  The interplay between magnetism and band topology is a focus of current
research on magnetic topological systems. Based on first-principle calculations
and symmetry analysis, we reveal multiple intriguing topological states can be
realized in a single system EuAgAs, controlled by the magnetic ordering. The
material is Dirac semimetal in the paramagnetic state, with a pair of
accidental Dirac points. Under different magnetic configurations, the Dirac
points can evolve into magnetic triply-degenerate points, magnetic linear and
double Weyl points, or being gapped out and making the system a topological
mirror semimetal characterized by mirror Chern numbers. The change in bulk
topology is also manifested in the surface states, including the surface Fermi
arcs and surface Dirac cones. In addition, the antiferromagnetic states also
feature a nontrivial Z4 index, implying a higher order topology. These results
deepen our understanding of magnetic topological states and provide new
perspectives for spintronic applications.
