Spin magnetic susceptibility of ferromagnetic silicene in the presence of Rashba spin-orbit coupling

In the current work, the effect of extrinsic Rashba spin-orbit coupling (RSOC) on the electronic band structure (BS) and magnetic susceptibility (MS) of ferromagnetic silicene is investigated in the presence of external perpendicular electric field. The Kane-Mele Hamiltonian and Dirac cone approximation besides the Green’s functions approach have been used to study the MS of the spin-up and spin-down bands. By changing the electric field, energy of the inter-band transitions and MS are tuned. Our findings show that MS could be easily controlled by an external electric field and RSOC. The system shows three phases: Topological insulator (TI), valley-spin polarized metal (VSPM) and band insulator (BI) for various RSOC and electric field strengths. The maximum and minimum value of MS appears in the VSPM and BI regimes, respectively. RSOC leads to the distortion of BS and reduction of the effective mass which in combination with SOC provides some changes like phase transition of VSPM from antiferromagnetic to the paramagnetic phase. Strong RSOC results to the drastic reduction of MS and double peak of the spin-up or spin-down curves at low temperatures.