  The nuclear spin systems in CdTe/(Cd,Zn)Te and CdTe/(Cd,Mg)Te quantum wells
(QW) are studied using a multistage technique combining optical pumping and
Hanle effect-based detection. The samples demonstrate drastically different
nuclear spin dynamics in zero and weak magnetic fields. In CdTe/(Cd,Zn)Te, the
nuclear spin relaxation time is found to strongly increase with the magnetic
field, growing from 3 s in zero field to tens of seconds in a field of 25 G. In
CdTe/(Cd,Mg)Te the relaxation is an order of magnitude slower, and it is
field-independent up to at least 70 G. The differences are attributed to the
nuclear spin relaxation being mediated by different kinds of resident electrons
in these QWs. In CdTe/(Cd,Mg)Te, a residual electron gas trapped in the QW
largely determines the relaxation dynamics. In CdTe/(Cd,Zn)Te, the fast
relaxation in zero field is due to interaction with localized donor-bound
electrons. Nuclear spin diffusion barriers form around neutral donors when the
external magnetic field exceeds the local nuclear field, which is about
$B_L\approx$0.4 G in CdTe. This inhibits nuclear spin diffusion towards the
donors, slowing down relaxation. These findings are supported by theoretical
modeling. In particular, we show that the formation of the diffusion barrier is
made possible by several features specific to CdTe: (i) the large donor binding
energy (about 10 meV), (ii) the low abundance of magnetic isotopes (only
$\approx$30 % of nuclei have nonzero spin), and (iii) the absence of nuclear
quadrupole interactions between nuclei. The two latter properties are also
favorable to nuclear spin cooling via optical pumping followed by adiabatic
demagnetization. Under non-optimized conditions we have reached sub-microkelvin
nuclear spin temperatures in both samples, lower than all previous results
obtained in GaAs.
