Magnetic anisotropy in twisted bilayer graphene and ABC-trilayer graphene aligned with hexagonal boron nitride*

We and others have previously reported ferromagnetism in both twisted bilayer graphene (tBLG) and ABC-trilayer graphene aligned with hexagonal boron nitride (hBN) evinced by a large (or even quantized) hysteretic anomalous Hall effect. These systems are composed entirely of non-magnetic elements; the magnetism arises from the strong electronic correlations of these moiré systems. Here, we report that when tilting the sample in an external magnetic field, the ferromagnetism of the two systems is highly anisotropic. In tBLG, the magnetism switches at a threshold out-of-plane component of the magnetic field down to tilt angles of about 5°. Because spin–orbit coupling is weak in graphene, such anisotropy is unlikely to come from spin but rather favors theories in which the ferromagnetism is orbital. The situation is less clear in the ABC-trilayer graphene moiré. The magnetic state at -2.3 electrons per moiré unit cell exhibits similar behavior to tBLG, switching at a threshold out-of-plane field. However, the other magnetic state observed at -1 electrons per moiré unit cell does not exhibit such a threshold, suggesting that either the spin of the electron is playing a role or the in-plane field is directly coupling to the orbital degree of freedom.