Interlayer coupling of the Kittel mode and the perpendicular standing spin wave in magnetic multilayers

Magnetic/nonmagnetic multilayers are complex and fascinating systems with immense potential for various technological applications. To meet the requirements of spintronic devices, it is essential to comprehend their magneto -dynamic behaviour and interlayer coupling mechanisms. Here, we systematically study the static and dynamic coupling of different spin precession modes, including the Kittel mode and the perpendicular standing spin wave (PSSW) mode, between permalloy (Py) layers with variable thicknesses. Our main focus centers around three distinct types of magnetic multilayers featuring different spacers (Ta, Pt, Ru). According to the ferromagnetic resonance results, we find that the nonmagnetic layers inside these structures display distinct magnetic static and dynamic characteristics over varying ranges of magnetic layer thickness. When the thickness of the Py layer is 10 nm, it demonstrates a ferromagnetic exchange coupling between the Py layers via the Ta and Pt layers. Conversely, when the spacer layer is composed of Ru, a clear antiferromagnetic coupling is detected. All of the multilayers, however, exhibit increased ferromagnetic exchange coupling as the thickness of the Py layer increases. Furthermore, it is found that the Pt spacer layer still plays a crucial role in dynamic interlayer coupling in the uniform precession mode, while the Py/Ru multilayer exhibits a stronger coupling in the non -uniform precession mode.