Angular dependence of the high-frequency vortex response in YBa2Cu3O7-x thin film with self-assembled BaZrO3 nanorods

Nanosize particles are known to increase dramatically the vortex pinning in YBa2Cu3O7-x (YBCO). Among the various inclusions that give rise to an increased pinning, BaZrO3 (BZO) is one of the most studied. Interestingly, under certain circumstances BZO spontaneously self-assemble along columnar-like structures, with a diameter of a few nm and directed approximately along the c-axis of the YBCO film. This feature has relevant consequences for the practical use of YBCO superconductors. In this work we present a microwave study of the enhancement of pinning in YBCO thin films due to the addition of BZO particles, with particular emphasis on the angular dependence. The samples under study have been grown by pulsed laser ablation using a composite YBCO/BZO target containing BZO at 5 mol %. X-ray diffraction and TEM analysis were performed, and confirmed the excellent orientation of the YBCO film and the presence of columnar-like structures across the film. Microwave measurements were performed by means of a dielectric-loaded resonator operating at 48 GHz, in the temperature range between 60 K and Tc and in a static magnetic field up to 0.8 T, applied with a variable angle with the c-axis. Comparison with a pure YBCO sample revealed a very strong increase in the pinning strength, particularly relevant in the small-vortex-displacement regime here probed. The angular dependence of the complex microwave response directly showed that the balance between vortex dissipation and reactance, which is a measure of the pinning strength, changes from nearly unity (dissipation = reactance) when the field is directed along the c-axis (thus, along the BZO nanorods), to more dissipative when the field is directed in-plane. Thus, BZO nanorods are found to be more efficient in pinning the vortices in YBCO than the anisotropic (layered) structure itself. In order to describe more quantitatively the experimental results, we extract from our data the vortex parameters (vortex drag coefficient, vortex pinning frequency). We developed a model for the anisotropic motion of vortices in uniaxially anisotropic superconductor, at an arbitrary angle with the crystallographic axes, from which an expression of the effective anisotropic vortex drag coefficient is derived. The known limiting cases of vortices and motion along the crystallographic axes are recovered. We discuss our results in the light of the mentioned model. This work has been partially supported by the Italian FIRB project "SURE:ARTYST" and by EURATOM. N.P. acknowledges support from Regione Lazio