Dispersion of spin waves in magnetic bilayer structures in the presence of interlayer Dzyaloshinskii-Moriya interaction

In this work, we carried out a theoretical analysis of the dispersion relation $\ensuremath{\omega}(k)$ for spin waves in a layered structure comprising two ferromagnetic layers and a nonmagnetic spacer sandwiched between them. The spin-wave configuration considered is that of the Damon-Eshbach magnetostatic surface spin wave, characterized by a static magnetic field applied in the structure plane and perpendicular to the direction of wave propagation. We assumed that, in addition to the conventional ferromagnetic interlayer Heisenberg exchange via the Ruderman-Kittel-Kasuya-Yosida interaction, the ferromagnetic layers are also coupled by the recently discovered interlayer Dzyaloshinskii-Moriya interaction (IL-DMI). We found that the presence of IL-DMI modifies the eigenfrequencies of both fundamental modes of the structure---acoustic and optical. The acoustic mode experiences a downward shift in frequency and a reduction in slope. Conversely, the optical mode is shifted upward and develops a significant positive slope, whereas it remains dispersionless across most of the wave-number range accessible with Brillouin light-scattering spectroscopy in the absence of IL-DMI. Numerical calculations of the dispersion relation demonstrate that it will be possible to experimentally identify the presence of IL-DMI in such layered structures using Brillouin light scattering. Additionally, the value of the Dzyaloshinskii constant for the ferromagnetic/nonmagnetic/ferromagnetic interface pair can be extracted from the measurement results.