APPLIED PHYSICS LETTERS 91, 202510 共2007兲
Superconducting microrings as magnetic pinning centers
W. Gillijns,a兲 A. V. Silhanek, and V. V. Moshchalkov
INPAC-Institute for Nanoscale Physics and Chemistry, Nanoscale Superconductivity and Magnetism
and Pulsed Fields Group, Katholieke Universiteit Leuven, Celestijnenlaan 200D,
B-3001 Leuven, Belgium
共Received 23 August 2007; accepted 30 October 2007; published online 16 November 2007兲
The nucleation of the superconducting condensate in an Al film deposited on top of a periodic array
of microsized Pb rings is investigated using transport measurements. We demonstrate that these Pb
rings form tunable pinning sites which can be switched at will to repel or attract vortices in the Al
film, depending on their magnetic history. After zero field cooling, a repulsive interaction between
the rings and the vortices is observed, while after field cooling, the interaction becomes attractive.
The flexibility of such current-induced pinning centers can lead to an enhanced control over the
vortex motion. © 2007 American Institute of Physics. 关DOI: 10.1063/1.2815656兴
Superconductivity is a collective coherent quantum state
of electron pairs which can carry electrical current without
any losses. Unfortunately, already small external currents can
threaten this fragile dissipationless state, thus limiting the
possibilities of its practical applications. Since the appearance of losses is a direct consequence of the motion of quantum flux lines,1 it is imperative to impede their free motion
under external currents or thermal fluctuations. To this end,
all sorts of artificial pinning centers, either randomly
distributed2 or ordered in a periodic3 and quasiperiodic
array,4 have been studied, ranging from antidots3 and blind
holes5 to magnetic dots.6 For antidots, the attractive potential
results from the gain in condensation energy per unit volume,
which is limited by ␮0H2c / 2, where Hc is the thermodynamic
critical field. On the other hand, pinning by magnetic dots
results from the interaction between a magnetic dipole and a
flux line. It has recently been demonstrated that this pinning
potential Upin is proportional to −mb, where m is the magnetic moment of the dipole and b is the field of the vortex at
the position of the dipole.6–10 Interestingly, the depth of this
potential well is limited only by the maximum obtainable m,
i.e., the saturation magnetization of the chosen magnetic material. Maxwell’s equations11 provide us with an alternative
way of generating a magnetic dipolelike stray field: by sending circulating currents in a ring. In this case, since the dipolar moment m is directly proportional to the current, the
net magnetic moment can readily be controlled and can lead
to further enhanced pinning properties. A practical way of
generating a tunable moment m is to use microrings made of
a hard type II superconductor. Screening currents can be induced in such structures by different field cooling procedures, hereby generating the necessary dipole moment m. In
this work, we demonstrate that a periodic array of Pb rings
underneath a weak-pinning type II superconductor such as
Al, can lead to a clear enhancement of the pinning properties
in the Al when persistent currents are induced 共or equivalently flux lines trapped兲 in the microrings. For high persistent currents, field induced superconductivity is observed,
where the maximal critical temperature is located at a nonzero magnetic field. These persistent current induced dipoles
are a first step toward an externally controlled pinning potential by using metallic coils.
a兲
Electronic mail: werner.gillijns@fys.kuleuven.be
The studied sample consists of a 50 nm thick Al film
deposited on top of a square array 共period d = 2 ␮m兲 of Pb
rings with internal 共external兲 diameter of R1 = 0.6 ␮m
共R2 = 1.5 ␮m兲 and 45 nm thickness. These superconducting
materials were electrically separated by a 100 nm thick Ge
layer. The lateral structure of the rings is imaged by scanning
electron microscopy in Fig. 1共b兲, while the cross section of
the multilayered structure is schematically illustrated in Fig.
1共c兲. After deposition, the trilayer is patterned in a well defined transport bridge. The superconducting properties of the
Pb rings are characterized in a commercial Quantum Design
superconducting quantum interference device magnetometer.
