Intersubband spin-density excitations in quantum wells with Rashba spin splitting

In inversion-asymmetric semiconductors, spin-orbit coupling induces a $\mathbf{k}$-dependent spin splitting of valence and conduction bands, which is a well-known cause for spin decoherence in bulk and heterostructures. Manipulating nonequilibrium spin coherence in device applications thus requires understanding how valence and conduction band spin splitting affects carrier spin dynamics. This paper studies the relevance of this decoherence mechanism for collective intersubband spin-density excitations (SDE’s) in quantum wells. A density-functional formalism for the linear spin-density matrix response is presented that describes SDE’s in the conduction band of quantum wells with subbands that may be nonparabolic and spin split due to bulk or structural inversion asymmetry (Rashba effect). As an example, we consider a 40 nm ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_{0.3}{\mathrm{Ga}}_{0.7}\mathrm{As}$ quantum well, including Rashba spin splitting of the conduction subbands. We find a coupling and wave-vector-dependent splitting of the longitudinal and transverse SDE’s. However, decoherence of the SDE’s is not determined by subband spin splitting, due to collective effects arising from dynamical exchange and correlation.