We report on imaging of the nonuniform superconducting states in a Pb thin-film bridge on top of a ferromagnetic BaFe 12 O 19 single crystal with a single straight domain wall along the center of the bridge by low-temperature scanning laser microscopy. We have visualized domain-wall superconductivity (DWS) close to the critical temperature of Pb, when the Pb film above the domain wall acts as a superconducting path for the current. The evolution of the DWS signal with temperature and the external-field-driven transition from DWS to reverse-domain superconductivity was visualized. It is well known that so-called surface or bound states can be generated by the presence of boundaries in a material. For example, the formation of surface states for a single electron wave function in a semi-infinite crystalline lattice due to the modification of the boundary conditions was described by Tamm 1 and by Shockley. 2 Other examples of bound states are surface plasmons, propagating along the interface between a dielectric and a metal, [3][4][5] and surface acoustic waves traveling along the surface of a material exhibiting elasticity. 6,7 In both latter cases these waves are confined in the direction perpendicular to the wave vector, i.e., their amplitudes decay exponentially far from the interface or surface. The formation of surface bound states for the superconducting order-parameter wave function was considered by Saint-James and de Gennes. 8,9 They showed that localized superconductivity at a superconductor (S)/vacuum or S/insulator interface can appear at an applied magnetic field H ext above the upper critical field H c2 for bulk superconductivity. Similarly to this surface superconductivity, localized superconductivity can also nucleate near the sample edge in a thin semi-infinite superconducting film 10 or in a thin superconducting disk of very large diameter 11 in a perpendicular magnetic field. Such so-called edge superconductivity (ES), with transition temperature T c2 .
15For flux-coupled S/F structures of finite lateral size the localized states of ES and DWS may compete as illustrated in Fig. 1 for the case of a thin-film S strip of finite width above a F substrate with a domain wall along the center of the bridge, for H c2 < B 0 < H c3 . For a domain structure with steplike b z (x) profile and H ext = 0, ES and DWS nucleate simultaneously in the S strip as shown in Fig. 1(a). Figure 1(b) shows the case of a domain wall with finite width and H ext = 0. Here, DWS becomes energetically more favorable compared to ES and only DWS nucleates. 16 For H ext = 0, the local field is compensated above the domain with magnetization direction opposite to H ext . If ||H ext | − B 0 | < H c2 superconductivity is turned on above this reverse domain while it is still suppressed above the parallel domain [cf. Fig. 1(c)]. This effect is termed reverse-domain superconductivity (RDS). 17,18 We note that when H c2 becomes larger than |H ext | + B 0 (e.g., upon cooling) above the parallel domain, superconductivity may also nucleate...