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

Realizations of Majorana fermions in solid state materials have attracted great interest 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 noncollinear magnetic order turns a spin-singlet superconductor with nodes into a topological superconductor with a stable Majorana bound state in the vortex core, at a topologically stable magnetic point defect, and on the edge. We argue that such an exotic non-Abelian phase can be realized in extended t-J models on the triangular and square lattices. It is promising to search for Majorana fermions in correlated electron materials where nodal superconductivity and magnetism are two common caricatures.