Magnetic properties dependence on stacking configurations of a trilayer graphene bond-diluted Ising model

Abstract

This work aims to conduct a comparative analysis of the phase diagrams and the magnetizations of diverse stacking configurations in trilayer graphenes (TLGs) as described in a bond-diluted Ising model, within the finite cluster approximation (FCA). When the middle layer is occupied by mixed spin-1/2 and spin-1, the outer layers consist of spin-1/2 atoms interconnected ferromagnetically via a diluted bond J₁. In the pure case (p = 1), all transition temperatures T_c are of second-order; meanwhile enhancing dilution through reducing the concentration p results in a decrement of T_c. At a low-temperature regime, for the AAA- and ABA-stacked (TLGs), all T_c-lines coincide at p = 0 to a non-zero minimum value, with a horizontal reentrance observed specifically for the ABA-stacked case. In the case of the ABC-stacked (TLG), we identify according to J₁ strength, a vertical or double vertical reentrances succeeded by vanishment of the ferromagnetic order at a critical bond percolation threshold p_c. The inclusion of the crystal fields D_s plays a relevant role in the appearance of the tricritical behavior exclusively for the AAA and ABA stackings.