Spin-wave softening and the emergence of stripe domains in synthetic antiferromagnetic multilayers

Spin-wave soft modes are fundamental indicators of instabilities and phase transitions in magnetic systems. Here the role of soft modes in the nucleation of stripelike domains in synthetic antiferromagnetic multilayers is theoretically studied. Using a dynamic matrix formalism and micromagnetic simulations, the phase diagrams for the parallel, antiparallel, and spin-flop states are determined, along with the critical anisotropy fields that facilitate the formation of stripe domains. It is demonstrated that, in the parallel configuration, stripelike domains are predicted by softening at both positive and negative critical wave vectors (${k}_{\mathrm{c}}$), whereas, in the antiparallel configuration, the stripe-domain instability is direction selective, with softening at only one propagation direction (nonreciprocal). Furthermore, stripe domains are predicted to form in multilayers with structural asymmetry (thickness variation in an outer layer), which breaks the $\ifmmode\pm\else\textpm\fi{}{k}_{\mathrm{c}}$ degeneracy of soft modes and enforces single-${k}_{\mathrm{c}}$ selection. The predicted stripe periods ${\ensuremath{\lambda}}_{\mathrm{c}}=2\ensuremath{\pi}/{k}_{\mathrm{c}}$ (90--250 nm) exhibit strong dependence on anisotropy strength and layer number. Therefore, spin waves provide a predictive and quantitative route to delineate phase boundaries and texture periods from soft modes, offering a versatile framework for engineering stripe-domain states in synthetic antiferromagnets and providing new opportunities for spintronic and magnonic applications.