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Enhanced vortex trapping by a composite antidot lattice in a superconducting Pb film
Physica C 460–462 (2007) 1434–1435 www.elsevier.com/locate/physc
Enhanced vortex trapping by a composite antidot lattice in a superconducting Pb film A.V. Silhanek a
a,*
, L. Van Look a, R. Jonckheere b, B.Y. Zhu c, S. Raedts a, V.V. Moshchalkov a
INPAC–Institute for Nanoscale Physics and Chemistry, Nanoscale Superconductivity and Magnetism & Pulsed Fields Group, K.U. Leuven, Celestijnenlaan 200 D, B-3001 Leuven, Belgium b IMEC vzw, Kapeldreef 75, B-3001 Leuven, Belgium c National Laboratory for Superconductivity, Institute of Physics, Chinese Academy of Sciences, Beijing 100080, China Available online 18 April 2007
Abstract Using electrical transport measurements, we study a composite antidot lattice consisting of two interpenetrating antidot square arrays with a different antidot size and the same lattice period. We show that placing an additional small antidot in the unit cell of the array a higher number of flux quanta per unit cell can be trapped inside the antidots, compared to a reference antidot film without the additional small antidots. As a consequence, the field range in which an enhanced critical current is observed is considerably expanded. Ó 2007 Elsevier B.V. All rights reserved.
The introduction of an array of holes (antidots) in a superconducting film strongly influences its critical current Jc and the critical temperature Tc [1]. At low magnetic fields and temperatures close enough to Tc the antidots are able to trap only one flux quantum /0 before saturation sets in. In this case, after the first matching field H1 /0/ d2, where d is the period of the antidot lattice, interstitial vortices appear in the sample creating an interpenetrated lattice where some of the vortices are strongly pinned at the antidots and the rest occupies interstitial positions in between the antidots. Due to their higher mobility, the presence of interstitial vortices lowers the critical current and broadens the superconducting transition [2]. This situation naturally suggests that the superconducting parameters could be further enhanced by simply adding efficient pinning sites exactly at the locations where the interstitial vortices would appear. In this work we experimentally verify this prediction using a composite antidot array consisting of two square lattices with the same period *
Corresponding author. Tel.: +32 016 327175; fax: +32 016 327983. E-mail address: [email protected] (A.V. Silhanek). 0921-4534/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2007.04.144
d = 1.5 lm but different antidot size (a1 = 0.55 lm and a2 = 0.25 lm) as shown in the top right atomic force microscopy image in Fig. 1. The phase boundaries for the composite array, a reference antidot sample with identical periodicity and a plain film, are shown in the upper panel of Fig. 1. A clear enhancement of Tc(H) is observed as a result of the lateral nanostructuring. For the composite lattice the phase boundary exhibits a parabolic background for fields H < 8H1 (or T/Tc(0) > 0.991) where the superconducting coherence length n(T) becomes larger than half the distance between holes 1/2(d a1) 0.48 lm. Within this collective regime p[3] Tc(H)/Tc(0) = 1 (aH)2 where a = n(0)p(d a1)/2 3/0. Using this expression to fit the data shown in Fig. 1 we obtain 1/2(d a1) 0.55 lm which is in good agreement with the expected value. Due to the presence of the regular array of holes (in the collective regime) matching features appear at multiples of H1 = 9.2 G for the reference antidot sample. Strikingly, the same periodicity is observed for the composite array. This is a non trivial result since the composite lattice can be regarded as a square lattice tilted 45° with a unit cell twice as small as that of the reference antidot sample. Thus, the main period felt by the vortices is that imposed by the
A.V. Silhanek et al. / Physica C 460–462 (2007) 1434–1435
Fig. 1. Upper panel: superconductor-normal phase boundary using 10% criterion for a plain film, an antidot sample and a composite sample. Lower panel: normalized critical current as a function of field at T/ Tc(0) = 0.993 for the antidot sample (filled circles) and the composite array (open circles).
