Impact of the interfacial Dzyaloshinskii-Moriya interaction on the band structure of one-dimensional artificial magnonic crystals: A micromagnetic study

•Magnonic bands of two different one-dimensional magnonic crystals in the presence of DMI.•For weak DMI the folding property of the MCs band structure permits to extend the sensitivity of Brillouin Light Scattering.•For large DMI the SW dispersion relation presents flat modes separated by forbidden frequency gaps whose amplitude depends on the value of D.•The flat modes are confined in specific regions of the samples and are characterized by a non-reciprocal character.