žiii. Pinning sites have been
created, which trap the flux in the superconductor
Že.g., via irradiation damage of the sample w12x. or in
artificially patterned nonsuperconducting submicrometer holes w13,14x.
One of the most effective ways to create artificial
pinning sites in thin films is provided by the preparation of networks of submicrometer holes w15–18x.
0921-4534r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved.
PII: S 0 9 2 1 - 4 5 3 4 Ž 9 9 . 0 0 6 3 9 - 5
28
R. Wordenweber
et al.r Physica C 332 (2000) 27–34
¨
These defects can be placed arbitrarily in superconducting devices. For a periodic array of holes Žantidots. with radius r much smaller than the period d
of the antidot array, a well-defined pinning potential
is formed.
In this contribution, we demonstrated Ži. that arrays of submicrometer holes can be patterned into
YBa 2 Cu 3 O 7yd ŽYBCO. thin films without deterioration of the superconducting properties and commensurability effects can be observed for temperatures
down to 50 K via resistive and inductive measurements w18x, and Žii. that the attractive interaction
between vortices and antidots strongly affects the
1rf noise in HTS SQUIDs. The transfer of these
results to real SQUID systems is tested and problems
connected to the choice of the antidot lattice are
discussed.
2. Preparation of antidots in YBCO films
YBCO films are deposited via a high-pressure
on-axis magnetron-sputter technique on CeO 2
buffered sapphire and LaAlO 3 w19,20x. High struc-
tural perfection and, especially, extremely small surface roughness are required for our optimized patterning process for micrometer and submicrometer
structures of SQUIDs and holes in YBCO w21x. A
typical image of an antidot in a YBCO film is given
in Fig. 1.
3. Experimental results and discussion
3.1. ResistiÕe measurements
The critical current is derived from voltage–current characteristics, using standard four-probe dc
measurements on pairs of YBCO bridges with and
Žas a reference. without antidot lattice. The voltage
criterion used for the determination of critical currents is 1 mVrcm and the magnetic field is applied
normal to the film surface. Fig. 2 represents the
magnetic field dependence of critical current density,
Jc , and critical current, Ic , as a function of the
magnetic field for YBCO thin films with and without
antidots. A reference YBCO bridge Žpatterned simultaneously into the same film but without antidots.
shows the usually observed monotonic field dependence of Jc . In contrast, the perforated YBCO bridge
shows a number of interesting features: Ži. peaks or
cusps in the magnetic field dependence of the critical
current at well-defined matching fields nBm s
nŽFord 2 ., with the period of the quadratic antidot
lattice d; Žii. shifts of the position of these peaks for
increasing and decreasing magnetic field; and Žiii. an
increase of the volume pinning force with respect to
YBCO films without antidots. Matching peaks could
be resolved only at n s 1, 2, 3, 7r2, 4, 9r2 in these
experiments. For a detailed discussion of the resistive measurements, refer to Ref. w18x.
3.2. InductiÕe measurements
Fig. 1. SEM images of Ža. an antidot lattice Ž df1 mm and radius
r f 0.2 mm. and Žb. an antidot Ž r f1 mm. in YBCO films on
sapphire.
Inductive measurements have been performed on
YBCO films with regular square lattice of antidots
w23x. The experimental technique was based on a
lock-in detection of the induced signal produced in a
secondary coil due to a small ac field Ž Bac s 0.4–1.4
G parallel to the crystallographic c-axis of the film
R. Wordenweber
et al.r Physica C 332 (2000) 27–34
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Fig. 2. Critical current density and critical current Žinset. as a function of magnetic induction for YBCO with Ž r f 0.22 mm, d f 1 mm. and
without antidots. Both samples are obtained from the same film and have identical dimensions.
Y
Fig. 3. Out-of-phase susceptibility x Ž Bac s 1.2 G; 8.92 KHz. as a function of bias field for a YBCO film with a square antidot lattice
Ž d s 1 mm, r f 0.34 mm.; TrTc s 0.96. Inset displays the principle of the measurement.
R. Wordenweber
et al.r Physica C 332 (2000) 27–34
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30
at 8.93 kHz. in the primary coil Žsee inset, Fig. 3..
The in-phase and out-of-phase components of the
fundamental of the pick-up coils voltage are proportional to the out-of-phase and in-phase components
of the complex susceptibility x ŽT, B . s x X ŽT, B . q
i x Y ŽT, B .. The components represent the stored ŽWm
s x X Ba2r2 mo . and dissipated ŽWq s 2px Y . energy.
By varying an additional dc magnetic induction B
Žoriented parallel to the c-axis of the film., the
dissipated energy due to vortex motion in the film
can be recorded as a function of temperature and
field.
Fig. 3 shows the variation of x Y as a function of
the bias field at a constant temperature of 0.96Tc for
YBCO thin films with and without antidots. For the
measurements on the reference YBCO films without
antidots Žprepared simultaneously on the same wafer.,
x Y increases monotonically Žexcept for the fields
below the remanent field of f 5 G of the magnet..
