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. 2022 May 4;13:2431. doi: 10.1038/s41467-022-29990-2

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© The Author(s) 2022

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Fig. 1 — a Schematic of the device structure: a Cu strip (orange) is covered by a EuS layer (green) and a perpendicular Al strip (gray). Measurement setups: The electric current is applied (i) from the Al to the Cu strip or (ii) along the Cu strip. The voltage drop is measured between the Al and the Cu strip on the remaining two wires of the four-wire set-up. b Visible light microscopy image of the device. c Schematic of the DoS along the vertical axis of the structure (Al/EuS/Cu from top to bottom). The dashed line indicates the Fermi level. Note that the EuS layer induces spin splitting in the superconducting DoS, and spin filtering thanks to the different heights of the tunnel barrier for the two spin species. The red (blue) line corresponds to the spin up (down) DoS in the Al layer. d Exemplary differential conductance (black) measured as a function of voltage across the junction at an applied external magnetic field B of 0.1 T at ≃ 100 mK. By employing a numerical model (detailed in the Methods section, Eqs. (3) and (14)), the fit for the differential conductance (red) and the contributions of the spin up (light blue) and spin down (light red) electrons were calculated with these fitting parameters: Δ₀ = 0.33meV, h = 0.32Δ₀, P = 0.48, Γ = 0.01Δ₀, T = 300 mK. e Color map of the differential conductance dI/dV(V) measured for B ranging from −0.2 T to 0.2 T. The sweep direction is indicated by the arrow. The data in panel d corresponds to the dash-dotted line (B = 0.1 T). The coercive field at the temperature of this measurement (100 mK) corresponds to −9 mT, indicated by a dashed line. f Exchange field (h) induced in the superconducting Al strip (blue) and polarization (P) of the EuS tunnel barrier as a function of the external magnetic field B. Both quantities are extracted from the best fitting results of the data as shown in panel d. The sweep direction is again indicated by an arrow.