Nonreciprocal Directional Dichroism and Toroidalmagnons in Helical   Magnets
  We investigate a dynamical magnetoelectric effect due to a magnetic resonance in helical spin structures through the coupling between magnetization and electric polarization via a spin current mechanism. We show that the magnon has both the dynamical magnetic moment $\Delta M^\omega$ and the electric moment $\Delta P^\omega$ ($\perp \Delta M^\omega$), i.e., a dynamical toroidal moment, under external magnetic fields, and thus it is named the {\em toroidalmagnon}. The toroidalmagnon exists in most conical spin structures owing to the generality of the spin current mechanism. In the absorption of electromagnetic waves, the toroidalmagnon excitation process generally induces a nonreciprocal directional dichroism as a consequence of an interference of the magnetic and electric responses. 
Shin Miyahara and Nobuo Furukawa
cond-mat.str-el