Abstract
Noncollinear magnetic interfaces introduced in superconductor (SC)/ferromagnet/SC heterostructures allow for spin-flipping processes and are able to generate equal-spin spin-triplet pairing correlations within the ferromagnetic region. This leads to the occurrence of the so-called long-range proximity effect. Particular examples of noncollinear magnetic interfaces include Bloch and Néel domain walls. Here, we present results for heterostructures containing Bloch and Néel domain walls based on self-consistent solutions of the spin-dependent Bogoliubov–de Gennes equations in the clean limit. In particular, we investigate the thickness dependence of Bloch and Néel domain walls on induced spin-triplet pairing correlations and compare with other experimental and theoretical results, including conical magnetic layers as noncollinear magnetic interfaces. It is shown that both Bloch and Néel domain walls lead to the generation of unequal-spin spin-triplet pairing correlations of similar strength as for conical magnetic layers. However, for the particular heterostructure geometries investigated, only Bloch domain walls lead to the generation of equal-spin spin-triplet pairing correlations. They are stronger than those generated by an equivalent thickness of conical magnetic layers. In order for Néel domain walls to induce equal-spin spin-triplet pairing correlations, they have to be oriented such that the noncollinearity appears within the plane parallel to the interface region.
Highlights
Bringing a superconductor (SC) and a ferromagnetic (FM) material in close proximity to each other results in drastic changes for the spin-singlet Cooper pairs
The results presented are obtained for heterostructures containing Bloch domain walls of increasing thickness nBloch to either side of the FM middle layer
Starting the discussion again with the unequal-spin spintriplet pairing correlations f0 shown for Néel domain walls of varying thickness nNeé l in the lower panels of figure 2 one notices that they are nearly indistinguishable to the respective contributions from the Bloch domain walls shown in the middle panels of figure 2. It seems that the orientation of the noncollinear magnetic moments with respect to the interface plane does not influence the induced unequal-spin spin-triplet pairing correlations. This changes drastically when looking at the equal-spin spin-triplet pairing correlations where we find no contribution stemming from heterostructures containing Néel domain walls
Summary
Bringing a superconductor (SC) and a ferromagnetic (FM) material in close proximity to each other results in drastic changes for the spin-singlet Cooper pairs. (ii) Following a theoretical suggestion by Bergeret et al [6] it should be possible to induce equal-spin spin-triplet Cooper pairs which are compatible with and unaffected by the FM exchange field, leading to much larger penetration depths. This phenomenon requires spin-flip processes at the interface and is called the long-range proximity effect
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