Magnetic Q-balls

We study charged soliton branches in quasi-one-dimensional chiral magnetic systems with Dzyaloshinskii--Moriya (DM) interaction, easy-axis anisotropy, and Zeeman coupling. The same static magnetic functional is equipped with two different dynamical completions: an antiferromagnetic model with second-order time derivatives and a ferromagnetic model with Berry-phase dynamics. On the helical branch selected by the static DM interaction, the problem reduces to an analytically tractable one-dimensional system for the polar angle of the order parameter. We derive the existence conditions for polar Q-balls from the curvature of the reduced effective potential and the presence of a nonzero turning point. In the antiferromagnetic case, the allowed frequency window is symmetric and can be completely closed by the combined effect of the DM coupling and the Zeeman field. At zero Zeeman field, the same reduction also supports antiferromagnetic Q-kinks, for which we obtain explicit profiles, charges, energies, and reduced-sector fission criteria. In the ferromagnetic case, the Berry phase makes the rotation frequency act as a shifted Zeeman field. As a result, north- and south-pole charged droplets are selected by opposite signs of the shifted rotation. We also show that a formal pole-to-pole solution of the ferromagnetic mechanical problem does not generally correspond to a finite-energy magnetic soliton, because the Berry term does not renormalize the physical Hamiltonian. These results clarify how charged-soliton mechanisms depend on the underlying magnetic dynamics, even when the static chiral energy is the same.