By means of density functional theory, we investigate the magnetic ground
state of edge-sharing CuO_2 spin-chains, as found in the
(La,Ca,Sr)_14Cu_24O_41system, for instance. Our data rely on spin-polarized
electronic structure calculations including onsite interaction (LDA+U) and an
effective model for the interchain coupling. Strong doping dependence of the
magnetic order is characteristic for edge-sharing CuO_2 spin-chains. We
determine the ground state magnetic structure as function of the spin-chain
filling and quantify the competing exchange interactions.Comment: 5 pages, 2 figures, 3 tables, accepted by Phys. Rev. Let