A magnetic atomic impurity inside a superconductor locally distorts superconductivity. They scatter Cooper pairs as a potential with broken time-reversal symmetry, what leads to localized bound states with subgap excitation energies, named hereon Shiba states. Most conventional approaches to study Shiba states treat magnetic impurities as point scatterers with an isotropic exchange interaction, while the complex internal structure of magnetic impurities is usually neglected. Here, we show that the number and the shape of Shiba states are correlated to the spin-polarized atomic orbitals of the impurity, hybridized with the superconducting host, as supported by Density Functional Theory simulations. Using high-resolution scanning tunneling spectroscopy, we spatially map the five Shiba excitations found on sub-surface chromium atoms in Pb(111), resolving both their particle and hole components. While the maps of particle components resemble the textit{d} orbitals of embedded Cr atoms, the hole components differ strongly from them. The orbital fingerprints of Shiba states thus unveil the magnetic ground state of the impurity, and identify scattering channels and interactions, all valuable tools for designing atomic-scale superconducting devices.
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