Impact of layer count and thickness on spin wave modes in multilayer synthetic antiferromagnets.

In this study, the spin-wave spectrum in multilayer synthetic antiferromagnets is calculated. The analysis focuses on the effects of varying both the thicknesses and the number of ferromagnetic layers within these structures. The results reveal that a non-reciprocal spin-wave dispersion occurs in structures with an even number of layers, while a reciprocal dispersion of two counterpropagating waves is observed for systems with an odd number of layers. As the number of layers and their thickness increase, the study identifies the distinctive presence of bulk and surface modes, with the latter being strongly affected by dynamic dipolar interactions. In multilayers with an even number of layers, such surface modes exhibit nonreciprocal behavior, maintaining their surface character only in one propagation direction. Conversely, in odd-layer systems, the symmetric counterpropagating surface modes have similar properties. Additionally, the bulk modes for both even and odd numbers of layers converge towards similar dynamic behavior as the thickness and number of layers increase. As the thickness of the ferromagnetic layers increases, the surface modes in multilayers with an odd number of layers remain localized at either the top or bottom, depending on the sign of the wave vector. In contrast, for the even case, the surface modes appear in both the top and bottom ferromagnetic layers when the layers are thin or ultrathin. However, as the ferromagnetic layer thickness increases, these modes gradually become predominantly localized at either the top or bottom of the multilayer. Finally, the study explores the application of an external magnetic field, demonstrating that surface chiral modes are absent in the saturated state, resulting in a reciprocal spin-wave dispersion. This establishes a magnetic field-mediated control over non-reciprocal localized surface modes.