Spin-phonon relaxation of Silicene and Germanene from first-principles density-matrix dynamics*

Spin relaxation and decoherence due to coupling with lattice environment is of key importance to quantum information science and spintronics applications. Graphene (GR) has been one of the most popular spintronic materials with the long spin lifetime. Silicene or germanene has a similar Dirac cone linear dispersion to GR, but with larger spin-orbit coupling (SOC) and buckled structure, which exhibits properties of valleytronics and topological insulators. Here, we investigate spin relaxation of silicene and germanene with ab-initio density matrix dynamics with SOC and electron-phonon couplings. We find large spin lifetime anisotropy of two systems compared to GR. Under electric field, we found both the in-plane and out-of-plane spin lifetime strongly decreased, with spin lifetime anisotropy rather unchanged. In addition, the in-plane spin lifetime has weak temperature dependence, in sharp contrast to the out-of-plane one. The dominant electron-phonon coupling for spin relaxation changes from intravalley relaxation at low temperature to intervalley relaxation at high temperature, distinct from GR. Our ab-initio work provides unbiased insights to spin relaxation mechanism of topological 2D materials.