  The traditional theory of magnetic moments for chiral phonons is based on the
picture of the circular motion of the Born effective charge, typically yielding
a small fractional value of the nuclear magneton. Here we investigate the
adiabatic evolution of electronic states induced by lattice vibration of a
chiral phonon and obtain an electronic orbital magnetization in the form of a
topological second Chern form. We find that the traditional theory needs to be
refined by introducing a $\bm{k}$ resolved Born effective charge, and identify
another contribution from the phonon-modified electronic energy together with
the momentum-space Berry curvature. The second Chern form can diverge when
there is a Yang's monopole near the parameter space of interest as illustrated
by considering a phonon at the Brillouin zone corner in a gaped graphene model.
We also find large magnetic moments for the optical phonon in bulk topological
materials where non-topological contribution is also important. The magnetic
moment experiences a sign change when the band inversion happens.
