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 (θM) 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 (Pe). Electronic pressure, which provides another route to control the IEC, is simulated by varying the interlayer spacing in the nanoflake. Our result shows a Pe 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 Pe (−0.042 GPa) at h = 3.38 Å producing a θM of ∼2.4°. The higher value of θM at a negative Pe (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