Effect of the Interfacial Dzyaloshinskii–Moriya Interaction on the Spin Waves Eigenmodes of Isolated Stripes and Dots Magnetized In-Plane: A Micromagnetic Study

Abstract

The influence of the Dzyaloshinskii–Moriya interaction (DMI) on the eigenmodes of magnetic nanostructures is attracting interest for both fundamental reasons and prospects in applications. In this study, the characteristics of spin waves eigenmodes in either long stripes or elliptical dots magnetized in-plane, with lateral dimensions of the order of 100 nm, are analyzed by micromagnetic simulations in presence of a sizeable DMI. Using the GPU-accelerated software MuMax3, we show that the eigenmodes spectrum is appreciably modified by the DMI-induced non-reciprocity in spin-waves propagation: the frequencies of the eigenmodes are red-shifted and their spatial profiles appreciable altered due to the lack of stationary character in the direction orthogonal to the magnetization direction. As a consequence, one finds a modification of the expected cross-section of the different modes in either ferromagnetic resonance or Brillouin light scattering experiments, enabling one to detect modes that would remain invisible without DMI. In this respect, the modifications of the spectrum can be directly connected to a quantitative estimation of the DMI constant. Moreover, it is seen that for sufficiently large values of the DMI constant, the low-frequency odd eigenmode changes its profile and becomes soft, reflecting the transition of the ground state from uniform to chiral.

Effects of an external magnetic field on spin waves in finite-length ferromagnetic nanotubes

“…It is necessary only to use the generalized assumption for J n,m in the numerical calculations for the equilibrium tilt angles and for finding the eigenvalues and eigenvectors of the dynaical matrix in Eq. (11).…”

“…The characteristic DMI wave-vector dependence, which was mentioned above, and its consequences for unidirectional spin-wave propagation and/or for Brillouin light scattering (BLS), were elaborated further by several other authors, e.g. [5][6][7][8][9][10][11][12]. Some reviews covering the effects of DMI on the magnetization statics and dynamics in ferromagnetic nanostructures are [4,[13][14][15][16].…”

Spin Waves in Ferromagnetic Nanorings with Interfacial Dzyaloshinskii–Moriya Interactions: II. Directional Effects

“…Also, regarding the spin dynamics in bulk-like materials with no interfaces taken into account, it has been pointed out and verified experimentally that contributions linear in the wave-vector components occur in the dispersion relations at small wave vectors [3,[7][8][9][10][11][12][13], in addition to the quadratic contributions associated with the Heisenberg exchange. Several other studies have been conducted that elaborate on the wave-vector dependence of DMIs and their role in unidirectional spin-wave propagation and/or for Brillouin light scattering (BLS) (see [8][9][10][11][12][14][15][16]). The effects of DMIs on the statics and spin dynamics in ferromagnetic nanostructures have been reviewed, e.g., [3,4,17,18].…”