Hetero-interface effect on Gilbert damping in nonmagnetic metal/permalloy/nonmagnetic metal trilayers

Gilbert damping in nonmagnetic metal (NM)/permalloy (Py)/nonmagnetic metal (NM) trilayers was studied using ferromagnetic resonance (FMR) measurements for different constituent materials (NM = Pt, Ta, Cu, and Ti) of varying Py thickness (t = 2, 3, 4, 5, 6, 8, and 10 nm) fabricated using an ultrahigh vacuum sputtering system. We found that the Gilbert damping constant increases with decreasing Py thickness and varies for different constituents of nonmagnetic metals. For NM = Pt, the damping constant of Py increases with decreasing Py thickness more remarkably than for other nonmagnetic metals. According to quantitative estimations of the effective spin-mixing conductance $G_{\text{eff}}^{\text{mix}}$, it was found that the value of $G_{\text{eff}}^{\text{mix}}$ = 1.17 × 10¹⁵ Ω⁻¹·m⁻² for Pt is one order of magnitude greater than $G_{\text{eff}}^{\text{mix}}$ = 0.13 × 10¹⁵ Ω⁻¹·m⁻² for Cu and 0.11 × 10¹⁵ Ω⁻¹·m⁻² for Ti. The large $G_{\text{eff}}^{\text{mix}}$ value for Pt/Py/Pt is known to be caused by the strong spin-orbit coupling (SOC) of Pt. The effective spin-mixing conductance for Pt is 3 times greater than that (0.27 × 10¹⁵ Ω⁻¹·m⁻²) for Ta despite the SOC of both Pt and Ta is similar in magnitude. This work allows not only for an understanding of the interface effect of the Gilbert damping constant on NM/Py/NM trilayers but also for optimal design of low-power-consumption spintronic devices that are composed of a variety of hetero-interfaces between the different magnetic and nonmagnetic layers.