Reconfigurable spin-wave non-reciprocity induced by dipolar interaction in a coupled ferromagnetic bilayer

Non-reciprocity of wave phenomena describes the situation where wave dispersion depends on the sign of the wave-vector, i.e., counter-propagating waves exhibit di↵erent wavelengths for the same frequency. Such behavior has been recently observed in heavy-metal/ferromagnetic interfaces with Dzyaloshinskii-Moriya coupling, and has also been known for coupled magnetic bilayers, where non-reciprocity is enhanced when the two layers are antiparallel aligned. Besides the conventional uses of spin-waves, non-reciprocity adds further functionalities, such as its potential applications in communications technologies and logical operations. In the current manuscript, we thus examine the spin-wave non-reciprocity induced by dipolar interactions in a coupled bilayer consisting of two ferromagnetic layers separated by a non-magnetic spacer. We derive an easy-to-use formula to estimate the frequency di↵erence provided by the non-reciprocity, which allows for choosing an optimal system in order to maximize the e↵ect. For small wave-numbers, non-reciprocity scales linearly, while for larger wave-vectors the non-reciprocity behaves non-monotonically, with a well-defined maximum. The study is carried out by means of analytical calculations that are complemented by micromagnetic simulations. Furthermore, we confirmed our model by experimental investigation of the spin-wave dispersion in a prototype antiparallel-coupled bilayer system. Since the relative magnetic orientation can be controlled through a bias field, the magnon non-reciprocity can be then turned on and o↵, which lends an important functionality to the coupled ferromagnetic bilayers.