Chiral Asymmetry of the Spin-Wave Spectra in Ultrathin Magnetic Films

We raise the possibility that the chiral degeneracy of the magnons in ultrathin films can be lifted due to the presence of Dzyaloshinskii-Moriya interactions. By using simple symmetry arguments, we discuss under which conditions such a chiral asymmetry occurs. We then perform relativistic first principles calculations for an Fe monolayer on W(110) and explicitly reveal the asymmetry of the spin-wave spectrum in the case of wave vectors parallel to the (001) direction. Furthermore, we quantitatively interpret our results in terms of a simplified spin model by using calculated Dzyaloshinskii-Moriya vectors. Our theoretical prediction should inspire experiments to explore the asymmetry of spin waves, with a particular emphasis on the possibility to measure the Dzyaloshinskii-Moriya interactions in ultrathin films.

Figure 1

Sketch of the lattice positions (left) and of the surface Brillouin zone (right) of a bcc(110) plane. The high symmetry points of the surface Brillouin zone are also labeled.

Figure 2

Calculated adiabatic spin-wave spectrum of FeW(110) along the $X$ axis as given in Fig. 1.

Figure 3

Calculated adiabatic spin-wave spectra with chirality index $+1$ (triangles) and $-1$ (spheres) of FeW(110) along the $Y$ axis; see Fig. 1.

Figure 4

Sketch of the calculated Dzyaloshinskii-Moriya vectors between an atom (C) and its nearest (1) and next-nearest (2) neighbors in an Fe monolayer on W(110).

Figure 5

Squares: Asymmetry of the spin-wave spectrum of FeW(110) along the $Y$ axis as derived from the corresponding values in Fig. 3; solid line: the function [Eq. (2)] obtained from a second-nearest-neighbor model with the calculated DM interactions.