The Dzyaloshinskii–Moriya interaction is an antisymmetric exchange interaction, which originates from the spin–orbit coupling.

By investigating the magnon excitations in a 2 ML Fe film on W(110), we have demonstrated that the spin–orbit coupling breaks the energy degeneracy of the magnons via the Dzyaloshinskii–Moriya interaction [1]. Figure 3 shows the magnon dispersion relation measured on a 2 ML Fe film on W(110) for two opposite magnetization directions  ([110] and [110] directions).

As another consequence of the spin–orbit coupling, the lifetime, amplitude, group, and phase velocity of the magnons propagating along two opposite (but crystallographically equivalent) directions perpendicular to the magnetization are different [2].

Fig. 3: (a) Magnon dispersion relation measured on a 2 ML Fe film on W(110) at room temperature and for two different magnetization directions. The splitting of the magnon dispersion relation is very similar to the Rashba effect for electrons and maybe called magnon Rashba effect. (b) The energy splitting obtained from (a).