  We study electric polarization and nonlinear optical effects in spin systems
with broken inversion symmetry. We apply strong coupling expansion to the
underlying electronic Hamiltonians, and systematically derive expressions for
electric polarization in spin systems that are represented in terms of spin
operators. Magnon representation of the obtained electric polarization operator
allows us to compute linear and nonlinear optical responses by the standard
diagrammatic method. We apply our formalism to Heisenberg model and $J_1$-$J_2$
model with inversion symmetry breaking. We demonstrate that these inversion
broken spin systems support dc current flow upon magnon excitations which
arises from the shift current mechanism.
