Exchange-dominated frequency shift of spin-wave nonreciprocal dispersion relation in planar magnetic multilayers

Spin-wave nonreciprocity, manifested as a frequency difference between counterpropagating modes, underpins many proposed magnonic devices. While this effect is commonly attributed to dipolar interactions or interfacial chirality, the microscopic origin of the frequency shift in nonreciprocal dispersion in magnetic multilayers remains under debate. Here, we analyze the frequency shift of nonreciprocal spin-wave dispersion in planar multilayer heterostructures without Dzyaloshinskii-Moriya interaction. Using a frequency-shift dynamic matrix formalism, we show that the frequency asymmetry cannot generally be ascribed to dipolar effects alone. Instead, once counterpropagating modes differ in their geometric structure along the thickness, interlayer exchange dominates the frequency shift. Applied to representative multilayer systems, we find that the interlayer exchange contribution exceeds dipolar and intralayer exchange effects by up to two to three orders of magnitude over a broad wave-vector range. Our results establish interlayer exchange as the primary mechanism contributing to the frequency shift of nonreciprocal dispersion in multilayer magnonic systems and provide a quantitative framework for engineering large frequency shifts in nonreciprocal magnonic devices.