Induced energy gap in finite-sized superconductor/ferromagnet hybrids

Abstract

We theoretically study self-consistent proximity effects in finite-sized systems consisting of ferromagnet (F) layers coupled to an s-wave superconductor (S). We consider both SF1F2 and SH nanostructures, where the F1F2 bilayers are uniformly magnetized and the ferromagnetic H layer possesses a helical magnetization profile. We find that when the F1F2 layers are weakly ferromagnetic, a hard gap can emerge when the relative magnetization directions are rotated from parallel to antiparallel. Moreover, the gap is most prominent when the thicknesses of F1 and F2 satisfy dF1≤dF2, respectively. For the SH configuration, increasing the spatial rotation period of the exchange field can enhance the induced hard gap. Our investigations reveal that the origin of these findings can be correlated with the propagation of quasiparticles with wave vectors directed along the interface. To further clarify the source of the induced energy gap, we also examine the spatial and energy-resolved density of states, as well as the spin-singlet and spin-triplet superconducting correlations, using experimentally accessible parameter values. Our findings could be beneficial for designing magnetic hybrid structures where a tunable superconducting hard gap is needed.

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