The Unusual Nature of Confined Modes in a Chiral System
  Nonreciprocity of spin wave propagation is a well-known consequence of antisymmetric exchange contributions possible in magnetic spin systems that lack inversion symmetry. In this case, it is possible for the energy of a state to depend on the sign of its momentum as {\omega}(k) ${\neq}$ {\omega}(-k). We discuss here the consequences of this nonreciprocity on counterpropagating travelling spin wave states. In a confined geometry we find states with well-defined nodes but with amplitudes that are modulated such that inversion symmetry of the mode profile is lost. This feature leads to the suggestion that additional features may become visible in, for example, ferromagnetic resonance studies of ferromagnetic micro-elements with DMI, allowing a quantification of the amplitude and direction of the DMI. Moreover, this interference between nonreciprocal modes forms the basis for a generalized concept of mode confinement. 
Benjamin W. Zingsem, Michael Farle, Robert L. Stamps and Robert E.   Camley
cond-mat.str-el cond-mat.mtrl-sci