Recent observations of quantum anomalous Hall effects in moiré systems have revealed the emergence of interaction-driven ferromagnetism with significant orbital contributions. To capture this physics, we extend the modern theory of orbital magnetization to Hartree–Fock states and show that the standard expression remains valid with Hartree–Fock orbitals and Hamiltonians. Then, we benchmark our theory against the extended Kane-Mele-Hubbard model in a weak field, which yields excellent agreement with direct numerical calculations. Applying our theory to twisted ${\mathrm{MoTe}}_2$ bilayers, we find orbital magnetization of order one Bohr magneton per moiré cell with a nonmonotonic twist-angle dependence. Our work establishes a general theory of orbital magnetization in interacting moiré systems and provides quantitative guidance for interpreting recent experiments.

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• Magnetization dynamics
• Strong interaction
• Superlattices
• Transition metal dichalcogenides
• Twisted heterostructures
• Hartree-Fock methods
• Mean field theory