Enhancement of magnetization damping coefficient of permalloy thin films with dilute Nd dopants

For spintronics application, which requires fast field switching, it is important to have a kind of soft magnetic material with large damping coefficient. Here, we present the studies of the Nd dopant-level-dependent damping coefficient of Nd${}_{x}$-Py${}_{(1\ensuremath{-}x)}$ thin films (30 nm) in a dilute region utilizing ferromagnetic resonance (FMR). With the Nd content increasing, the film structure was found to be changing from polycrystalline to amorphous when the Nd content is around 3.4%. Meanwhile, the magnetization decreases linearly. Interestingly, we find that along the easy axis, both low coercivity and high hysteresis squareness are simultaneously maintained in the system; i.e., the magnetic softness has been well kept. By theoretical fitting of the angular dependence of the FMR field, the first- and second-order magnetic anisotropy constants, ${K}_{1}$ and ${K}_{2}$, and the Lande $g$ factor are obtained and discussed quantitatively. The measurements of angular and frequency dependence of the ferromagnetic resonance linewidth, as well as the theoretical fitting by considering the contributions of Gilbert damping, two-magnon scattering, and inhomogeneous broadening, show that the damping coefficient $\ensuremath{\alpha}$ increases rapidly (about 25-fold) as the Nd content increases to 11.6%, which is mainly due to the enhanced spin-orbit coupling by the Nd additives, supported by x-ray magnetic circular dichroism measurements.