In contrast, the out of phase component for the film
with antidots is constant up to the matching field,
Bm s 20.7 G. Above Bm , the curve rises with a
similar slope observed for the reference sample.
Small curvatures are observed for matching fields
2 Bm and 3 Bm . The inductive measurements confirm
the presence of matching. At low fields, vortices are
trapped in the antidots. Once the antidot lattice is
completely occupied with single-quanta vortices, interstitial vortices form, which can be moved by the
small ac field and lead to a field-dependent dissipation. An even more interesting aspect of this kind of
measurement is represented by the fact that the
presence of multiquanta vortices can be tested. According to a simple model based upon flux penetration in rectangular-shaped superconductors w22x, a
saturation number w18x:
n s) s
Bcl d 2
Fo
(tr Ž d y 2 r .
Ž 1.
for multiquanta vortices consisting of flux n sFo can
be predicted, which depends on temperature, film
thickness, t, and size and periodicity of the antidots.
Fig. 4 represents x Y Ž B . for d s 5 mm and r s 1.75
mm. The onset of dissipation is shifted from f 1.6 Bm
for T s 0.99Tc towards f 2.5Bm for T s 0.98Tc ,
indicating the increase of saturation number with
decreasing temperature. A detailed description of
Y
Fig. 4. Out-of-phase susceptibility x Ž Bac s 0.4 G; 8.92 KHz. as
a function of bias field for a YBCO film with a square antidot
lattice Ž ds 5 mm, r f1.75 mm.. The insert shows an SEM
picture of the square lattice of submicrometer holes.
these experiments and their interpretation is scheduled for Ref. w23x.
3.3. Noise reduction by antidots
In order to demonstrate the effect of vortex–antidot interaction upon the low-frequency noise in HTS
devices, a characteristic property of bicrystal rfSQUIDs ŽBS. is exploited. At magnetic inductions
B f 200 nT far below the penetration field Bp f 1–2
mT, at which flux penetrates the washer in step-edge
SQUIDs ŽSES. of identical geometry, the grain
boundary in the washer of the BS Žsee Fig. 6. serves
as a channel for flux motion. This flux motion causes
a drastic increase of 1rf noise as shown in Fig. 5.
The further increase of the low frequency noise
agrees with the expected field dependence given by:
(S
F
ABn
Ž 2.
with n f 0.5 Žsee Fig. 5..
In order to examine the interaction between antidot and vortex lattices a YBCO film with an antidot
lattice Ž d s 5 mm. was mounted in flip-chip configuration on top of the grain boundary of the BS washer
Žsee Fig. 6.. For these measurements, the quadratic
antidot lattice is oriented with one axis along the
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Fig. 5. Magnetic field dependencies of the noise of SES Žopen symbols. and BS Žsolid symbols.. The noise is characterized by integration of
the noise spectra in the low-frequency regime between 0.5 and 10 Hz normalized to 1 Hz, HSf Ž B .1r 2 d frHd f. The dotted lines represent the
theoretical field dependence of the low-frequency noise, Eq. Ž2..
grain boundary Žsee sketch, Table 1.. Field and
zero-field cooled noise measurements are executed
in a magnetically shielded environment. No signifi-
Fig. 6. Sketch of the experimental arrangement. The square
antidot lattice Ž ds 5 mm. is mounted in flip-chip configuration on
top of the grain boundary of a BS.
cant difference between the resulting noise spectra
obtained via the different experimental approaches
was found.
Typical low-frequency noise spectra of BS with a
square antidot lattice in flip-chip configuration on
the grain boundary of the washer are given in Fig. 7.
Naturally, the lowest flux noise is recorded for zero
field, for which SF1r2 Ž f . f 170 and 670 mFo Hzy1 r2
for frequencies of 10 and 0.3 Hz, respectively. At
nonzero field, the low-frequency noise strongly depends upon the exact values of the applied magnetic
induction; it nonmonotonically varies over several
orders of magnitude. Therefore, this behavior cannot
be explained by Eq. Ž2. Žsee Figs. 7 and 8.. For
example, the noise at fields of 750 and 900 nT is
enlarged by more than two orders of magnitude to
SF Ž0.3 Hz.1r2 f 0.1Fo Hzy1r2 compared to fields of
B s 828 or 845 nT at which the noise is nearly the
zero field value.
The effect of an antidot lattice placed in flip-chip
configuration upon the grain boundary of the washer
and oriented with one axis along the grain boundary
is summarized in Fig. 8. Each data point in the figure
has been measured three times in different measuring
sessions. The noise data could be reproduced within
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Table 1
Matching conditions between 255 and 900 for, and schematic
sketch of different orientations of a quadratic vortex lattice Žsolid
circles., the quadratic antidot array Žopen circles. Ž ds 5 mm. and
the grain boundary in the washer Žgrey line.. M1 – M4 label the
different orientations of the vortex lattice
n
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
M1
Ž a0 s d .
wnTx
828
684
575
490
422
368
323
287
256
M2
Ž a 0 s n62 d .
wnTx
845
647
511
414
342
288
M3
Ž a 0 s n65d .
wnTx
662
460
338
259
M4
Ž a0 s n610 d .
wnTx
518
331
the experimental error. The data given in the plot are
obtained by averaging the experimental results for
each magnetic field. Compared with the reference
measurements, which show the usually observed behavior w13,14x, the following observations can be
stated.
