\textbf{Perpendicular reading of single confined magnetic skyrmions}

We present the first fully self-consistent first-principles investigation of single chiral magnetic skyrmions as entire entities based on density functional theory. The work is tied to skyrmions with sub-5nm diameters embedded within thin ferromagnetic films stabilized through interfacial Dzyaloshinskii-Moriya interactions. We found that the non-collinearity of the magnetic texture inside the skyrmions leads to spin-mixing of the electronic structure, which can be probed as site-dependent tunneling spin-mixing magnetoresistance (TXMR). The conduction inhomogeneity can reach values up to 20{\%} in Pd/Fe/Ir(111) samples [1]. The non-collinear component of the TXMR has been experimentally verified [2], validating our theoretical calculations and showing the capability of the TXMR to resolve complex nanoscale spin-textures. The work is carried out with the newly developed J\"{u}lich relativistic Korringa-Kohn Rostoker Green function method [3]. [1] Crum, D.M. et al. Perpendicular reading of single confined magnetic skyrmions. Nat. Commun. \textbf{6 }8541 (2015). [2] Hanneken, C. et al. Electrical detection of magnetic skyrmions by tunnelling non-collinear magnetoresistance. Nat. Nanotech. doi:10.1038/nnano.2015.218 (2015). [3] Bauer, D.S.G., Schriften des Forschungszentrum, Key Technology \textbf{79} (2014).