Spin wave resonance frequency in ferromagnetic thin film with the biquadratic exchange interaction

Spin wave resonance (SWR) frequency in ferromagnetic thin film with the biquadratic exchange interaction, interlayer exchange coupling, film thickness, surface anisotropy field, and the external magnetic field has been investigated by using the linear spin-wave approximation and Green's function techniques. In comparison to previous studies without considering the biquadratic exchange interaction, the SWR frequency behaviors of the energetically mid-higher modes were found to be highly sensitive to biquadratic exchange interaction. SWR frequencies of all modes are linearly proportional to external magnetic field. However, the SWR frequency has nonlinear dependence on the interlayer exchange coupling and surface anisotropy field. Moreover, the biquadratic exchange interaction enabled a considerable improvement in the effects of surface anisotropy field, interlayer exchange coupling, and external magnetic field on SWR frequency. Our results also reveal that a decrease in the SWR frequency of the corresponding mid-lower modes as the thickness of film is increased while the almost the same frequency gap between the energetically highest mode and lowest mode is obtained for the thicker film. These results could help improve the understanding of magnetic properties and promote magnetic materials applications in spintronic devices.

Automated summary

This study investigates the spin wave resonance (SWR) frequency in ferromagnetic thin film with the biquadratic exchange interaction, interlayer exchange coupling, film thickness, surface anisotropy field, and the external magnetic field. The results show that the SWR frequency behaviors of the mid-higher modes are highly sensitive to the biquadratic exchange interaction. The SWR frequencies are linearly proportional to the external magnetic field, but nonlinearly depend on the interlayer exchange coupling and surface anisotropy field. The biquadratic exchange interaction improves the effects of surface anisotropy field, interlayer exchange coupling, and external magnetic field on SWR frequency. An increase in film thickness leads to a decrease in the SWR frequency of the corresponding mid-lower modes, but the frequency gap between the energetically highest mode and lowest mode remains almost the same.