Phase transition from a nonmagnetic to a ferromagnetic state in a twisted bilayer graphene nanoflake: the role of electronic pressure on the magic-twist.

The electronic properties of a bilayer graphene nanoflake (BLGNF) depend sensitively upon the strength of the inter-layer electronic coupling (IEC) energy. Upon tuning the IEC via changing the twist angle between the layer, a ferromagnetic gap state emerges in a BLGNF due to spontaneous symmetry breaking at the magic-twist. Herein, using first-principles density functional theory, we demonstrate the magic twist angle ( θ M ) in a bilayer graphene nanoflake at which the transition from a nonmagnetic to a ferromagnetic phase occurs can be tuned by exerting uniaxial electronic pressure ( P e ). Electronic pressure, which provides another route to control the IEC, is simulated by varying the interlayer spacing in the nanoflake. Our result shows a P e of 0.125 GPa corresponding to interlayer spacing ( h ) of 3.58 Å yielding a magic twist angle of ∼1° and a negative value of P e (-0.042 GPa) at h = 3.38 Å producing a θ M of ∼2.4°. The higher value of θ M at a negative P e (smaller h ) is attributed to an increase in the energy gap due to strong inter-layer electronic coupling energy in the nanoflake under uniaxial compression. This finding in the nanoflake agrees with the experimental observation in two-dimensional bilayer graphene (M. Yankowitz, S. Chen, H. Polshyn, Y. Zhang, K. Watanabe, T. Taniguchi, D. Graf, A. F. Young and C. R. Dean, Science , 2019, 363 , 1059-1064) that indicated an increase in the magic angle value for the phase transition upon application of hydrostatic pressure.