Twisted bilayer graphene exhibits many intriguing behaviors ranging from superconductivity to the anomalous Hall effect to ferromagnetism at a magic angle of ∼1°. Here, using a first-principles approach, we reveal ferromagnetism in a twisted bilayer graphene nanoflex. Our results demonstrate that when the energy gap of a twisted nanoflex approaches zero, electronic instability occurs and a ferromagnetic gap state emerges spontaneously to lower the energy. Unlike the observed ferromagnetism at a magic angle in the graphene bilayer, we notice the ferromagnetic phase appearing aperiodically between 0 and 30° in the twisted nanoflex. The origin of electronic instability at various twist angles is ascribed to the several higher-symmetry phases that are broken to lower the energy resulting from an aperiodic modulation of the interlayer interaction in the nanoflex. Besides unraveling a spin-pairing mechanism for the reappearance of the nonmagnetic phase, we have found orbitals at the boundary of nanoflex contributing to ferromagnetism.
Keywords: bilayer graphene nanoflex; broken symmetry; electronic structure; ferromagnetism.