Anisotropic splitting of intersubband spin plasmons in quantum wells with bulk and structural inversion asymmetry

In semiconductor heterostructures, bulk and structural inversion asymmetry and spin-orbit coupling induce a $\mathbf{k}$-dependent spin splitting of valence and conduction subbands, which can be viewed as being caused by momentum-dependent crystal magnetic fields. This paper studies the influence of these effective magnetic fields on the intersubband spin dynamics in an asymmetric n-type ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_{0.3}{\mathrm{Ga}}_{0.7}\mathrm{As}$ quantum well. We calculate the dispersions of intersubband spin plasmons using linear-response theory. The so-called D’yakonov-Perel’ decoherence mechanism is inactive for collective intersubband excitations, i.e., crystal magnetic fields do not lead to decoherence of spin plasmons. Instead, we predict that the main signature of bulk and structural inversion asymmetry in intersubband spin dynamics is a threefold, anisotropic splitting of the spin plasmon dispersion. The importance of many-body effects is pointed out, and conditions for experimental observation with inelastic light scattering are discussed.