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We present the results of a systematic micromagnetic study of the effect ofthe Dzyaloshinskii-Moriya interaction (DMI) on the spin wave band structure oftwo one-dimensional magnonic crystals (MCs), both with the same periodicityp=300 nm, but different implementation of the DMI modulation. In the firstsystem the artificial periodicity was achieved by modulating the interfacialDMI constant D, while in the second system also the sample morphology wasmodulated. Due to the folding property of the band structure in the dispersionrelations of the magnonic crystals it is possible to extend the sensitivity ofBrillouin light scattering towards weak DMI strength (D in the range from 0 to0.5 mJ/m2), by measuring the frequency splitting of folded modes in high-orderartificial Brillouin zones, since the splitting increases almost linearly withthe band index. For relatively large values of the DMI (D in the range from 1.0to 2.0 mJ/m2) the spin waves dispersion relations present flat modes forpositive wavevectors, separated by forbidden frequency gaps whose amplitudedepend on the value of D. These frequency gaps are more pronounced for thesample with morphology modulation. The non-reciprocal, localised, spatialprofiles of these modes in both MCs are discussed with reference to spin wavesin plain films and in isolated stripes of the same thickness.

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