  Real Chern insulators have attracted great interest, but so far, their
material realization is limited to nonmagnetic crystals and to systems without
spin-orbit coupling. Here, we reveal magnetic real Chern insulator (MRCI) state
in a recently synthesized metal-organic framework material Co3(HITP)2. Its
ground state with in-plane ferromagnetic ordering hosts a nontrivial real Chern
number, enabled by the C2zT symmetry and robust against spin-orbit coupling.
Distinct from previous nonmagnetic examples, the topological corner zero-modes
of MRCI are spin-polarized. Furthermore, under small tensile strains, the
material undergoes a topological phase transition from MRCI to a magnetic
double-Weyl semimetal phase, via a pseudospin-1 critical state. Similar physics
can also be found in closely related materials Mn3(HITP)2 and Fe3(HITP)2, which
are also existing. Possible experimental detections and implications of an
emerging magnetic flat band in the system are discussed.
