Non-reciprocity of spin wave propagation induced by the interface   Dzyaloshinskii-Moriya interaction in Py/Pt film structures
  Results of a comprehensive study by means of Brillouin spectroscopy, complemented by Ferromagnetic Resonance characterization, of spin waves (SW) propagating in Py/Pt bi-layers, characterized by pronounced interface Dzyaloshinskii-Moriya interactions (IDMI) are reported. Non-conventional wave behavior of SW travelling in opposite directions, characterized by non-reciprocity with respect to the inversion of the sign of the SW wave-number, has been revealed. The value of the effective IDMI constant D has been estimated. 
A. A. Stashkevich, M. Belmeguenai, Y. Roussign\'e, S.M.Cherif, M.   Kostylev, M. Gabor, D. Lacour, C. Tiusan, M. Hehn
cond-mat.mtrl-sci