  Self-assembled quantum dots (QDs) are born out of lattice mismatched
ingredients where strain plays an indispensable role. Through the electric
quadrupolar coupling, strain affects the magnetic environment as seen by the
nuclear spins. To guide prospective single-QD nuclear magnetic resonance (NMR)
as well as dynamic nuclear spin polarization experiments, an atomistic insight
to the strain and quadrupolar field distributions is presented. A number of
implications of the structural and compositional profile of the QD have been
identified. A high aspect ratio of the QD geometry enhances the quadrupolar
interaction. The inclined interfaces introduce biaxiality and the tilting of
the major quadrupolar principal axis away from the growth axis; the alloy
mixing of gallium into the QD enhances both of these features while reducing
the quadrupolar energy. Regarding the NMR spectra, both Faraday and Voigt
geometries are investigated, unraveling in the first place the extend of
inhomogeneous broadening and the appearance of the normally-forbidden
transitions. Moreover, it is shown that from the main extend of the NMR spectra
the alloy mole fraction of a single QD can be inferred. By means of the
element-resolved NMR intensities it is found that In nuclei has a factor of
five dominance over those of As. In the presence of an external magnetic field,
the borderlines between the quadrupolar and Zeeman regimes are extracted as 1.5
T for In and 1.1 T for As nuclei. At these values the nuclear spin
depolarization rates of the respective nuclei get maximized due to the
noncollinear secular hyperfine interaction with a resident electron in the QD.
