Strong field-matching effects in superconducting YBa2Cu3O7-δ δ films with vortex energy
landscapes engineered via masked ion irradiation
I. Swiecicki1, C. Ulysse2, T. Wolf3, R. Bernard1, N. Bergeal3, J. Briatico1, G. Faini2, J.
Lesueur3, and Javier E. Villegas1,*
1 Unité Mixte de Physique CNRS/Thales, 1 avenue A. Fresnel, 91767 Palaiseau, and
Université Paris Sud 11, 91405 Orsay, France
2 CNRS, Phynano Team, Laboratoire de Photonique et de Nanostructures, route de Nozay,
91460 Marcoussis, France.
3 LPEM, CNRS-ESPCI, 10 rue Vauquelin 75231 Paris, France
We have developed a masked ion irradiation technique to engineer the energy
landscape for vortices in oxide superconductors. This approach associates the possibility to
design the landscape geometry at the nanoscale with the unique capability to adjust depth of
the energy wells for vortices. This enabled us to unveil the key role of vortex channeling in
modulating the amplitude of the field matching effects with the artificial energy landscape,
and to make the latter govern flux dynamics over an usually wide range of temperatures and
The energy landscape for vortices in superconductors can be engineered via the
introduction of ordered distributions of sub-micrometric structures –e.g. holes or inclusions–
which create the energy wells (pinning sites) for vortices. This possibility has opened the door
to a wide spectrum of fundamental studies, and to a number of applications (for a review, see
Ref. 1). From the fundamental point of view, the interest of flux dynamics on artificial energy
landscapes reaches beyond vortex physics, as it has become a model system to study a variety
of problems which involve interacting particles (e.g. colloids, atoms, or charge density waves)
moving on a pinning substrate2,3. Regarding the applications, the ability to manipulate
vortices has brought forth the so-called “fluxtronics”, in which vortex confinement, guidance4-
7 and rectification8-11 via energy landscapes with special geometries constitute the basis of
superconducting diodes9-13, signal processing14 and novel computing applications15-17.
While much of the progress in this area has been done with low critical-temperature
(TC) superconductors1,2,4,5,8,10,11, extending this research to high-TC materials6,7,14,18-22 is
particularly interesting. For the latter, the interplay between the artificial ordered pinning, the
characteristic anisotropy, and the strong thermal fluctuations predisposes to a richer
phenomenology. However, in the presence of strong intrinsic random pinning, the impact of
the artificial energy landscape on vortex dynamics –as measured e.g. by the amplitude of the
field matching effects observed in the magnetotransport– is generally found to be much
weaker in high-TC (e.g. YBa2Cu3O7-δ)18,21,22 than in low-TC superconductors (e.g. Nb)1.
In this paper, we show how to make the artificial energy landscape prevail over the
intrinsic random pinning and govern vortex dynamics in YBa2Cu3O7-δ (YBCO) thin films, in
an unusually wide range of temperatures, and in relatively high magnetic fields. We use a
combination of e-beam lithography and ion irradiation to engineer the vortex energy
landscape via the modulation of the local electronic properties produced by ion damage23.
This form of “electronic patterning” allows shaping the vortex energy landscape at the scale
of only a few tenths of nanometers. That is about one order-of-magnitude better than achieved
by physically patterning the superconductors via lithography and etching (e.g. introducing
arrays of holes)6,7,9,14,18-20, which dramatically increases –up to the kGauss range– the field
range in which the artificial energy landscape is dominant. In addition, and crucially, the
method developed here provides with the unique ability to adjust the depth of the landscape
energy wells. By systematically varying both parameters (geometry and depth) in a series of
experiments, we actually obtained field matching effects which are as strong as for clean low-
TC materials, and we gained understanding on the mechanism determining their amplitude. In
particular, our experiments evidence the key role played by vortex channeling effects, which
critically depend on the distance between energy wells in the landscape. In addition to its
fundamental interest, all of the above makes of our approach a powerful, versatile method for
vortex manipulation in oxide superconductors, in applied magnetic fields up to two orders of
magnitude higher than with other techniques6,7,9,14,18-20. This is specially relevant for
fluxtronic devices, because higher applied magnetic fields B imply a higher the vortex
Bnvα , and therefore greater data storage capacity in devices conceived for logic
operation15-17, and larger output signals in those for signal processing14.
