  We introduce a novel class of interaction-enabled topological crystalline
insulators in two- and three-dimensional electronic systems, which we call
"topological crystalline magnet." It is protected by the product of the
time-reversal symmetry $\mathcal{T}$ and a mirror symmetry or a rotation
symmetry $\mathcal{R}$. A topological crystalline magnet exhibits two
intriguing features: (i) it cannot be adiabatically connected to any Slater
insulator and (ii) the edge state is robust against coupling electrons to the
edge. These features are protected by the anomalous symmetry transformation
property $(\mathcal{R} \mathcal{T})^2=-1$ of the edge state. An anisotropic
response to the external magnetic field can be an experimental signature.
