  We investigate the general conditions to achieve the adiabatic charge and
spin polarizations and quantized pumping in 2D magnetic insulators possessing
inhomogeneous spin structures. In particular, we focus on the chiral
ferrimagnetic insulators which are generated via spontaneous symmetry breaking
from correlated two dimensional topological insulators. Adiabatic deformation
of the inhomogeneous spin structure generates the spin gauge flux, which
induces adiabatic charge and spin polarization currents. The unit pumped
charge/spin are determined by the product of two topological invariants which
are defined in momentum and real spaces, respectively. The same topological
invariants determine the charge and spin quantum numbers of skyrmion textures.
It is found that in noncentrosymmetric systems, a new topological phase, dubbed
the topological chiral magnetic insulator, exists in which a skyrmion defect is
a spin-1/2 fermion with electric charge $e$. Considering the adiabatic current
responses of generic inhomogeneous systems, it is shown that the quantized
topological response of chiral magnetic insulators is endowed with the second
Chern number.