The samples fabrication is done as follows. The YBCO superconducting thin films (50
nm thick; grown by pulsed laser deposition on (100) SrTiO3 substrates) are covered with a
thick (~800 nm) resist for e-beam lithography (PMMA). The lithography process allows us to
create periodic hole arrays in the PMMA [see Figs. 1 (a) and (b)], with the desired geometry
(square, rectangular, etc), distance between holes d (center to center; ranging from 80 to 180
nm), and holes diameter ∅. The experiments in this paper are for square arrays of holes with
fixed ∅=40 nm and variable d=120, 150 and 180 nm. After lithography, the resulting nano-
perforated PMMA layer on top of the YBCO layer is used as a mask [Fig. 1 (d)] through
which we irradiate with O+ ions (with energy E=110 keV and fluence ranging f=1013 cm-2 to 5
1013 cm-2). After irradiation, the resistance vs. temperature R(T) of the YBCO films [Fig. 1
(c)] reveal a depression of TC and an increase of the normal-state resistivity ρN as compared to
the fresh films. As we show below, these effects depend on the irradiation fluence f and on
the mask density of holes.
The projected range of penetration of the 110 keV O+ ions into PMMA is ~600 nm
(obtained from Monte-Carlo simulations)24. Therefore the ions are fully stopped by the mask
and reach the YBCO film only through the mask holes. O+ ion bombardment does not change
the YBCO surface morphology21, but creates point defects within the bulk of the material21.
Since the O+ track length into YBCO (~ 150 nm)22 is much longer than the film thickness (50
nm), ion-induced damage within the films is expected in depth from the exposed surface,
down into the SrTiO3 substrate. The local density of point defects σ –defined as the ratio of
displaced atoms per existing ones– can be calculated via Monte Carlo simulations24 which
take into account the irradiation energy E, the fluence f and the PMMA mask geometry. σ
(averaged over the film thickness) for different arrays and f are shown as contour plots in
Figs. 2 (d)-(h). Note that the point defects appear not only underneath the hole areas directly
exposed to be ion beam, but also in between these, because the ions spread out as they
impinge on the YBCO film. The density of defects in the non-exposed areas of the film
strongly depends on the fluence f and the distance between mask holes d. The presence of
point defects implies a local depression of the critical temperature, according to an
Abrikosov-Gorkov depairing law25. This allows us to calculate the local critical temperature
tC expected from σ. tC(x) [with x the position along the dashed lines shown in Figs. 2(d)-(f)]
is displayed in Figs. (a)-(c) . For the highest f=5 1013 cm-2 [black curves in Figs. 2(a)-(c)], tC
is completely suppressed in the hole areas directly exposed to the ion beam. Lower f imply a
depressed but finite tC in the hole areas (see red and green curves in Fig. 2 (a) for 2⋅1013 and
1013 cm-2 respectively). Thus, tuning of f and d enables us to tailor the spatial modulation of
tC. Because it is energetically favourable for flux quanta to locate in regions with depressed
tC26, this allows us to design the vortex energy landscape with nanometric resolution. The
potential energy wells for vortices will be formed in areas where tC is more substantially
depressed (i.e. the circular areas exposed to the ion beam).
Fig. 2 shows that the experimental critical temperatures TC of the films after
irradiation (defined by R(TC)=0.9RN, with RN the normal-state resistance at the onset of the
transition) are in good agreement with the above simulations. The experimental TC
(normalized to the critical temperature prior to irradiation TC VIRG ~ 80-85 K for all samples)
as a function d and f is shown with solid symbols in Figs. 2 (i) and (j), respectively. Note that
in both cases the experimental trends are closely reproduced if one plots as a function of d and
f the maximum tC (which is in the areas non-exposed to the ion beam) obtained from
simulations. Finally, we observe that the increase of the normal-state resistivity (at 100 K)
with respect to that of the fresh samples (ρ0~500-700 μΩ cm for all samples) scales with f/d2,
which means that the films resistivity is proportional to the average irradiation dose.
We show in what follows that the modulation of tC creates an energy landscape for
vortices, and that slight changes of the irradiation fluence and array parameter d produce
dramatic effects on flux dynamics. Figs. 3 (a)-(f) depict the resistance vs. applied field B for
different d and f [each panel correspond to each of the cases for which simulations are shown
in Figs. 2 (d)-(h)]. B is applied perpendicular to the film plane. The temperatures for the
measurements in Fig. 3(a)-(e) were chosen for all the samples to display similar zero-field
resistance (normalized to the normal-state one RN). This criterion enables the direct
comparison between the curves, and is more appropriate than the absolute temperature T or
the reduced one T/TC, provided the different TC and transition widths depending on f and d. A
series of pronounced periodic oscillations are observed in the curves (note that the y axis is in
logarithmic scale). The amplitude of the magneto-resistance oscillations decreases with
increasing spacing d [for fixed f, Figs, 3(a)-3c)], and also when the f is decreased [for fixed d,
Figs. 3(a)-(d)-(e)]. For each curve, the more pronounced minima correspond to the
“matching field” B=±B1, with B1≡φ0/d2 the field at which the external field induces one flux
quantum per unit cell of the square array. This is shown in Fig. 3 (h), in which the
experimental B1 are plotted vs. φ0/d2. The sample with highest f=5 1013 cm-2 and shortest
d=120 nm (Fig. 3a and 3f) presents clear minima also at B=±2B1 (two flux quanta per unit
cell). However, the second-order minima become less pronounced as d is increased (Figs. 3(a)
→(b)→ 3c)). For lower f [Figs. 3(d)-(e)], only first-order matching effects are visible. Note
finally that a closer look to the curve in Fig. 3 (f) (see inset) unveils the presence of clear
fractional matching at B=0.5B1, for which minima are shallower as expected27. In summary,
the strongest matching effects (characterized by deeper minima, and the by presence of
clearer second order and fractional matching) are observed for the shortest d and highest f.
