We explore topological electronic structure of magnetic phases in a multiorbital Hubbard model with spin-orbit interactions. To account for more general antiferromagnetic orders that go beyond the collinear Néel order, two different spin-orbit interactions, Dresselhaus and Rashba spin-orbit interactions, are considered. By performing the canonical transformation, we derive the corresponding generalized $t\text{−}J$ model. At half-filling, employing self-consistent magnetic order calculations, we find distinctive spin arrangements under Dresselhaus or Rashba spin-orbit interactions. For the Dresselhaus spin-orbit interaction, the spin configuration exhibits collinear antiferromagnetic order. On the other hand, the Rashba interaction results in spins antiferromagnetically aligning in the $xy$ plane and a small interaction controlled by hopping parameter induces spin tilting, causing antiferromagnetic alignment in the $xy$ plane but ferromagnetic alignment in the $z$ direction. We categorize topological properties of these phases for low doping in the generalized $t\text{−}J$ model: for three-dimensional collinear antiferromagnetic order, the system possesses a modified time-reversal symmetry, characterized by the $Z_2$ index. In contrast, for systems with tilted antiferromagnetic orders, it is protected by inversion symmetry and characterized by the $Z_4$ index. We further examine the bulk-edge correspondence for noncollinear magnetic phases, revealing that the glide-symmetry-protected gapless surface state emerges when the surface is parallel to the ferromagnetic component of tilted antiferromagnetic order; otherwise, the surface state exhibits a gap. Our findings offer a comprehensive topological characterization for doped and canted antiferromagnetic insulators with spin-orbit interactions, providing valuable insights into the interplay between spin arrangements, symmetries, and topological properties in systems governed by the multiorbital Hubbard model.

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• Symmetry protected topological states
• Antiferromagnets
• Hubbard model
• Mean field theory