Spin-wave resonance frequency in ferromagnetic thin film with interlayer exchange coupling and surface anisotropy

- In a sense, the study of spin wave resonance frequency in ferromagnetic thin film, is developed.
- The interlayer exchange coupling and surface anisotrpy are considered in the paper.
- We found that the interlayer exchange coupling is more important for the energetically higher modes than for the energetically lower modes.

We have investigated the dependence of spin-wave resonance(SWR) frequency on the surface anisotropy, the interlayer exchange coupling, the ferromagnetic layer thickness, the mode number and the external magnetic field in a ferromagnetic superlattice film by means of the linear spin-wave approximation and Green's function technique. The SWR frequency of the ferromagnetic thin film is shifted to higher values corresponding to those of above factors, respectively. It is found that the linear behavior of SWR frequency curves of all modes in the system is observed as the external magnetic field is increasing, however, SWR frequency curves are nonlinear with the lower and the higher modes for different surface anisotropy and interlayer exchange coupling in the system. In addition, the SWR frequency of the lowest (highest) mode is shifted to higher (lower) values when the film thickness is thinner. The interlayer exchange coupling is more important for the energetically higher modes than for the energetically lower modes. The surface anisotropy has a little effect on the SWR frequency of the highest mode, when the surface anisotropy field is further increased.

The figure shows how the interlayer coupling affects the SWR frequency with different interfacial couplings. Let us look at the details. In case of the interfacial coupling JAB = 0.2 (Fig. a), the SWR frequency is obviously increased for all modes with interlayer coupling increasing. The SWR frequency of the energetically lowest mode (m = 1) is zero, namely, the effect of interlayer coupling on resonance frequency of spin wave with the lowest mode is not pronounced. However, for the highest mode (m = 12), SWR frequency presents a nonmonotonic dependence on interlayer coupling. When the interfacial coupling is increased to JAB = 0.5 (Fig. b), the highest mode (m = 12) evolve nonlinearly to higher with the interlayer coupling. When JAB is sequentially increased to 0.8 (Fig. c) and 1.1 (Fig. d), the gap between m = 11and m = 12is increasing. In addition, at strong interlayer coupling effect, the gap of any adjacent modes tend to uniform distribution. Interesting, if setting JAB → 0, these neighbouring two curves become coincident. It may be a reason that the bialyer ferromagnetic film will turn to two independent ferromagnetic thin film at JAB → 0.192