Reconfigurable Spin-Wave Nonreciprocity Induced by Dipolar Interaction in a Coupled Ferromagnetic Bilayer

Frequency nonreciprocity of wave phenomena describes the situation where the wave dispersion depends on the sign of the wave vector, i.e., counterpropagating waves exhibit different wavelengths for the same frequency. Such behavior has recently been observed in heavy-metal-ferromagnetic interfaces with Dzyaloshinskii-Moriya coupling, and is also known for coupled magnetic bilayers, where the nonreciprocity is enhanced when the two layers are aligned antiparallel. Besides the conventional uses of spin waves, nonreciprocity adds further functionalities, such as its potential applications in communication technologies and logic operations. In the current paper, we thus examine the spin-wave nonreciprocity induced by dipolar interactions in a coupled bilayer consisting of two ferromagnetic layers separated by a nonmagnetic spacer. We derive an easy-to-use formula to estimate the frequency difference provided by the nonreciprocity, which allows one to choose an optimal system in order to maximize the effect. For small wave numbers, the nonreciprocity scales linearly, while for larger wave vectors the nonreciprocity behaves nonmonotonically, with a well-defined maximum. The study is carried out by means of analytical calculations that are complemented by micromagnetic simulations. Furthermore, we confirm 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 nonreciprocity can then be turned on and off, which lends an important functionality to the coupled ferromagnetic bilayers.