Role of Interfacial Dzyaloshinskii–Moriya Interactions on Dipole-Exchange Spin Waves in Finite-Width Ferromagnetic Nanostripes

In this paper, we explore the magnetization dynamics in a long ferromagnetic nanostripe with finite width in the presence of antisymmetric Dzyaloshinskii–Moriya exchange interactions (DMIs). It is known that DMIs, which are currently of great interest because they give rise to chiral and nonreciprocal properties and influence surface topologies, can be enhanced by interfacing the nanostripe with a heavy metal. Our theoretical approach employs a microscopic (or Hamiltonian-based) analysis that includes symmetric bilinear exchange, antisymmetric DMI, long-range dipole–dipole interactions, and Zeeman energy due to an external magnetic field applied out of the plane of the nanostripe. In this geometry, we calculate the frequencies and amplitudes of the discrete spin-wave modes that have a standing-wave character across the finite width of the stripe and a propagating character (with wavenumber k) along the stripe length. The individual spin-wave modes display nonreciprocal propagation in their dispersion relations due to DMI. We also find that there may be localized edge spin waves with amplitudes that undergo spatial decay near the stripe edges.