Isospin symmetry breaking induced magnetotransport behaviors in twisted double bilayer graphene

Twisted double bilayer graphene (tDBG) with a twist angle θ∼1.3° possesses a tunable flat Moiré band structure, which makes it a platform for exploring novel electrical and magnetic properties in correlated states. The tunability of tDBG can be realized through gating, magnetic fields, and current bias. We report the observation of an anomalous Hall effect (AHE) hysteresis in out-of-plane magnetic field (B⟂) and an extremely sharp in-plane (B∥) negative magnetoresistance in the correlated states of tDBG. The AHE was observed by us when the Moiré conduction band is nearly fully filled. The coercive B⟂ of the hysteresis is hundreds of mT. The hysteresis stays robust against a high B∥ till ∼5T and responds isotropically to B∥. Based on the obviously greater sensitivity to B⟂ than to B∥, we attribute the AHE hysteresis observed in tDBG to valley (orbital) ferromagnetism. The sharp B∥ negative magnetoresistance was observed by us within the valley polarized states and exhibits several unique characteristics. The resistance is reduced by a half with a mT-scale B∥ applied. This reaction to B∥ is much more sensitive than to B⟂. The exhibition of this sharp B∥ negative magnetoresistance depends on the history of states of tDBG. Current bias can also affect this sharp B∥ negative magnetoresistance effect. These behaviors can be phenomenologically explained by the transition of spin orientation on the valley polarized domain walls.