Strongly hybridized dipole-exchange spin waves in thin Fe-N ferromagnetic films

Spin waves propagation in ferromagnetic films, several tens of nanometers thick, have recently received increasing attention, in view of the development of magnonic devices operating in the GHz range of frequencies. A detailed knowledge of the dispersion curves and of the spatial characteristics of the spin-wave modes is preliminary to any technological application, particularly in the "mesoscopic range" (50-200 nm) of film thickness, where several dipole-exchange modes may appear in the spectrum, exhibiting frequency crossing and hybridization as a function of their wave number. In this work, the mutual interaction and the hybridization of the dipole-exchange spin-wave modes was investigated in a nitrogen-implanted iron (Fe-N) film, 78-nm-thick, in-plane magnetized. The spin-wave dispersion curves were measured by using Brillouin light scattering, and the experimental results were interpreted combining micromagnetic simulations and theoretical calculations in the framework of a dipole-exchange spin-wave mode approach. A noticeable hybridization between the spin-wave modes was observed, due to the simultaneous presence of a marked perpendicular magnetic anisotropy and a rather high saturation magnetization. The hybridization was found to induce a very large gap (\Delta\nu \approx 5 GHz) between the low-frequency spin waves at high wave vector (k \approx 10^5 rad/cm). Consequently, in such a k range the simultaneous presence of two spin-wave modes with sizeable (v_g \approx 1.5 km/s) but opposite group velocity was observed, opening a way for the potential use of Fe-N films in magnon spintronics.