Xiaoyu Liu, Chong Wang, Haoran Chen, Xiaowei Zhang, Ting Cao, Di Xiao
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 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.