Spin-wave propagation in the presence of interfacial Dzyaloshinskii-Moriya interaction

In ferromagnetic thin films, broken inversion symmetry and spin-orbit coupling give rise to interfacial Dzyaloshinskii-Moriya interactions. Analytic expressions for spin-wave properties show that the interfacial Dzyaloshinskii-Moriya interaction leads to nonreciprocal spin-wave propagation, i.e., different properties for spin waves propagating in opposite directions. In favorable situations, it can increase the spin-wave attenuation length. Comparing measured spin-wave properties in ferromagnet/normal metal bilayers and other artificial layered structures with these calculations could provide a useful characterization of the interfacial Dzyaloshinskii-Moriya interactions.

Figure 1

Geometry under consideration in this paper.

Figure 2

Snapshot images of spin-wave distribution along the $x$ axis for (a) $D=0$ mJ/m${}^2$ and (b) $D=1.5$ mJ/m${}^2$. The spin-wave frequency $f$ is 11 GHz.

Figure 3

Asymmetric spin-wave propagation induced by an interfacial DM interaction in the large-$k$ limit. (a) Dispersion relation. (b) Attenuation length $\Lambda$ as a function of the frequency $f$. (c) Amplitude ratio $\kappa$ as a function of $f$. Symbols and lines correspond to numerical and analytic results, respectively.

Figure 4

Asymmetric spin-wave propagation induced by an interfacial DM interaction in the small-$k$ limit. (a) Dispersion relation. (b) Attenuation length $\Lambda$ as a function of the frequency $f$. Symbols and lines correspond to numerical and analytic results, respectively.