Ži. Above B f 200 nT, flux seems to enter the
grain boundary in both experimental setups ŽBS with
and without antidot lattice.. Whereas the reference
measurement on the bare BS shows a strong increase
of the integral noise at ; 200 nT to ; 0.3Fo Hz 1r2
followed by the small field-dependent increase according to SF A B 0.5 Žsee dashed line in Fig. 8., the
integral low-field noise measured for the BS with
antidots is strongly field-dependent. The maxima
exceed the noise values measured in the reference
SQUID, whereas the minima are close to the value
measured at zero field.
Žii. The minima in the low-frequency noise for the
SQUID with antidot lattice occur at field values for
which particular matching conditions between the
square vortex and antidot lattices, on one hand, and
vortex lattice and grain boundary, on the other hand,
are satisfied. The matching fields for different vortex
lattice orientations Žsee Table 1. are defined by M1:
ao s nd, M2 : ao s Ž'2 . nd, M3 : a o s Ž'5 . nd, etc.
In the experimental regime between 250 and 900 nT,
minima in the low-frequency noise are observed for
all fields at which matching conditions M1 or M2
are fulfilled. At the resulting field values, noise data
comparable to the values measured for B - 200 nT
are present, i.e., at which no external magnetic flux
has entered the grain boundary of the washer.
Žiii. The maxima in the integral low-frequency
noise exceed the noise values measured for the bare
SQUID by more than one order of magnitude. They
are observed for magnetic inductions at which
matching between vortex and antidot lattice and
matching between vortex lattice and grain boundary
do not coincide and therefore compete.
These observations can be explained by commensurability effects between vortex and antidot lattices
in the presence of the grain boundary of the washer.
The vortices are exposed to the attractive pinning
potentials of the grain boundary and the antidot
lattice. On one hand, the grain boundary represents a
one-dimensional pinning potential for the flux lines.
The vortices can move easily along the boundary
and, thus, a vortex lattice would preferentially be
oriented along the grain boundary. On the other
hand, the antidot lattice defines a two-dimensional
potential with well-defined minima at the submicrometer holes w18x. Due to the presence of two
different interactions, two matching conditions have
to be considered: Ža. matching between the vortex
lattice and the grain boundary in the washer and Žb.
matching between the vortex and the antidot lattice.
As a consequence, we observe Ži. a reduction of the
1rf noise at magnetic inductions for which both
matching conditions are fulfilled Že.g., M1 and M2 .,
and Žii. an enhancement of the 1rf noise contribution at fields for which adjacent positions in the
antidot lattice or grain boundary are equally likely to
be populated by vortices. In this case, vortices are
exposed to a kind of double-potential similar to the
model of Dutta et al. w24,25x, which leads to excess
1rf noise due to thermally activated vortex motion
within the double potential w1x.
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Fig. 7. Typical low-frequency noise spectra of a BS with an additional layer with antidots, which is placed in flip-chip configuration upon
the grain boundary of the washer, for different magnetic inductions. M1 and M2 label matching conditions Žsee Table 1..
3.4. Conclusions and outlook
In conclusion, antidot lattices with antidot diameter down to 250 nm and lattice parameters down to
500 nm have been prepared into HTS thin films
without degradation of the superconducting properties and the presence of an attractive interaction
between antidots and vortices has been demonstrated
Fig. 8. Magnetic field dependence of the integrated noise spectrum of a BS with and without an additional YBCO layer with antidots. The
dashed–dotted line represents the theoretical field dependence Eq. Ž2. of the SQUID without antidot lattice.
34
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et al.r Physica C 332 (2000) 27–34
¨
via resistive, inductive and SQUID measurements.
Matching effect could be observed down to extremely small fields Ž247 nT s Bm r324.. The existence of multiquanta vortices Ždepending on antidot
lattice parameters and temperature. could be demonstrated. Finally, it has been proven that the attractive
vortex–antidot interaction can strongly affect the
low-frequency 1rf noise in active devices. The
transfer of this very promising technology for 1rf
noise reduction to standard HTS SQUIDs used in
applications Že.g., nondestructive evaluation of doping profiles, magneto-encephalography. is presently
under way w26x.
Acknowledgements
We thank A. v.d. Hart, H.P. Bochem, F.J.
Schroteler,
J. Einfeld, R. Kutzner, A.I. Braginski and
¨
J.R. Clem for technical assistance, helpful discussions and valuable information. A. Castellanos acknowledges the financial support from DAAD Germany.
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