Spin orientation and spin precession in inversion-asymmetric quasi-two-dimensional electron systems

Inversion-asymmetry-induced spin splitting of the electron states in quasi-two-dimensional (quasi-2D) systems can be attributed to an effective magnetic field $\mathcal{B}$ which varies in magnitude and orientation as a function of the in-plane wave vector ${\mathbf{k}}_{\Vert }.$ Using a realistic $8\times 8$ Kane model that fully takes into account spin splitting because of both bulk inversion asymmetry and structure inversion asymmetry we investigate the spin orientation and the effective field $\mathcal{B}$ for different configurations of a quasi-2D electron system. It is shown that these quantities depend sensitively on the crystallographic direction in which the quasi-2D system was grown as well as on the magnitude and orientation of the in-plane wave vector ${\mathbf{k}}_{\Vert }.$ These results are used to discuss how spin-polarized electrons can precess in the field $\mathcal{B}\left({\mathbf{k}}_{\Vert }\right).\mathrm{}$ As a specific example we consider ${\mathrm{Ga}}_{0.47}$${\mathrm{In}}_{0.53}\mathrm{A}\mathrm{s}-\mathrm{I}\mathrm{n}\mathrm{P}$ quantum wells.