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

Abstract

The competition between two regimes of the nucleation of superconductivity is investigated experimentally and theoretically in a mesoscopic disk-shaped superconductor/ferromagnet hybrid. By changing the magnetic state of a multilayered Co/Pt disk one can reversibly affect the magnetic-field dependence of the critical temperature T c ͑H͒ of an Al layer. We demonstrate that an enhancement of the magnetic field near the edge of the out-of-plane magnetized disk either stimulates the nucleation of superconductivity at the disk perimeter due to the field compensation effect or prevents it due to edge magnetic barrier ͑for relatively low ͉H͉ values͒. As a consequence, the presence of such magnetic-field pattern makes it possible to eliminate boundary effects for mesoscopic superconducting samples. Switching from one nucleation regime to another while sweeping H leads to an abrupt change of the slope of the T c ͑H͒ envelope. The coexistence of superconductivity and magnetic order has been intensively studied for several decades ͑see review 1 and references therein͒. Recent achievements in nanotechnology make it possible to prepare hybrid superconductor/ ferromagnet ͑S/F͒ structures and study experimentally different aspects of the nontrivial interaction between the S and F components. 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. 2-9 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.The sample's imperfections or boundaries also stimulate the appearance of localized superconductivity in real samples. 10 As a result, a competition between different regimes of the order-parameter ͑OP͒ nucleation leads to additional modifications of the phase boundary T c ͑H͒. The OP nucleation in S/F hybrids with different competing confinements was recently studied theoretically in Refs. 3-6, 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. Switching between these regimes induced by varying the external field has been predicted to result in an abrupt change of the slope of T c ͑H͒. 5 These important theoretical findings have not yet been verified experimentally.In this work we check experimen...

Little-Parks oscillations in hybrid ferromagnet–superconductor systems

“…Note, that a similar shift of the main T c maximum has been observed in mesoscopic S/F hybrid structures without the proximity effect 5,8 and in the quasi-twodimensional organic conductors 25,26 . In the latter case, an applied magnetic field compensates the exchange fields of the paramagnetic ions and neutralizes the destructive action of these fields 27 .…”

“…The solution of Eqn. (8) in F metal can be expressed via the confluent hypergeometric function of the second kind U (a, b, z) 24 ,…”

“…Little-Parks effect, 1 i.e., the oscillations of the critical temperature T c of multiply-connected superconducting samples in an applied magnetic field H, is one of the striking phenomena demonstrating coherent nature of the superconducting state. Nevertheless, such oscillatory phase transition line T c (H) was shown to be inherent to simply connected mesoscopic samples with the lateral size of the order of several coherence lengths ξ 2,3,4 and to hybrid ferromagnet (F)-superconductor (S) systems with magnetic dots or domains 5,6,7,8 , that create a "magnetic template" for nucleation of the superconducting order parameter. These T c (H) oscillations reflect the switching between vortex states characterized by different winding numbers and are associated with the orbital effect 9 .…”

Nucleation of superconductivity and vortex matter in superconductor–ferromagnet hybrids

“…Figure 13. (color online) The phase transition lines Tc(Hext), obtained experimentally for the mesoscopic S/F hybrid system with a 0.1 Rn criterion for three different magnetic states (completely magnetized, partly magnetized and demagnetized states), Rn and Hm being the normal-state resistance and the magnetizing field, adapted from Schildermans et al[137]. The considered S/F system consists of superconducting Al disk covered by ferromagnetic Co/Pt multilayered film of the same radius Rs = R f = 0.825 µm.…”

Current-induced giant vortex and asymmetric vortex confinement in microstructured superconductors

“…This is a particular relevant issue since one of the most popular ways to determine the change in vorticity of mesoscopic superconductors is through electrotransport measurements. 16,17 In this paper, we study the influence of a bias external current on the vortex dynamics in a square mesoscopic superconductor by solving numerically the timedependent Ginzburg-Landau ͑TDGL͒ equations. The most interesting result is the unexpected formation of a giant vortex as a result of two single-quantized vortices collision.…”