The temperature dependence of the magnetization shows a
critical temperature of the Pb rings of about 7.0 K. The magnetization m of the Pb rings as a function of external field H
after a zero field cooling at 5 K is shown in Fig. 1共a兲. The
general features of this hysteresis loop are similar to those
previously reported for mesoscopic superconducting samples
by Hall magnetometry measurements.12,13 On the one hand, a
clear irreversible magnetization indicates the existence of
metastable states, corresponding to vortex trapping at remanence. On the other hand, the asymmetric shape of the magnetization loop with respect to the m = 0 axis suggests that
strong Bean-Livingston edge barriers delay the flux penetration but not the flux exit through the sample’s border.14 By
increasing the magnetic field, screening currents expel the
applied field 共Meissner state兲, leading to the typical linear
increase of the magnetization. At a field of approximately
12 mT, vortices enter the rings hereby decreasing the magnetization in discontinuous steps, as can be seen in the inset
of Fig. 1共a兲. The periodicity of these jumps is approximately
1.5 mT and corresponds to one flux quantum confined in a
circle with radius of approximately 660 nm. Considering that
5 K
the penetration depth of Pb at 5 K ␭Pb
is about 100 nm, this
result indicates that the screening currents mainly flow in the
outer perimeter of the rings. Interestingly, a different scenario occurs in the returning branch of the magnetization
loop. Indeed, now a series of jumps with a considerably
larger periodicity of 5 mT in m共H兲 can be observed as a
consequence of quantized flux removal from the rings. This
value, corresponding to a circle with radius of approximately
360 nm, is close to the inner diameter of the used rings
taking the penetration depth into account. It is worth noticing
that the state at remanence 共H = 0兲 exhibits a nonzero mag-
0003-6951/2007/91共20兲/202510/3/$23.00
91, 202510-1
© 2007 American Institute of Physics
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202510-2
Gillijns, Silhanek, and Moshchalkov
Appl. Phys. Lett. 91, 202510 共2007兲
FIG. 1. 共Color online兲 共a兲 Magnetization loop at 5 K
for a square array of Pb rings after a zero field cooling
procedure. The inset is a zoom in on the increasing field
branch. 共b兲 Scanning electron microscopy image of the
array of Pb rings. 共c兲 Cross section of the multilayered
sample.
netization, indicating the existence of flux trapping into the
rings. This metastable state persists due to screening currents
in the rings and corresponds to the highest possible trapped
flux. After applying fields above H 艌 17 mT, the final remanent state becomes field independent. By properly choosing
the maximum excursion field H 艋 17 mT after a zero field
cooling procedure, it is possible to obtain a different number
of trapped flux quanta per ring. Alternatively, the multiquanta
flux trapped in each Pb microring can be adjusted by performing field cooling experiments at different cooling fields.
As expected, both procedures lead to the same final conclusion. In principle, the flux lines can either be trapped inside
the rings by the screening currents or can be pinned somewhere between the inner and the outer borders of the rings,
0 K
is approximately 50 nmⰆ R2 − R1. The former scesince ␭Pb
nario is more likely to occur since it has been extensively
demonstrated that antidots in Pb films represent an efficient
way to pin vortices.15 Now, the flux trapped by the Pb rings
can be used to control the superconducting properties of the
Al film deposited on top of the Pb ring array.
Figure 2 summarizes the normal/superconductor phase
boundary Tc共H兲 of the Al film, as determined by a 10% of
the normal state resistance criterion, after following different
magnetic histories to vary m. In the zero field cooling experiment 关Fig. 2共a兲兴, a linear Tc共H兲 with no discernable features
can be observed. From the slope of this phase boundary, we
estimate a coherence length at zero temperature ␰共0兲 of about
127 nm for the Al film. The lack of features in this virgin
state is a result of the repulsive interaction between the rings
and vortices. This repulsion is caused by the fact that the
magnetic moment m共H兲 of the rings, which is field dependent due to Meissner screening, will always be antiparallel to
the field b of a nearby vortex in the Al due to the diamagnetic
character of the superconductor, regardless of the polarity of
the applied field. Under these circumstances, for all fields,
vortices sit at interstitial positions between neighboring rings
where a weak-pinning potential is developed. The high mobility of these vortices prevents the formation of ordered
states, thus conspiring against commensurability effects. This
result has analogies with the recently reported contrasting
pinning properties of quantum-growth voids and mesas in
thin Pb layers.16 We would like to mention that in this state
the rings represent a “soft” magnetic material since their net
magnetic moment changes when vortices are present.
