Flux avalanches triggered by AC magnetic fields in superconducting thin films

Physica C 479 (2012) 134–136

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Flux avalanches triggered by AC magnetic fields in superconducting thin films M. Motta a,⇑, F. Colauto a, T.H. Johansen b,c, R.B. Dinner d, M.G. Blamire d, G.W. Ataklti e, V.V. Moshchalkov e, A.V. Silhanek e,f, W.A. Ortiz a,c a

Departamento de Física, Universidade Federal de São Carlos, 13565-905 São Carlos, SP, Brazil Department of Physics, University of Oslo, POB 1048, Blindern, 0316 Oslo, Norway c Centre for Advanced Study, Norwegian Academy of Science and Letters, NO-0271 Oslo, Norway d Department of Materials Science, University of Cambridge, Pembroke Street, Cambridge CB2 3QZ, UK e INPAC- Institute for Nanoscale Physics and Chemistry, Nanoscale Superconductivity and Magnetism Group, KU Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium f Département de Physique, Université de Liège, B-4000 Sart Tilman, Belgium b

a r t i c l e

i n f o

Article history: Accepted 27 December 2011 Available online 5 January 2012 Keywords: Superconducting thin film Flux avalanches Magneto optical imaging Antidot array

a b s t r a c t Flux avalanches are known to occur as a consequence of thermomagnetic instabilities. Some of their fingerprints are jumps in magnetization curves, or a paramagnetic reentrance in AC susceptibility measurements. In this work we have studied flux avalanches triggered by an AC field cycle by means of AC susceptibility and residual magnetization after an applied AC field measured as a function of an AC excitation field (h). These measurements allow comparing both results with magneto-optical imaging carried out in similar conditions. The results show a correspondence for the onset of the avalanche activity, as well as between the residual magnetic moment and the mean gray value calculated from the magneto-optical images in the remanent state. Ó 2012 Elsevier B.V. All rights reserved.

1. Introduction Flux avalanches in films of type-II superconductors are characterized by sudden bursts which develop as a consequence of thermomagnetic instabilities that take place when heat dispersion is slower than magnetic diffusion. In fact, when the movement of a group of vortices releases enough heat to increase the temperature locally, the screening critical current decreases, allowing for further field penetration which feeds back the process positively [1]. Under certain conditions of temperature and magnetic field, some of the fingerprints of such avalanches can be detected in magnetic measurements, taken while varying the temperature (T), the magnetic field (H) or the AC excitation amplitude (h). These avalanches are associated with jumps in magnetization curves [2,3]; reentrances in AC susceptibility measurements made with constant h [4]; or even as a noisy response of the susceptibility components when the amplitude of the AC excitation is the experimental variable [5]. The impressive manner in which avalanches develop in thin films is evidenced through magneto-optical imaging (MOI) [6]. Through this technique one can visualize sudden flux penetration in patterns of dendritic shape. Several specimens exhibit such behavior, as has been reported for Nb [7], MgB2 [6,8], Nb3Sn [9], NbN [10], YNi2B2C [11], and YBCO [12]. Flux avalanches have also been studied in superconducting films decorated with arrays of antidots (ADs). The addition of ADs causes a ⇑ Corresponding author. Tel.: +55 16 3351 8228; fax: +55 16 3361 4835. E-mail address: [email protected] (M. Motta). 0921-4534/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2011.12.030

change in the number of avalanches and on their format [13], which are guided by the rows of such defects, as revealed by MOI experiments [14,15]. Moreover, there is also an enlargement of the instability region on the HT-diagram [4,13]. The avalanches cited above have been observed in isothermal experiments, in which the external parameter that has been changed is the DC applied field. Since a field variation is crucial for the occurrence of avalanches, one expects that the thermomagnetic instability might be enhanced by application of an AC excitation. Silhanek et al. [4] have reported features in the AC response that evidences an enlargement of the instability region in Pb films decorated with an array of ADs. A reentrant response in the AC susceptibility as a function of temperature – as well as of the magnetic field – was related to avalanches that decrease the efficiency of the AC screening. In the present work we have studied avalanches generated by an alternating field. Application of an AC excitation of sufficiently large amplitude triggers avalanches and leaves a residual magnetic moment on the sample. This residual magnetic response has been measured in the SQUID magnetometer and visualized by magnetooptical imaging. As shown below, the obtained results allow a consistent interpretation. 2. Materials and methods The specimen employed in this study is a Nb film with 50 nm thickness, decorated with antidots (ADs) of 0.4 lm in a square periodic array with a lattice constant of 1.5 lm. The pattern was produced by electron beam lithography [16] and the material

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Fig. 1. Scheme of a measurement for increasing values of the amplitude of the AC excitation field. Measurements of the residual magnetic moment, as well as MO images, were taken after a train of AC cycles.

