  In the present study topologically nontrivial edge and vortex bound states
are described in the coexistence phase of chiral spin-singlet superconductivity
and noncollinear spin ordering on a triangular lattice in the presence of few
(up to four) vortices. We consider the topological phase transition induced by
the magnetic order between the phase hosting Majorana modes and the initial
phase of the chiral d-wave superconductivity supporting non-Majorana modes
which is also topologically nontrivial. The change of the excitation spectrum
at the critical point is obtained in both cases of open and periodic boundary
conditions in the presence of vortices. It is proved that zero energy Majorana
modes localized at vortex cores are caused by noncollinear long-range magnetic
ordering. Even though nearby excitation energies of subgap states including the
edge-localized and vortex-localized states are very close to each other, the
energy difference between different vortex bound states is an order of
magnitude higher. This difference determines the energy gap for Majorana vortex
modes separating them from other vortex bound states. It is found that even in
the presence of noncollinear spin ordering its value can be estimated from the
excitation energy of vortex bound states in the pure chiral d-wave state for
the nonmagnetic case. By studying local density of states near the vortex cores
the possibility to experimentally detect the described Majorana vortex modes by
scanning tunneling microscopy is discussed. It is demonstrated that Majorana
vortex modes and Majorana antivortex modes induced by noncollinear magnetism
have different features in energy and spatially resolved density of states due
to the chiral symmetry on the superconducting order parameter.
