Magnon dispersion shift in the induced-ferromagnetic phase of the   noncentrosymmetric MnSi
  Small angle neutron inelastic scattering measurement has been performed to study the magnon dispersion relation in the field-induced-ferromagnetic phase of the noncentrosymmetric binary compound MnSi. For the magnons propagating parallel or anti-parallel to the external magnetic field, we experimentally confirmed that the dispersion relation is asymmetrically shifted along the magnetic field direction. This magnon dispersion shift is attributed to the relativistic Dzyaloshinskii-Moriya interaction, which is finite in noncentrosymmetric magnets, such as MnSi. The shift direction is found to be switchable by reversing the external magnetic field direction. 
Taku J Sato, Daisuke Okuyama, Tao Hong, Akiko Kikkawa, Yasujiro   Taguchi, Taka-hisa Arima, Yoshinori Tokura
cond-mat.str-el