Infoscience

Thesis

Effects of magnetism in superconducting hybrid structures

In this thesis we study various effects of magnetism in proximity structures, composed of superconducting electrodes in contact with a normal metal. Magnetism can be present in the system through the Zeeman and the orbital coupling. Proximity structures offer in particular a unique opportunity to study the interplay between ferromagnetism and conventional superconductivity, which can hardly coexist in bulk samples. The orbital effect of an external magnetic field applied to a Josephson junction results in interference effects between local currents. In Chapter 1, we give an introduction to the main features of the proximity effect and to the theoretical formalism used throughout the thesis. In Chapter 2 we study the Josephson effect in a superconductor–ferromagnet–superconductor (SFS) junction with ferromagnetic domains of noncollinear magnetization. It is well known [1] that as a consequence of the exchange splitting of the Fermi level [2] the Cooper pair wave function shows damped oscillations in a ferromagnet, leading to the appearance of the so-called "π state" in SFS junctions [3]. In the π state, the superconducting order parameter is of opposite sign in the two S electrodes of the Josephson junction, and a spontaneous non-dissipative current can appear in a ring containing such a junction. As a model for our study of the influence of magnetic domains on the π state formation, we consider a diffusive junction with two ferromagnetic domains along the junction. We find analytically the critical current as a function of domain lengths and of the angle between the orientations of their magnetizations. Varying those parameters, the junction may undergo transitions between 0 and π phases. We find that the presence of domains reduces the range of junction lengths at which the π phase is observed. For the junction with two domains of the same length, the π phase totally disappears as soon as the misorientation angle exceeds π/2. We further comment on possible implications of our results for experimentally observable 0–π transitions in SFS junctions. Experimentally, π junctions are realized as thin films deposited in layers. In Chapter 3, we study therefore the influence of in-plane magnetic domains on the Josephson current. We find that the properties of the junction depend on the size of the domains relative to the magnetic coherence length. In the case of large domains, the junction exhibits transitions to the π state, similarly to a single-domain SFS junction. In the case of small domains, the magnetization effectively averages out, and the junction is always in the zero state, similarly to a superconductor–normal metal–superconductor (SNS) junction. In both those regimes, the influence of domain walls may be approximately described as an effective spin-flip scattering. We also study the inhomogeneous distribution of the local current density in the junction. Close to the 0–π transitions, the directions of the critical current may be opposite in the vicinity of the domain wall and in the middle of the domains. In Chapter 4, we discuss the orbital effects of an external magnetic field in a SNS junction. In the limit of a long junction, we find that the properties of such a system depend on the width of the junction relative to the length associated with the magnetic field. We compute the critical width separating the regime of pure decay (narrow junction) and the regime of damped oscillations (wide junction) of the critical current as a function of the magnetic flux through the junction. We find an exponential damping of the current, different from the well known Fraunhofer limit which corresponds to the limit of a tunnel junction. In the limit of a wide junction, the superconducting pair correlations and the critical current become localized near the border of the junction.

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