  We develop the effective field theoretical descriptions of spin systems in
the presence of symmetry-breaking effects: the magnetic field, single-ion
anisotropy, and Dzyaloshinskii-Moriya interaction. Starting from the lattice
description of spin systems, we show that the symmetry-breaking terms
corresponding to the above effects can be incorporated into the effective field
theory as a combination of a background (or spurious) $\SO(3)$ gauge field and
a scalar field in the symmetric tensor representation, which are eventually
fixed at their physical values. We use the effective field theory to
investigate mode spectra of inhomogeneous ground states, with focusing on
one-dimensionally inhomogeneous states, such as helical and spiral states.
Although the helical and spiral ground states share a common feature of
supporting the gapless Nambu-Goldstone modes associated with the translational
symmetry breaking, they have qualitatively different dispersion relations:
isotropic in the helical phase while anisotropic in the spiral phase. We also
discuss the magnon production induced by an inhomogeneous magnetic field, and
find a formula akin to the Schwinger formula. Our formula for the magnon
production gives a finite rate for antiferromagnets, and a vanishing rate for
ferromagnets, whereas that for ferrimagnets interpolates between the two cases.
