Chirality- and Rashba- related effects in the spin texture of a two-dimensional centrosymmetric ferromagnet: The case of the CrI3 bilayer

The newly discovered two-dimensional (2D) magnetic semiconductors such as CrI${}_3$ have triggered a surge of interest stemming from their exotic spin-dependent properties and potential applications in spintronics and magneto-optoelectronics. Using first-principle density-functional-theory calculations, we investigate the properties of the spin-polarization texture in momentum space in the prototype 2D centrosymmetric ferromagnetic (FM) bilayer of CrI${}_3$ with perpendicular magnetization, with a goal of identifying general features due to interlayer interaction and their microscopic origins in 2D centrosymmetric FM materials. The FM CrI${}_3$ bilayer displays a rich in-plane spin texture in its highest valence bands. We show the existence of two distinct spin canting effects induced by the coupling of the two FM layers in establishing the in-plane spin texture. The first effect is generated by the mirror-related chirality of the layer stacking and the spin–orbit-polarized nature of the valence states, and yields the same canting on both layers. The second effect is a Rashba-related effect, which in a centrosymmetric ferromagnet induces in a single electronic state two opposite spin-canted components on the two layers, resulting in a notable frustration effect on the energy of the bonding states. Finally, we show that the above effects can be effectively used to manipulate the spin texture via compressive vertical strain, which induces in the FM CrI${}_3$ bilayer valence-band-edge states with canted spins.