  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.
