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Scanning tunnelling microscopy and density functional theory studies ofmanganese chains adsorbed on Cu$_2$N/Cu (100) reveal an unsuspected electronicedge state at $\sim 1$ eV above the Fermi energy. This Tamm-like state isstrongly localised to the last Mn atom of the chain and fully spin polarised.However, no equivalence is found for occupied states, and the electronicstructure at $\sim -1$ eV is mainly spin unpolarised due to the extended$p$-states of the N atoms that mediate the coupling between the Mn atoms in thechain. Odd-numbered Mn chains present an exponentially decreasing directcoupling with distance between the two edges, leading to a vanishingbonding/anti-bonding splitting of states while even-numbered Mn chains presentperfect decoupling of both edges due to the the antiferromagnetic ordering ofMn chains.

Electronic structure of atomic manganese chains supported on Cu$_2$N / Cu (100)