  We present additional magic wavelengths ($\lambda_{\rm{magic}}$) for the
clock transitions in the alkaline-earth metal ions considering circular
polarized light aside from our previously reported values in [J. Kaur et al.,
Phys. Rev. A {\bf 92}, 031402(R) (2015)] for the linearly polarized light.
Contributions from the vector component to the dynamic dipole polarizabilities
($\alpha_d(\omega)$) of the atomic states associated with the clock transitions
play major roles in the evaluation of these $\lambda_{\rm{magic}}$, hence
facilitating in choosing circular polarization of lasers in the experiments.
Moreover, the actual clock transitions in these ions are carried out among the
hyperfine levels. The $\lambda_{\rm{magic}}$ values in these hyperfine
transitions are estimated and found to be different from $\lambda_{\rm{magic}}$
for the atomic transitions due to different contributions coming from the
vector and tensor part of $\alpha_d(\omega)$. Importantly, we also present
$\lambda_{\rm{magic}}$ values that depend only on the scalar component of
$\alpha_d(\omega)$ for their uses in a specially designed trap geometry for
these ions so that they can be used unambiguously among any hyperfine levels of
the atomic states of the clock transitions. We also present $\alpha_d(\omega)$
values explicitly at the 1064 nm for the atomic states associated with the
clock transitions which may be useful for creating "high-field seeking" traps
for the above ions using the Nd:YAG laser. The tune out wavelengths at which
the states would be free from the Stark shifts are also presented. Accurate
values of the electric dipole matrix elements required for these studies are
given and trends of electron correlation effects in determining them are also
highlighted.
