Dynamic interlayer exchange coupling in magnetic anisotropic FeCoB/Ru/FeCoB sandwich trilayers

Transverse and longitudinal vector network analyzer ferromagnetic resonance (VNA-FMR) spectroscopy, which can easily distinguish the optical and acoustic modes of FMR, is used to study the dynamic interlayer exchange coupling (IEC) in the oblique sputtered Fe₅₆Co₂₄B₂₀(26.5 nm)/Ru($t_{\mathrm{Ru}}$)/Fe₅₆Co₂₄B₂₀(26.5 nm) trilayers with various Ru thicknesses $t_{\mathrm{Ru}}$. Comparing with the static IEC research method, the dynamic method not only analyzes the frequency response characteristics caused by IEC, but also identifies the nature of IEC. In the studied system, an oscillatory interlayer coupling shows up in the VNA-FMR dynamic measurement. An antiferromagnetic (AFM) coupling appears at 0.35 nm < $t_{\mathrm{Ru}}\le$0.9 nm, while a strong ferromagnetic coupling dominates at $t_{\mathrm{Ru}}\le$0.3 nm and a weak ferromagnetic coupling dominates at $t_{\mathrm{Ru}}\ge$1 nm. The strongest AFM coupling with coupling coefficient J₁ of −0.87 erg/cm² occurs at the intermediate thickness of$t_{\mathrm{Ru}}$ ~0.5 nm, while a strong FM coupling with J₁ as large as 1.1 erg/cm² dominates in the relatively thin 0.23 nm Ru spacers. The coupling mechanism is simulated with Layadi's rigid model and the oscillatory behavior of the bilinear IEC coefficient J₁ versus $t_{\mathrm{Ru}}$ is obtained.