Nonreciprocal spin waves of helical magnetization states in CoFeB/NiFe bilayers
We investigated the nonreciprocal spin-wave properties, including the frequency shift, of a helical equilibrium state in a versatile CoFeB/NiFe bilayer. Through an extension of the dynamic matrix formalism (developed in this work) to an arbitrary non-collinear configuration along a heterostructured multilayered system thickness, we explained the frequency shift via differences in the dynamic dipolar and interlayer exchange interactions arising from the distinct spin-wave mode profiles across the bilayer thickness for counterpropagating modes at the same wave vector. In contrast to recent literature wherein the frequency shift is attributed solely to the dipolar interaction, our results and explanations hereby presented involve a starring role of the interlayer exchange interaction not accounted in current literature. Furthermore, we also found a combination of large frequency shift values and sub-100 nm spin wave wavelengths that can be tuned or even enhanced with the twisting degree of the helical magnetization state by the application of the external field, and with the thickness of the NiFe sublayer, which might be highly relevant for magnonic applications. We validated our model and the physical mechanism that explains the frequency shift using recent simulations and experimental results.