Multiquanta Vortex Entry and Vortex-Antivortex Pattern Expansion in a Superconducting Microsquare with a Magnetic Dot

Abstract

We investigate the nucleation of superconductivity in a microsquare with a magnetic dot on top. The cusplike behavior of the calculated normal-superconducting phase boundaries, T c H, shows a transition between short-period to long-period oscillations when going from positive to negative applied fields, H. Vorticity changes by more than 1, indicating multiquanta vortex entries, have been detected along this asymmetric T c H boundary. The dot also expands dramatically the symmetry-consistent vortexantivortex patterns, thus facilitating their experimental observation. DOI: 10.1103/PhysRevLett.95.237003 PACS numbers: 74.78.Na, 74.20.De, 74.25.Dw, 75.75.+a The intrinsic quantum nature of superconductivity makes superconductors with dimensions of the order of 0, the Ginzburg-Landau (GL) coherence length, particularly sensitive to confinement effects. In the past years, significant advances in different nanofabrication techniques have promoted the systematic study of the properties of micro-and nanosuperconductors [1]. This research has demonstrated that the topology of the sample can be used to enhance considerably the superconducting critical parameters, thus opening new perspectives for the potential applications of superconductivity. Moreover, nanostructuring also strongly affects the vortex matter in these superconductors. For instance, in cylindrical geometries, the superconductivity nucleates in the form of a giant vortex in the center [2], while symmetry-consistent vortexantivortex patterns may be spontaneously created in both triangles [3] and squares [4]. This interest in the confinement effects has been recently extended to hybrid superconductor/ferromagnetic (SF) nanosystems [5,6]. In the case of individual nanostructures, these studies have been focused on a cylindrical symmetry of the superconductor, but they have already revealed new physical phenomena arising from the interaction between superconductivity and magnetism at this submicrometer scale. A good example is the profound influence that a magnetic dot may have on the onset of superconductivity and vortex states in loops and disks [5,6].In this Letter, we investigate the nucleation of superconductivity in a square with a cylindrical magnetic dot on top. The existing analytic procedure to solve the linearized Ginzburg-Landau equation (LGLE) in regular polygons [7] has been adapted to include the contribution of the dot to the total magnetic field, allowing us to identify new quantum effects in the onset of superconductivity arising from the interplay between the finite rotational symmetry of the square and the inhomogeneous field of the dot. These effects, which include vorticity changes by more than 1 associated with multiquanta vortex entries in the sample and an expansion of the symmetry-consistent vortexantivortex patterns, are well beyond those expected for a cylindrical geometry of the superconductor [5,6,8].The most adequate tool to study the nucleation of superconductivity is the LGLE given by [9] ÿir ÿ 2 0Equation (1) is analogous to t...

Superconducting vortex pinning with artificial magnetic nanostructures

“…Changes may appear in the vortex phase transitions [199,200] and vortex-lattice geometry, for instance ''rings ''or ''shells'' as opposed to the usual triangular Abrikosov lattice. Moreover, theoretical studies predict that a magnetic nanodot on top of a mesoscopic superconductor can enhance superconductivity in hybrid structures [201] and can enforce or even induce symmetry-consistent vortex-antivortex molecules [202,203]. These predictions have been recently confirmed experimentally [204].…”

Nucleation of superconductivity and vortex matter in superconductor–ferromagnet hybrids

“…(color online) A comparison between the vortex-antivortex patterns that can be observed for L = 3 (a) with and (b) without the magnetic dot on top of the superconducting square, a is the lateral size of the sample, adapted from Carballeira et al[138]. As can be seen, the vortex-antivortex pattern rotates 45 • and expands dramatically in the presence of the magnetic dot.…”

Different regimes of nucleation of superconductivity in mesoscopic superconductor/ferromagnet hybrids

“…The OP nucleation in S/F hybrids with different competing confinements was recently studied theoretically in Refs. [3][4][5][6]8, and 9. For example, for a generic S/F hybrid, consisting of a mesoscopic superconducting disk and a small magnetic particle, theory predicts two well-defined regimes: superconductivity can nucleate either near the disk center ͑under the magnetic particle͒ or at the disk edge.…”

“…In the case of spatially separated S and F subsystems, when the direct exchange of electrons at the interface between the two materials becomes suppressed, the interaction is dominated by the slow decaying magnetic fields b͑r͒ induced by the ferromagnet. In particular, the inhomogeneous b͑r͒ field generated by magnetic domains in the F layer affects strongly the nucleation of the superconductivity in the S layer and leads to exotic dependences of the critical temperature T c on an external magnetic field H. [2][3][4][5][6][7][8][9] Indeed, the presence of inhomogeneous fields results in the appearance of places where the transverse component of the total magnetic field ͉b z ͑r͒ + H͉ reaches a local minimum and thus the nucleation of localized superconductivity in thin superconducting films will be promoted due to the field compensation effect.…”