large antidots. For H > 8H1 the single object regime is entered and a linear phase boundary slightly modulated by /0/a2 7H1 oscillations is expected. The influence of the small hole is not limited to the phase boundary but it also affects to properties deep into the superconducting state. The lower panel of Fig. 1 shows the normalized critical current Jc/Jc(0) at T/Tc(0) = 0.993 for both the reference antidot and the composite arrays. At this temperature, a strong enhancement of Jc in the film with a composite antidot lattice is found for fields higher than the first matching field H1, compared to the reference antidot lattice. The reason for this lies in the ability of the composite antidot lattice to pin more flux quanta inside the antidots compared to the reference antidot array. Indeed, up to H1, the vortices will be attracted towards the large antidots. Between H1 and 2H1, vortices begin to
1435
occupy the small antidots. Due to their size, these small antidots trap at most a single quantum vortex. Therefore, they will be completely saturated at 2H1, creating a repulsive potential at the position of the small antidot. Since the large antidots pin one flux quantum, at H1 a surface barrier emerges at the antidot edges. For 2H1, the contribution to the potential of the small antidot at the center of the unit cell is strongly repulsive. When additional vortices enter the sample, they will be pushed towards the large antidots thus leading to an increase of their effective saturation number. This additional repulsive potential at the small antidots helps to increase the saturation number of the larger antidots [4]. We therefore conclude that of the four flux quanta trapped per unit cell of the composite antidot lattice, one is pinned by the small antidot, while three are pushed into the larger holes. This leads to a substantial broadening of the field range where a strong Tc(H) enhancement is observed. A similar picture was introduced by Doria and co-workers [5] to explain the multiple trapping of vortices at high fields, as a result of the pressure exerted by the external vortices into the pinning site. Concluding, measurements of the critical temperature and critical current as a function of magnetic field, show that the composite antidot lattice can trap a considerably higher amount of vortices per unit cell inside the antidots, compared to a reference antidot film without the additional small antidots. This indicates that the appearance of interstitial vortices in the composite antidot lattice is delayed to higher magnetic fields. The presence of the smaller antidots has therefore increased the effective saturation number of the large antidots, which in turn led to a considerable expansion of the field range in which an enhanced critical current is observed. References [1] V.V. Moshchalkov, M. Baert, V.V. Metlushko, E. Rosseel, M.J. Van Bael, K. Temst, Y. Bruynseraede, Phys. Rev. B 57 (1998) 3615. [2] V. Metlushko, U. Welp, G.W. Crabtree, R. Osgood, S.D. Bader, L.E. DeLong, Zhao Zhang, S.R.J. Brueck, B. Ilic, K. Chung, P.J. Hesketh, Phys. Rev. B 60 (1999) R12585. [3] B. Pannetier, in: B. Kramer (Ed.), Quantum Coherence in Mesoscopic Systems, Plenum Press, New York, 1991, p. 457 (Chapter 9). [4] A.V. Silhanek, L. Van Look, R. Jonckheere, B.Y. Zhu, S. Raedts, V.V. Moshchalkov, Phys. Rev. B 72 (2005) 014507; G.R. Berdiyorov, M.V. Milosevic, F.M. Peeters, Europhys. Lett. 74 (2006) 493. [5] M.M. Doria, G.F. Zebende, Phys. Rev. B 66 (2002) 064519.
Enhanced vortex trapping by a composite antidot lattice in a superconducting Pb film A.V. Silhanek a
a,*
, L. Van Look a, R. Jonckheere b, B.Y. Zhu c, S. Raedts a, V.V. Moshchalkov a
INPAC–Institute for Nanoscale Physics and Chemistry, Nanoscale Superconductivity and Magnetism & Pulsed Fields Group, K.U. Leuven, Celestijnenlaan 200 D, B-3001 Leuven, Belgium b IMEC vzw, Kapeldreef 75, B-3001 Leuven, Belgium c National Laboratory for Superconductivity, Institute of Physics, Chinese Academy of Sciences, Beijing 100080, China Available online 18 April 2007
Abstract Using electrical transport measurements, we study a composite antidot lattice consisting of two interpenetrating antidot square arrays with a different antidot size and the same lattice period. We show that placing an additional small antidot in the unit cell of the array a higher number of flux quanta per unit cell can be trapped inside the antidots, compared to a reference antidot film without the additional small antidots. As a consequence, the field range in which an enhanced critical current is observed is considerably expanded. Ó 2007 Elsevier B.V. All rights reserved.
