Dynamical spin-spin susceptibility of Silicene

We present a detailed study of the imaginary and real parts of the spin-susceptibility of silicene which can be generalized to other buckled honeycomb structure. We find that while the off-diagonal components are non-zero in individual valleys, they add up to zero upon including contributions from both the valleys. We investigate the interplay of the spin-orbit interaction and an external electric field applied perpendicular to the substrate and find that although the xx and yy components of the susceptibility are identical, they differ from the zz-component. The external electric field plays an important role in modifying the allowed inter-subband regions. In the dynamic limit, the real part of the susceptibility exhibits log-divergence, position of which can be tuned by the electric field and therefore has implications for spin-collective excitations. The effect of the electric field on the static part of the susceptibility and its consequence for the long distance decay of the spin-susceptibility have been explored.