Many low-dimensional systems, such as nanoscale islands, thin films, and multilayers, as well as bulk systems, such as multiferroics, are characterized by the lack of inversion symmetry, a fact that may give rise to a Dzyaloshinskii-Moriya (DM) interaction. For sufficient strength, the DM interaction will favor spiral spin configurations of definite chirality. In order to harness such systems for applications, it is important to understand the conditions under which these spiral spin configurations form and how they can be controlled via an external field. Here, we present exact solutions of the 1D magnetization profiles in such systems for arbitrary material parameters in closed form. Determining the energy per unit length exactly, we are able to present the critical strength of the DM interaction, at which spiral solutions are energetically favorable. These magnetization profiles, in general, take the form of a domain wall or soliton lattice, with all solitons having the same chirality, whose sign is dictated by DM interaction. Conversely, given an energetically favorable spiral solution, we determine quantitatively how the magnetization profile changes as a function of the applied field.

Magnetic domain wall racetrack memory samples allow for the controlled motion of isolated magnetic domain walls in a quasi one-dimensional geometry. Here we consider the possibility of the dynamical formation of bound states of domain walls that can be prepared via a suitably chosen external field. Upon switching off the external field, these domain walls oscillate around their common center of mass, with a frequency depending on the relative initial handedness of the domain wall. Such breather states may be observed by detecting the resulting magnetization oscillations.