The introduction of an array of holes (antidots) in a superconducting film strongly influences its critical current Jc and the critical temperature Tc [1]. At low magnetic fields and temperatures close enough to Tc the antidots are able to trap only one flux quantum /0 before saturation sets in. In this case, after the first matching field H1 /0/ d2, where d is the period of the antidot lattice, interstitial vortices appear in the sample creating an interpenetrated lattice where some of the vortices are strongly pinned at the antidots and the rest occupies interstitial positions in between the antidots. Due to their higher mobility, the presence of interstitial vortices lowers the critical current and broadens the superconducting transition [2]. This situation naturally suggests that the superconducting parameters could be further enhanced by simply adding efficient pinning sites exactly at the locations where the interstitial vortices would appear. In this work we experimentally verify this prediction using a composite antidot array consisting of two square lattices with the same period *
Corresponding author. Tel.: +32 016 327175; fax: +32 016 327983. E-mail address: [email protected] (A.V. Silhanek). 0921-4534/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2007.04.144
d = 1.5 lm but different antidot size (a1 = 0.55 lm and a2 = 0.25 lm) as shown in the top right atomic force microscopy image in Fig. 1. The phase boundaries for the composite array, a reference antidot sample with identical periodicity and a plain film, are shown in the upper panel of Fig. 1. A clear enhancement of Tc(H) is observed as a result of the lateral nanostructuring. For the composite lattice the phase boundary exhibits a parabolic background for fields H < 8H1 (or T/Tc(0) > 0.991) where the superconducting coherence length n(T) becomes larger than half the distance between holes 1/2(d a1) 0.48 lm. Within this collective regime p[3] Tc(H)/Tc(0) = 1 (aH)2 where a = n(0)p(d a1)/2 3/0. Using this expression to fit the data shown in Fig. 1 we obtain 1/2(d a1) 0.55 lm which is in good agreement with the expected value. Due to the presence of the regular array of holes (in the collective regime) matching features appear at multiples of H1 = 9.2 G for the reference antidot sample. Strikingly, the same periodicity is observed for the composite array. This is a non trivial result since the composite lattice can be regarded as a square lattice tilted 45° with a unit cell twice as small as that of the reference antidot sample. Thus, the main period felt by the vortices is that imposed by the
A.V. Silhanek et al. / Physica C 460–462 (2007) 1434–1435
Fig. 1. Upper panel: superconductor-normal phase boundary using 10% criterion for a plain film, an antidot sample and a composite sample. Lower panel: normalized critical current as a function of field at T/ Tc(0) = 0.993 for the antidot sample (filled circles) and the composite array (open circles).
large antidots. For H > 8H1 the single object regime is entered and a linear phase boundary slightly modulated by /0/a2 7H1 oscillations is expected. The influence of the small hole is not limited to the phase boundary but it also affects to properties deep into the superconducting state. The lower panel of Fig. 1 shows the normalized critical current Jc/Jc(0) at T/Tc(0) = 0.993 for both the reference antidot and the composite arrays. At this temperature, a strong enhancement of Jc in the film with a composite antidot lattice is found for fields higher than the first matching field H1, compared to the reference antidot lattice. The reason for this lies in the ability of the composite antidot lattice to pin more flux quanta inside the antidots compared to the reference antidot array. Indeed, up to H1, the vortices will be attracted towards the large antidots. Between H1 and 2H1, vortices begin to
1435
occupy the small antidots. Due to their size, these small antidots trap at most a single quantum vortex. Therefore, they will be completely saturated at 2H1, creating a repulsive potential at the position of the small antidot. Since the large antidots pin one flux quantum, at H1 a surface barrier emerges at the antidot edges. For 2H1, the contribution to the potential of the small antidot at the center of the unit cell is strongly repulsive. When additional vortices enter the sample, they will be pushed towards the large antidots thus leading to an increase of their effective saturation number. This additional repulsive potential at the small antidots helps to increase the saturation number of the larger antidots [4]. We therefore conclude that of the four flux quanta trapped per unit cell of the composite antidot lattice, one is pinned by the small antidot, while three are pushed into the larger holes. This leads to a substantial broadening of the field range where a strong Tc(H) enhancement is observed. A similar picture was introduced by Doria and co-workers [5] to explain the multiple trapping of vortices at high fields, as a result of the pressure exerted by the external vortices into the pinning site. Concluding, measurements of the critical temperature and critical current as a function of magnetic field, show that the composite antidot lattice can trap a considerably higher amount of vortices per unit cell inside the antidots, compared to a reference antidot film without the additional small antidots. This indicates that the appearance of interstitial vortices in the composite antidot lattice is delayed to higher magnetic fields. The presence of the smaller antidots has therefore increased the effective saturation number of the large antidots, which in turn led to a considerable expansion of the field range in which an enhanced critical current is observed. References [1] V.V. Moshchalkov, M. Baert, V.V. Metlushko, E. Rosseel, M.J. Van Bael, K. Temst, Y. Bruynseraede, Phys. Rev. B 57 (1998) 3615. [2] V. Metlushko, U. Welp, G.W. Crabtree, R. Osgood, S.D. Bader, L.E. DeLong, Zhao Zhang, S.R.J. Brueck, B. Ilic, K. Chung, P.J. Hesketh, Phys. Rev. B 60 (1999) R12585. [3] B. Pannetier, in: B. Kramer (Ed.), Quantum Coherence in Mesoscopic Systems, Plenum Press, New York, 1991, p. 457 (Chapter 9). [4] A.V. Silhanek, L. Van Look, R. Jonckheere, B.Y. Zhu, S. Raedts, V.V. Moshchalkov, Phys. Rev. B 72 (2005) 014507; G.R. Berdiyorov, M.V. Milosevic, F.M. Peeters, Europhys. Lett. 74 (2006) 493. [5] M.M. Doria, G.F. Zebende, Phys. Rev. B 66 (2002) 064519.