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Silicene have been proposed to host multiple topological phases depending onthe environmental parameters such as gated voltage and proximity inducedexchange field. Two typical topological phase are quantum spin Hall phase andquantum anomalous Hall phase. We found that in the presence ofantiferromagnetic exchange field and (or) gated voltage, the bilayer silicenehost a topological phase that the Chern numbers of the two spin are differentin both sign and magnitude, .i.e the anomalous Hall effects of the two spinsare imbalanced. The topological phase is generated by triple band inversionthat changes the Chern number of the upper and lower bands by $\pm3$. The phasehost large anomalous spin Hall respondence. Meanwhile, because of the largetrigonal warping in bilayer silicene near to the triple band inversion regime,the Magnus Hall effect is large. This finding enriches the topological systemsof bilayer silicene as candidate for spintronic devices.

Spin Imbalanced anomalous Hall effect and Magnus Hall effect of Bilayer Silicene