Evidence of orbital ferromagnetism in twisted bilayer graphene aligned to hexagonal boron nitride

We have previously reported ferromagnetism evinced by a large hysteretic anomalous Hall effect in twisted bilayer graphene (tBLG). Subsequent measurements of a quantized Hall resistance and small longitudinal resistance confirmed that this magnetic state is a Chern insulator. Here we report that, when tilting the sample in an external magnetic field, the ferromagnetism is highly anisotropic. Because spin-orbit coupling is negligible in graphene such anisotropy is unlikely to come from spin, but rather favors theories in which the ferromagnetism is orbital. We know of no other case in which ferromagnetism has a purely orbital origin. For an applied in-plane field larger than $5\ \mathrm{T}$, the out-of-plane magnetization is destroyed, suggesting a transition to a new phase.