  The spin-orbit (SO) coupling parameters for lowest conduction subband due to
structural (SIA) and bulk (BIA) inversion asymmetry are calculated for a range
of carrier densities in [001]-grown delta-doped n-type InSb/In1-xAlxSb
asymmetric quantum wells using the established 8 band k.p formalism [PRB 59,8
R5312 (1999)]. We present calculations for conditions of zero bias at 10 K. It
is shown that both the SIA and BIA parameters scale approximately linearly with
carrier density, and exhibit a marked dependence on well width when alloy
composition is adjusted to allow maximum upper barrier height for a given well
width. In contrast to other material systems the BIA contribution to spin
splitting is found to be of significant and comparable value to the SIA
mechanism in these structures. We calculate the spin lifetime for spins
oriented along [11-0] based on D'yakonov-Perel mechanism using both the theory
of Averkiev et al. [J. Phys.:Condens. Matter 14 (2002)] and also the rate of
precession of spins about the effective magnetic field, taking into account all
three SO couplings, showing good agreement.Spin lifeime for this direction is
largest in the narrow wells over the range of moderate carrier densities
considered, which is attributed to the reduced magnitude of the k-cubic BIA
parameter in narrow wells. The inherently large BIA induced SO coupling in
these systems is shown to have considerable effect on the spin lifetime, which
exhibits significant reduction in the maximum spin lifetime compared to
previous studies which consider systems with relatively weak BIA induced SO
coupling. The relaxation rate of spins oriented in the [001] direction is
dominated by the k-linear SIA and BIA coupling parameters and at least an order
of magnitude greater than in the [11-0] direction.