The commensurability effects described above are the well-known fingerprint of
periodic flux pinning in superconductors1,4,5,8,10,14,18-20. Matching of the flux lattice to the
square geometry of the artificial energy landscape produces an enhancement of the vortex-
lattice pinning, which slows-down vortex motion and leads to a resistance decrease. In the
present experiments, these effects appear in an unusually wide range of temperatures below
TC. When considering the magneto-resistance measured at constant injected current, the
effects typically smooth out with increasing temperature [see Fig. 3(f)]. In the non-ohmic
regimes of the resistance, increasing the injected current also leads to smoothing of the
magnetoresistance oscillations. Notably, for the samples irradiated with higher fluences (f=5
1013 cm-2), the matching effects are present both above and below the irreversibility line24
(which was determined from the curvature of I(V) characteristics). In the latter case, the
matching effects are also visible in the critical depinning current JC vs. field, very far below
TC [see Fig. 3(g)]. This behaviour is unusual in samples with strong random pinning (such as
Nb and PLD-grown YBCO thin films), in which that type matching effects are typically found
only very close to TC and gradually disappear for lower temperatures as the disordered
pinning prevails over the artificial pinning landscape.1,18
The results shown in Fig. 3 illustrate the potential of the irradiation technique to finely
tailor the energy landscape for flux quanta. Varying f changes the strength of the
commensurability effects [Figs. 3(a)→(d)→(e)], because the amplitude of the tC modulation
diminishes as the irradiation fluence is decreased, which leads to shallower potential energy
wells and thus to weaker flux pinning. Interestingly, relatively small variations of the array
dimensions also produce dramatic changes on flux dynamics: for fixed f, the amplitude of the
magneto-resistance oscillations decreases as d is increased [Figs. 3(a)→(c)]. We argue that
this behaviour is connected to flux channelling across the energy landscape,1,5-7 Besides
directing vortex motion along preferred directions5-7 (the energy landscape x and y axes),
channelling enhances vortex mobility for fields in which the flux lattice does not match the
pinning potential (i.e. for fields different from B=B1,2B1… etc)1. Therefore, in the presence of
strong vortex channelling, the amplitude of the magneto-resistance oscillations is larger than
when channelling is weak, due to a greater difference between the resistances at the matching
condition and out-of-matching. Channelling is caused by the overlap of the potential energy
wells. The shorter the distance between them, the stronger the channelling effects1,5-7. In the
present experiments, this effect is exacerbated because the ion damage -and therefore tC-
within the areas in between the mask holes strongly depends on the array parameter d, as
illustrated by Fig. 2. Therefore, when d is the shortest, channelling effects are the strongest,
and the magneto-resistance oscillations the largest.
Further evidence for the above scenario is found by comparing the mixed-state
magneto-resistance with the magnetic field applied in-plane (i.e. parallel to the ab plane; B||)
and out-of-plane (perpendicular to the ab plane, B⊥). This is shown in Fig. 4 for the sample
that exhibits the strongest matching effects (f=5 1013 cm-2 and d=120 nm). The electrical
current is perpendicular to the applied field in both cases.
The inset of Fig. 4 shows the raw R(B). As expected, the commensurability effects are
absent when the applied field is parallel to the film plane: in this case, the Lorentz force is
perpendicular to the film plane, and therefore the vortices are forced to move in the direction
perpendicular to the periodic energy landscape. The background magneto-resistance is very
different depending on the applied field direction. In particular, R(B||)<<R(B⊥) as is expected
for anisotropic superconductors26. We quantitatively analyzed this behaviour via the
anisotropic Ginsburg-Landau approximation.24 In the absence of artificial pinning, this allows
scaling the external field via the anisotropy parameter γ and the rule B=γ-1B||=B⊥, so that R(γ-
1B||)=R(B⊥). For pristine YBCO films γ~5-7. For the irradiated film, however, such scaling is
not possible over the entire field range, but only for B>~5 kOe. This is shown in the main
panel of Fig. 4, which displays the collapse of R(γ-1B||) and R(B⊥), obtained with γ~4. The
comparison of R(γ-1B||) and R(B⊥) in the field range within which they do not coincide
provides with valuable information. Below the first matching field, when the vortex density is
low, channelling along the energy landscape principal axes yields a higher vortex mobility for
out-of-plane than for in-plane fields; in the latter case there is no channelling since vortices
move perpendicularly to the artificial energy landscape. This accounts for R(B⊥)<R(γ-1B||).
