Spin resolved Andreev reflection in ferromagnet-superconductor junctions with Zeeman splitting

Andreev reflection in ferromagnet-superconductor junctions is derived in a regime in which Zeeman splitting dominates the response of the superconductor to an applied magnetic field. Spin-up and spin-down Andreev reflections are shown to be resolved as voltage is increased. In the metallic limit, the transition from Andreev to tunnel conductivity in the spin-up channels has a non trivial behavior when spin polarization is increased. The conductance is asymmetric in a voltage reversal. PACS numbers: 74.80.Fp, 72.10.Bg, 74.50.+r Typeset using REVTEX 1 The interplay between Andreev reflection and spin polarization has generated recently an important interest, both theoretical [1–5] and experimental [6–11]. The subgap conductance in normal metal-superconductor (NS) junctions originates from Andreev reflection [12]: a spin-σ electron incoming from the N side is reflected as a hole in the spin-(−σ) band while a spin-zero Cooper pair is transferred into the superconductor. Since the incoming electron and outgoing hole belong to opposite spin bands, Andreev reflection couples to a Fermi surface polarization in the N side of the junction. de Jong and Beenakker [1] showed theoretically that increasing the Fermi surface polarization in ferromagnet-superconductor (FS) junctions suppresses Andreev reflection because Andreev reflection is limited by the minority-spin channels. Their prediction was verified experimentally by Soulen et al. [10] and Upadhyay et al. [11], who used this effect to measure the Fermi surface polarization. On the other hand, Tedrow and Meservey [13] demonstrated that under specific conditions, a magnetic field can be used to tune a Zeeman splitting of the quasiparticle excitations in a superconductor [13], and used it to perform a spin resolved tunnel spectroscopy in FS junctions [13]. I show in the present Letter that Zeeman splitting can be used to resolve spin-up and spin-down Andreev reflections, with a different threshold voltage eV± = ∆ ∓ μBH for the transition from Andreev to tunnel conductivity in a magnetic field H . In NS junctions with Zeeman splitting, the spin-up and spin-down differential conductances have the same behavior at the Andreev reflection threshold voltages V±. In FS junctions with Zeeman splitting, a non trivial behavior at the spin-up threshold voltage V+ is predicted. In addition, the conductance is asymmetric in a voltage reversal. These behaviors can be probed experimentally. Our modeling neglects disorder in the superconductor, as well as the proximity effect in the N side of the junction [9,14–20]. This approximation is justified in FS junctions, where superconducting correlations do not extend in the ferromagnet beyond the exchange length