  Spin-orbital interactions (SOI) in silicene results in the quantum spin Hall
effect, while the Hubbard-induced Coulomb interaction in zigzag nanoribbons
often generates a band gap with the anti-ferromagnetic (AF) spin orders on two
edges. In this paper we systematically study these two joint contributions to
the zigzag silicene-like nanoribbons (zSiNR). Some topological and magnetic
phase transitions are investigated with different material parameters and
external fields. We find when the ribbon width or the SOI value exceeds some
critical value, the SOI may overcome the Coulomb interaction and the system
transits from a band insulator to a topological insulator: the
quantum-spin-Hall or the spin quantum-anomalous Hall state. We also find some
magnetic phase transition exist in the Hubbard-dominated zSiNR systems when the
exchange field or the electric field goes beyond some critical values. At last
we observe a double topological/magnetic phase transition in a
Hubbard-SOI-balanced zSiNR system before the magnetic and topological phases
are destroyed by a strong electric field.
