  Heat capacity of the nuclear spin system (NSS) in GaAs-based microstructures
has been shown to be much greater than expected from dipolar coupling between
nuclei, thus limiting the efficiency of NSS cooling by adiabatic
demagnetization. It was suggested that quadrupole interaction induced by some
small residual strain could provide this additional reservoir for the heat
storage. We check and validate this hypothesis by combining nuclear spin
relaxation measurements with adiabatic remagnetization and nuclear magnetic
resonance experiments, using electron spin noise spectroscopy as a unique tool
for detection of nuclear magnetization. Our results confirm and quantify the
role of the quadrupole splitting in the heat storage within NSS and provide
additional insight into fundamental, but still actively debated relation
between a mechanical strain and the resulting electric field gradients in GaAs.