Fig. 2. Residual magnetic moment taken after application of an AC field as a function of h. The inset shows both components of vac(h) taken in connection with mres.

was deposited on a Si(1 0 0) substrate using a UHV dc magnetron sputtering system. The sample has a superconducting transition temperature of 7.4 K. We have employed the following techniques in this study: (i) DC magnetization; (ii) AC susceptibility (vac) and (iii) MOI. Magnetic measurements were performed in a Quantum Design magnetometer MPMS-5S. The MOI experiments, which are based on the Faraday effect occurring in a garnet indicator with in-plane magnetization [17], were carried out in a setup similar to that described elsewhere [18]. Concerning the sample mounting, the garnet indicator is placed on top of the superconductor, which is fixed with Dow Corning grease on the cold finger of the cryostat. A split pair coil provides the applied magnetic field. Since the conductance of metals is enhanced at low temperatures, thus increasing the eddy currents which attenuate the AC field, we have calibrated our MOI setup for AC fields as large as 30 Oe, at frequencies up to 100 Hz and temperatures below 10 K, to compensate for the presence of the cold finger at the experimental region. The protocol of the experiment is illustrated in Fig. 1. Both measurements – the DC magnetic moment and the MOI – were performed after application of a train of AC cycles, which results, respectively, in a residual magnetic moment (mres), measured with the squid magnetometer; or a retained flux profile, captured by the magneto-optical image. There is also the additional information represented by the AC response, since mres is obtained after a measurement of the AC susceptibility, vac = v0 + iv00 . All measurements were carried out as a function of the AC amplitude (h) at 10 Hz, and null DC field. Before each run, the sample was zero-field-cooled from a temperature above Tc down to 3 K.

screening capability is reduced and the imaginary one reveals the existence of vortex viscous movement. Since AC and DC measurements were taken sequentially, a consistent correspondence can be observed between both approaches. The above mentioned rise and fall in the magnetic response suggests that flux avalanches are occurring. To certify this, MOI was performed at similar conditions. Fig. 3a–c shows the distribution of flux trapped in the sample following AC excitations of amplitudes h = 1.2 Oe, 2.4 Oe and 3.8 Oe, respectively. The images correspond to the states indicated by blue arrows in Fig. 2. Bright indicates positive flux, dark is negative, whereas medium gray stands for zero flux (Meissner state). At low h, there is no flux penetration and the images are completely gray (images not included). As the amplitude of the field cycle increases, bright and dark regions appear, what correspond to penetration of flux and antiflux, respectively. Image (a), taken after an excitation of 1.2 Oe, shows the beginning of flux invasion. The image is an enlargement of a portion of the sample. The abrupt formation and the shape of the

3. Results and discussion The magnetic response as a function of the AC excitation is shown in Fig. 2. At the main panel mres exhibits an evident change of slope. For low h, mres is zero – within the accuracy of the equipment – up to 1.1 Oe. Above this value, mres starts increasing, and an always growing fluctuation develops. The inset shows both components of vac, normalized by the lowest value of v0 . The real part is constant at low h, revealing that the AC screening is kept at this regime. Similarly, the imaginary part is zero, a confirmation that the processes are non-dissipative. The h value for which vac changes its regime from constant to increasing is about 1 Oe. Above this point, both real and imaginary components are noisy. Furthermore, the real part exposes that the

Fig. 3. MO images taken at 3 K with after an excitation field of (a) 1.2 Oe, (b) 2.4 Oe, (c) 3.8 Oe and (d) zoom up of the selected area on panel (b).

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sively as h increases, besides fluctuations similar to those reported above. More MOI studies are needed for a thorough understanding of avalanches occurring under combinations of AC and DC fields. 4. Conclusion

Fig. 4. Comparison between the Mean Gray Value of the MO images and mres, indicating the expected correspondence between both.

flux penetration indicate that those protuberances are avalanches, all fully consistent with the fluctuations found in mres beginning at approximately the same value of h. For higher field amplitudes, even more flux penetrates into the sample, as shown in images (b) and (c). Both reveal a quite disordered mixture of bright and dark. This complex profile is a consequence of subsequent avalanches of flux and antiflux provoked while the sample is submitted to the alternating field. Panel (d) presents a magnified view of the area indicated by a box in panel (b). It shows that, as already discussed in Ref. [5] for DC applied fields, once an avalanche is triggered by the AC field, the roots of the tracks are partially reused during subsequent stages of flux entrance and exit. Another important feature is the morphology of the avalanches. The MO images show that the avalanches triggered by the AC field are guided along the principal axes of the AD lattice. This is similar to the behavior exhibited when a DC field is changed, as already observed previously [5,14,15]. A general aspect of the flux landscape is a random arrangement of tracks with trapped flux and antiflux. MOI reveals that, for higher values of h, the flux penetration is deeper and the number of tracks with trapped flux/antiflux is higher. Such behavior explains the fluctuating response observed in Fig. 2 for values of h above 1.1 Oe. The higher the excitation field, the larger is the magnitude of the fluctuation of mres. Each pixel in the images in Fig. 3 can be assigned with a number corresponding to the gray level, spanning from black to white. The mean gray value is an alternative way to estimate the amount of penetrated flux in the sample. Abrupt variations on this value can be related to the occurrence of avalanches [19]. Fig. 4 compares the residual magnetic moment and the mean gray value for a set of images, both as a function of h. The correspondence is evident: a constant behavior at low h and a clear slope for excitations above approximately 1 Oe. The MOI setup allows the application of higher AC fields, what reveals that the magnitude of the fluctuations keeps increasing with larger h. A natural continuation of the present work is the inclusion of a DC field superimposed to the AC excitation. A preliminary study shows that, in this condition, large steps in mres(h) occur succes-

