Spin Precession and Alternating Spin Polarization in Spin-$3/2$ Hole Systems

The spin density matrix for spin-$3/2$ hole systems can be decomposed into a sequence of multipoles which has important higher-order contributions beyond the ones known for electron systems [R. Winkler, Phys. Rev. B 70, 125301 (2004)]. We show here that the hole spin polarization and the higher-order multipoles can precess due to the spin-orbit coupling in the valence band, yet in the absence of external or effective magnetic fields. Hole spin precession is important in the context of spin relaxation and offers the possibility of new device applications. We discuss this precession in the context of recent experiments and suggest a related experimental setup in which hole spin precession gives rise to an alternating spin polarization.

Figure 1

Precession of the Bloch vector $\mathit{S}$ (bold arrow) about the wave vector $\mathit{k}$ when the angle between the two is initially 60°. We have assumed that $\mathit{S}(t=0)$ is parallel to the $z$ axis and $\mathit{k}$ lies in the $xz$ plane.

Figure 2

A bent structure allows holes to be driven around a corner [20, 21]. (a) An idealized representation of the corner device. (b) A more realistic model of the corner, as discussed in the text. In regions $C$ and $L_2$, the spin polarization oscillates as a function of time.