  The selective cooling of $^{75}$As spins by optical pumping followed by
adiabatic demagnetization in the rotating frame is realized in a nominally
undoped GaAs/(Al,Ga)As quantum well. The rotation of 6 kG strong Overhauser
field at the $^{75}$As Larmor frequency of 5.5 MHz is evidenced by the dynamic
Hanle effect. Despite the presence of the quadrupole induced nuclear spin
splitting, it is shown that the rotating $^{75}$As magnetization is uniquely
determined by the spin temperature of coupled spin-spin and quadrupole
reservoirs. The dependence of heat capacity of these reservoirs on the external
magnetic field direction with respect to crystal and structure axes is
investigated. The lowest nuclear spin temperature achieved is 0.54 $\mu$K,
which is the record low value for semiconductors and semiconductor
nanostructures.
