Dynamical spin-spin susceptibility of Silicene

TL;DR

This paper analyzes the spin susceptibility of silicene, revealing how electric fields and spin-orbit interactions influence its dynamic and static properties, with implications for spin excitations and long-range behavior.

Contribution

It provides a comprehensive analysis of silicene's spin susceptibility, including effects of electric fields and spin-orbit coupling, which was not thoroughly explored before.

Findings

Off-diagonal susceptibility components cancel out across valleys.

Electric field modifies inter-subband regions and susceptibility divergence.

Real susceptibility exhibits tunable log-divergence affecting spin excitations.

Abstract

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.