Majorana fermions in spin-singlet nodal superconductors with coexisting non-collinear magnetic order

Realizations of Majorana fermions in solid state materials have attracted great interests recently in connection to topological order and quantum information processing. We propose a novel way to create Majorana fermions in superconductors. We show that an incipient non-collinear magnetic order turns a spin-singlet superconductor with nodes into a topological superconductor with a stable Majorana bound state (MBS) in the vortex core or on the edge. Moreover the topologically-stable point defect of non-collinear magnetic order also hosts a zero-energy MBS. We argue that such an exotic non-Abelian phase can be realized in extended $t$-$J$ models on the triangular and square lattices. Our proposal suggests a new avenue for the search of Majorana fermions in correlated electron materials where nodal superconductivity and magnetism are two common caricatures.