For fields closer to the matching condition (B⊥=B1), the pinning enhancement occurring for
perpendicular field dramatically reduces the vortex mobility, and therefore R(B⊥)<<R(γ-1B||).
According to previous work28, R(B⊥)<<R(γ-1B||) at the matching fields (i.e. for B=B1 and 2B1)
confirms that the magneto-resistance oscillations are connected to flux pinning phenomena,
and rules out that the irradiated film was merely behaving as a superconducting wire
network29 and the oscillatory magneto-resistance originated from Little-Parks30 or closely
related effects31. This is further supported by the fact that the periodic field modulation can be
seen also in JC(B) [Fig. 3 (g)], at temperatures far below TC, contrary to what is observed for
flux quantization effects in superconducting wire networks31. Finally, in the high field regime
B>~5 kOe, even though the commensurability effects are not visible, the presence of the
periodic energy landscape produces a somewhat reduced anisotropy (γ~4) as compared to
In summary, we have a developed a masked irradiation technique to engineer the
energy landscape for flux quanta in high-temperature superconductors. This approach offers
the unique advantage that it allows i) shaping the vortex energy landscape at a nanometric
scale, and ii) independently tuning the depth of the energy wells. Based on this ability, our
experiments evidence the role of vortex channelling effects in determining the strength of
flied matching effects in artificial energy landscapes. Finally, we demonstrate the possibility
to finely control flux dynamics in fields up to two orders of magnitude higher than with
conventional lithography/etching techniques. Thus, besides its technological interest, our
realization enables access to a interesting a regime in which the flux lattice elastic energy and
the artificial pinning energy strongly compete. We stress at this point that, in addition to other
oxide superconductors, this masked irradiation technique could be applied to a variety of
functional oxides sensitive to local disorder (e.g. ferromagnets or semiconductors)32 in order
to engineer phase segregation at the nanoscale.
Work supported by the French ANR via “SUPERHYBRIDS-II”.
Figure 1 (a) Scanning electron microscopy of a PMMA mask (b) Zoom of the indicated area.
(d) Resistivity vs. temperature of a series of YBCO films, prior (VIRG) and after irradiation
through masks with different inter-hole distance d (see legend, in nm). Curves normalized to
the film resistivity at 100 K prior to irradiation. (c) Sketch of the ion irradiation of YBCO
through the PMMA mask.
Figure 2 (a)-(c) Local critical temperature tC along the array axes indicated by the dashed
lines in (d)-(f). Black curves for f=5 1013, green for f=103 and red for 2 1013 cm-2 (d)-(h)
Defect density σ from Monte-Carlo simulations for the parameters d and f indicated. The
color grade is in logarithmic scale (the legend must be multiplied by 10-3) and saturates above
5 10-3 and below 4 10-4. (i)-(j) Superconducting critical temperature after irradiation
(normalized to that measured prior to irradiation, TC VIRG) (i) as a function of the array
parameter d, (for fixed fluence f=5 1013 cm-2) and (j) as a function of f (for fixed d=120 nm).
Solid symbols are experimental data and hollow ones correspond to the values expected from
simulations. (k) Normal-state (at 100 K) resistivity of the irradiated samples, normalized to
that measured prior to irradiation (ρ0) as a function f/d2 . The lines are a guide to the eye.
Figure 3 (a)-(e) Mixed-state resistance (normalized to the normal-state one RN) as a function
of the applied field B, different d and f (see legends). The injected current was J=0.5 kA cm-2.
The vertical dashed lines mark the first and second order matching fields. (f) Same as in (a) at
two different temperatures and J=2.5 kA cm-2. B1=1.45 kGauss is the matching field. Inset:
zoom of the curve. (g) Critical current as a function of the applied field for the same sample as
in (a) at T=12K=0.19TC. (h) Experimental matching fields B1 as a function of φ0/d2.
Figure 4: Magneto-resistance with the field applied perpendicular (B⊥) and parallel (B||) to the
ab plane, for the sample with f=5 1013 cm-2 and d=120 nm, at T=27 K and with J=1.25 kA
cm-2. The inset shows the raw data and the main panel the curves collapse using the
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