  We study a chain of magnetic moments exchange coupled to a conventional three
dimensional superconductor. In the normal state the chain orders into a
collinear configuration, while in the superconducting phase we find that
ferromagnetism is unstable to the formation of a magnetic spiral state. Beyond
weak exchange coupling the spiral wavevector greatly exceeds the inverse
superconducting coherence length as a result of the strong spin-spin
interaction mediated through the subgap band of Yu-Shiba-Rusinov states.
Moreover, the simple spin-spin exchange description breaks down as the subgap
band crosses the Fermi energy, wherein the spiral phase becomes stabilized by
the spontaneous opening of a $p-$wave superconducting gap within the band. This
leads to the possibility of electron-driven topological superconductivity with
Majorana boundary modes using magnetic atoms on superconducting surfaces.
