  The absorption of bulk acoustic phonons in a two-dimensional (2D) GaAs/AlGaAs
heterostructure is studied (in the clean limit) where the 2D electron-gas
(2DEG), being in an odd-integer quantum-Hall state, is in fact a spin
dielectric. Of the two channels of phonon absorption associated with excitation
of spin waves, one, which is due to the spin-orbit (SO) coupling of electrons,
involves a change of the spin state of the system and the other does not. We
show that the phonon-absorption rate corresponding to the former channel (in
the paper designated as the second absorption channel) is finite at zero
temperature ($T$), whereas that corresponding to the latter (designated as the
first channel) vanishes for $T\to 0$. The long-wavelength limit, being the
special case of the first absorption channel, corresponds to sound (bulk and
surface) attenuation by the 2DEG. At the same time, the ballistic phonon
propagation and heat absorption are determined by both channels. The 2DEG
overheat and the attendant spin-state change are found under the conditions of
permanent nonequilibrium phonon pumping.

Mesoscale and Nanoscale Physics;Quantum Physics