Vortex oscillations in TFA-grown YBCO thin-films with BZO nanoparticles E. Bartolomé a,⇑ , A. Palau b , A. Llordés b , T. Puig b , X. Obradors b a Escola Universitaria Salesiana de Sarrià, Passeig Sant Joan Bosco 74, 08017 Barcelona, Spain b Institut de Ciència de Materials de Barcelona-CSIC, Campus UAB, 08193 Bellaterra, Spain article info Article history: Received 26 July 2010 Received in revised form 9 September 2010 Accepted 17 September 2010 Available online 24 September 2010 Keywords: YBCO thin-films TFA growth Vortex pinning BZO nanoparticles Ac susceptibility abstract An ac susceptibility methodology has been applied to investigate the vortex dynamics of YBa 2 Cu 3 O 7x – BaZrO 3 nanocomposites grown by the chemical solution deposition TFA route, close to the irreversibility line. By analysing the linear, non-dissipative Campbell regime at low ac fields, we determined the tem- perature and field dependence of the restoring pinning constant, a L (H dc , T), characterising the harmonic oscillation of vortices inside their potential wells. Different than standard TFA–YBCO films, BZO nano- composites displayed increasing a L (H dc ) curves in the whole studied (H dc , T) phase diagram, a behavior not predicted by the standard collective theory. We suggest results may be explained by the softening of the vortex-lattice, owed to the microstrain induced by the nanoparticles in the YBCO matrix. Ó 2010 Elsevier B.V. All rights reserved. 1. Introduction Vortex dynamics in high-T c superconductors is a topic of great interest both for fundamental and applied physics. In the last years, different successful nanoengineering approaches have been pro- posed to enhance vortex pinning, in the quest to reach coated con- ductors with higher current performances [1–4]. The growth of YBCO thin-films with BaZrO 3 (BZO) nanoparticles by the trifluoro- acetate (TFA) chemical solution deposition route is one of the most promising solutions, offering the advantages of a low-cost tech- nique and extremely high pinning forces (78 GN/m 3 at 65 K and 3T [4]). The isotropic strong-pinning [5] behavior shown by these nanocomposites has been associated to the high microstrain emerging from BZO nanoparticles in the YBCO matrix [6]. Ac susceptibility represents a powerful technique to explore vortex dynamics of superconductors at high temperatures, close to the irreversibility line (IL) [7]. However, the quantitative determination of vortex motion parameters from the macroscopic susceptibility measurements is not straightforward. Vortex dynam- ics in the liquid and glass regimes is influenced by pinning, viscosity and thermal fluctuations [8]. Furthermore, the ac response may be linear or non-linear, and critical-scaling may be observed close to the vortex-glass [9] or Bose transition [10]. Moreover, solutions to the ac electromagnetic problem are only available for particular sample geometries and field configurations [11]. The problem considerably simplifies in the particular vortex- liquid state with linear response. Indeed, at sufficiently low ac fields, a Campbell regime [12] is sustained, in which vortex motion can be modeled by a harmonic oscillator with restoring constant a L (the ‘‘Labusch constant” [13]). As the ac field is increased above a threshold value, H l ac (H dc , T), inter-valley vortex excitations become relevant, and the response becomes non-linear [14]. The analysis of the linear Campbell regime offers thus an attrac- tive approach to characterise the vortex pinning behavior and quantify the strength of different sorts of nanostructured defects in superconducting films. In the past, this method has been suc- cessfully applied for studying the pinning strength of anti-dots in Pb films [15], and defects in as-grown and ion-irradiated YBCO sin- gle crystals [16,17]. In this work, we report results on the ac response in the Camp- bell regime of TFA-grown YBCO thin-films with and without BZO nanoparticles. In a recent paper [18], we analysed the ac suscepti- bility of these same films in the critical state regime, where vorti- ces travel large average distances by overcoming the pinning potential wells as they follow the high ac drives; in that regime, we found anomalies in the dc-field dependence of the activation energy for depinning (related with the potential well depth), U e (H). The low amplitude ac measurements performed in the pres- ent work have allowed us to probe the average curvature of the pinning potential wells as a function of the dc-field and the tem- perature, a L (H, T), without modifying the vortex distribution. We show that BZO nanocomposites present a peculiar field depen- dence of the Labusch parameter different than that predicted by 0921-4534/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2010.09.009 ⇑ Corresponding author. Tel.: +34 932 805 244. E-mail address: ebartolome@euss.es (E. Bartolomé). Physica C 470 (2010) 2033–2039 Contents lists available at ScienceDirect Physica C journal homepage: www.elsevier.com/locate/physc