  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. We illustrate
such divergence by considering a phonon at a Brillouin zone corner in a gapped
graphene model. A minimal model for optical phonon and the contribution from
the Wannier orbitals are also studied, separately.
