Chern insulator ferromagnets are a fascinating area of research in condensed matter physics. These materials exhibit a quantized anomalous Hall effect, which has been observed experimentally in various systems including magnetically-doped topological insulator (MTI) thin films and bilayer graphene moiré superlattices. Chern insulator ferromagnets are classified into two categories, spin or orbital, based on the origin of their orbital magnetization. In the case of spin Chern insulator (e.g. MTIs), the orbital magnetization arises from spontaneous spin-polarization combined with spin-orbit interactions. In contrast, orbital Chern insulators (e.g. graphene-based moiré superlattices) exhibit spontaneous orbital currents that give rise to the orbital magnetization. Understanding the differences between these two types of Chern insulators is crucial for developing new materials with interesting properties. In this talk, I will emphasise the curious magnetic properties of orbital Chern insulator using magic-angle twisted bilayer graphene as an example.
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