We have observed flux avalanches triggered by a 10 Hz AC magnetic fields in a superconducting patterned Nb film. The AC field necessary to create avalanches at 3 K is only 1.1 Oe. MO images reveal that the resultant state after the application of a train of AC field cycles with amplitude of a few Oe has a highly inhomogeneous flux distribution. This strongly contrasts the smooth distribution expected for specimens obeying a critical state penetration profile. A global measurement of the residual magnetic moment shows a fluctuating response, which is a signature of the avalanches. On the other hand, images provide localized views of micrometer size areas with penetrated flux distributed randomly in opposite directions, which is the origin of the fluctuating response. Acknowledgments This work was partially supported by the Methusalem Funding of the Flemish Government, the NES-ESF program, the Belgian IAP, the Fund for Scientific Research-Flanders (FWO-Vlaanderen), the UK Engineering and Physical Sciences Research Council and by the Brazilian funding agencies FAPESP and CNPq. AVS is grateful for the support from the FWO-Vlaanderen. THJ acknowledges the financial support of the Norwegian Research Council. References [1] R.G. Mints, L. Rakhmanov, Rev. Mod. Phys. 53 (1981) 551. [2] S. Jin, H. Mavoori, C. Bower, R.B. van Dover, Nature 411 (2001) 563. [3] Z.W. Zhao, S.L. Li, Y.M. Ni, H.P. Yang, Z.Y. Liu, H.H. Wen, W.N. Kang, H.J. Kim, E.M. Choi, S.I. Lee, Phys. Rev. B 65 (2002) 064512. [4] A.V. Silhanek, S. Raedts, V.V. Moshchalkov, Phys. Rev. B 70 (2004) 144504. [5] M. Motta, F. Colauto, R. Zadorosny, T.H. Johansen, R.B. Dinner, M.G. Blamire, G.W. Ataklti, V.V. Moshchalkov, A.V. Silhanek, W.A. Ortiz, Phys. Rev. B 84 (2011) 214529. [6] T.H. Johansen, M. Baziljevich, D.V. Shantsev, P.E. Goa, Y.M. Galperin, W.N. Kang, H.J. Kim, E.M. Choi, M-S. Kim, S.I. Lee, Supercond. Sci. Tech. 14 (2001) 726. [7] C.A. Durán, P.L. Gammel, R.E. Miller, D.J. Bishop, Phys. Rev. B 52 (1995) 75. [8] T.H. Johansen, M. Baziljevich, D.V. Shantsev, P.E. Goa1, Y.M. Galperin, W.N. Kang, H.J. Kim, E.M. Choi, M.-S. Kim, S.I. Lee, Europhys. Lett. 59 (2002) 599. [9] I.A. Rudnev, S.V. Antonenko, D.V. Shantsev, T.H. Johansen, A.E. Primenko, Cryogenics 43 (2003) 663. [10] I.A. Rudnev, D.V. Shantsev, T.H. Johansen, A.E. Primenko, App. Phys. Lett. 87 (2005). [11] S.C. Wimbush, B. Holzapfel, C. Jooss, J. App. Phys. 96 (2004). [12] P. Leiderer, J. Boneberg, P. Brüll, V. Bujok, S. Herminghaus, Phys. Rev. Lett. 71 (1993) 2646. [13] S. Hebert, L. Van Look, L. Weckhuysen, V.V. Moshchalkov, Phys. Rev. B 67 (2003) 224510. [14] V. Vlasko-Vlasov, U. Welp, V. Metlushko, G.W. Crabtree, Physica C 341-348 (2000) 1281. [15] M. Menghini, R.J. Wijngaarden, A.V. Silhanek, S. Raedts, V.V. Moshchalkov, Phys. Rev. B 71 (2005) 104506. [16] S. Raedts, A.V. Silhanek, M.J. Van Bael, R. Jonckheere, V.V. Moshchalkov, Physica C 404 (2004) 298. [17] L.E. Helseth, R.W. Hansen, E.I. Il’yashenko, M. Baziljevich, T.H. Johansen, Phys. Rev. B 64 (2001) 174406. [18] E. Altshuler, T.H. Johansen, Rev. Mod. Phys. 76 (2004) 471. [19] F. Colauto, E.M. Choi, J.Y. Lee, S.I. Lee, V.V. Yurchenko, T.H. Johansen, W.A. Ortiz, Supercond. Sci. Technol. 20 (2007) L48.