A different situation emerges when the system is cooled
down below the critical temperature of the Pb rings in an
applied magnetic field. Figure 2共b兲 shows the Tc共H兲 boundary after field cooling in 6 mT. In this figure, clearly dis-
FIG. 2. Normal/superconductor phase boundary, as determined by a 10% of
the normal state resistance criterion, for the Al film deposited on top of the
Pb rings after following different field cooling procedures.
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202510-3
Appl. Phys. Lett. 91, 202510 共2007兲
Gillijns, Silhanek, and Moshchalkov
FIG. 3. 共Color online兲 Schematic representation of the pinning properties of
the rings after 共a兲 zero field cooling and 共b兲 field cooling.
cerned matching features appear at H = nH1, with n integer
and H1 = ␾0 / d2 ⯝ 0.52 mT, where the distribution of flux
lines commensurates with the underlying array of rings. In
addition, there is a clear asymmetry between positive and
negative fields. This can be explained by considering that the
persistent currents in the rings generate a fixed and robust
magnetic moment m0. Since this magnetic moment is positive 共after cooling in a positive field兲, positive vortices 共i.e.,
for H ⬎ 0兲 will be pinned more strongly than negative vortices 共i.e., for H ⬍ 0兲.7 The negative vortices will feel a repulsive interaction and will be located interstitially. In contrast
to the situation where the ring is in the Meissner state, now
clear matching features do appear. This is likely due to the
fact that m0 is larger than the field dependent magnetization
m共H兲 of the Meissner currents. Indeed, since the field of a
vortex is approximately Hc1 = ␾0 / 2␲␭2, a vortex in the Al
film will generate a relatively small magnetization since
␭Al ⬎ ␭Pb. Accordingly, the repulsion is stronger than in the
zero field cooled case, explaining the matching features for
H ⬍ 0. The two contrasting interactions between vortices and
the rings after zero-field cooling and field cooling are
stressed in Fig. 3. This field polarity dependent vortex pinning becomes even more pronounced when the rings are field
cooled at 10 mT 关Fig. 2共c兲兴. In this case, the maximum critical temperature is observed no longer at H = 0, but instead it
is shifted to H = H1. This behavior is entirely similar to that
obtained in a superconducting film deposited on top of an
array of out-of-plane magnetized dots and can be ascribed to
the field compensation of the externally applied field by the
dots’ stray field.17,18
Strikingly, after cooling the sample in fields higher than
20 mT, the same phase boundary corresponding to a shift of
one and a half-flux quanta per ring is obtained. This puzzling
effect is consistent with the above mentioned saturation of
the remanent magnetization for fields higher than 17 mT. For
the case shown in Fig. 2共d兲 of field cooling in 100 mT,
matching features are replaced by smooth field oscillations
only present at the left branch of the phase boundary. We
believe that the noninteger shift of the maximum Tc is a
consequence of the disorder introduced by the lithographically defined rings which, in turn, leads to a distribution of
maximum possible flux quanta trapped per ring. This kind of
disorder in the pinning energy could blur the commensura-
bility effects and eventually, unlike topological disorder,19
could significantly suppress all matching features.20 This
idea is further supported by the fact that the steps in the
returning branch of the magnetization loop arising from the
flux removal are not sharp but instead appear as a smooth
transition.
In brief, we have demonstrated that by inducing different
currents in an array of Pb microrings it is possible to switch
from a repulsive vortex-microring interaction to a strong attractive interaction in an overlying Al thin film. For the highest used persistent currents trapped in the rings, the superconducting phase boundary is shifted toward nonzero
magnetic field, thus signaling the presence of field induced
superconductivity. These findings pave the way toward more
controllable pinning centra by replacing the rings by coils in
which the applied current can be varied at will. In particular,
by individually addressing different rows of coils with different external currents, it would be possible to construct
flexible pinning landscapes to manipulate vortices, which is
of importance to realize fluxonics based devices.
This work was supported by the K.U.Leuven Research
Fund 共GOA/2004/02兲 program, the Belgian IUAP, the Fund
for Scientific Research-Flanders 共F.W.O.-Vlaanderen兲, and
the F.W.O. fellowship 共A.V.S.兲.
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