Spin properties of black phosphorus and phosphorene, and their prospects for spincalorics

Abstract Semiconducting black phosphorus attracts a lot of attention due to its extraordinary electronic properties. Its application to spincalorics requires the knowledge about the spin and thermal properties. Here, we describe first principles calculations of the spin–orbit coupling and spin scattering in phosphorene and bulk black phosphorus. We find that the intrinsic spin–orbit coupling is of the order of 20 meV for the valence and conduction band, both for phosphorene and bulk black phosphorus, and induces spin mixing with the probability b 2 ≈ 10 − 5 –10 −4 . A strong anisotropy of b 2 is observed. The calculated Elliott–Yafet spin relaxation times reach nanoseconds for realistic values of the momentum relaxation times. The extrinsic spin–orbit coupling, enabling the D’yakonov–Perel’ spin relaxation mechanism, is studied for phosphorene by application of a transverse electric field. We observe a strong anisotropy of the extrinsic effects for the valence band and much weaker for the conduction band. It is shown, that for small enough electric fields the spin relaxation is dominated by the Elliott–Yafet mechanism, while the D’yakonov–Perel’ matters for higher electric fields. Our theoretical results stay in a good agreement with the experimental findings, and indicates that long spin lifetimes in black phosphorus and phosphorene makes them prospective materials for spincalorics and spintronics.