We present a comparative study of pair correlations and currents through superconducting-magnetic hybrid systems with a particular emphasis on the tunable Bloch domain wall of an exchange spring. This study of the Gor'kov functions contrasts magnetic systems with domain walls that change at discrete points in the magnetic region with those that change continuously throughout. We present results for misaligned homogeneous magnetic multilayers, including spin valves, for discrete domain walls, as well as exchange springs and helical domain walls—such as Holmium—for the continuous case. Introducing a rotating basis to disentangle the role of singlet and triplet correlations, we demonstrate that substantial amounts of (so-called short-range) singlet correlations are generated throughout the magnetic system in a continuous domain wall via the cascade effect. We propose a classification of $0-\pi$ transitions of the Josephson current into three types, according to the predominant pair correlations symmetries involved in the current. Properties of exchange springs for an experimental study of the proposed effects are discussed. The interplay between components of the Gor'kov function that are parallel and perpendicular to the local magnetization lead to a novel prediction about their role in a proximity system with a progressively twisting helix that is experimentally measurable.

• Received 15 June 2016
• Corrected 30 September 2016

DOI:https://doi.org/10.1103/PhysRevB.94.104518