The influence of the Dzyaloshinskii-Moriya interaction on the spin-wave dispersion in an Fe double-layer grown on W(110) is measured for the first time. It is demonstrated that the Dzyaloshinskii-Moriya interaction breaks the degeneracy of spin-waves and leads to an asymmetric spin-wave dispersion relation. An extended Heisenberg spin Hamiltonian is employed to obtain the longitudinal component of the Dzyaloshinskii-Moriya vectors from the experimentally measured energy asymmetry. [5,6] and multiferroics [7,8].In nanomagnetism, where the surface effects are noticeable, the spin-orbit coupling is one of the most important intrinsic magnetic perturbations, which creates novel phenomena. Recently, it has been shown that a strong spin-orbit coupling in the presence of the broken inversion symmetry at the surface leads to the DM interaction, which stabilizes a noncollinear spin structure for a Mn monolayer on W(110) [9] and W(100) [10] surfaces.An ultrathin Fe film grown on W(110) is another system that is believed to show the DM interaction [11][12][13]. Magnetic excitations in this quasi-two-dimensional spin system have been studied theoretically since many years [14][15][16][17][18][19][20][21]. In the description of the collective magnetic excitations, only the symmetric exchange interaction was considered and the DM interaction has been neglected. In such systems, where DM interaction is relatively large, it should, in principle, change the intrinsic properties of the spin-waves (SWs). Only very recently, the influence of the DM interaction on the spin-wave dispersion has been predicted to give rise to an asymmetric spin-wave dispersion in an Fe monolayer on W(110) [22]. However, the effect of the DM interaction on the spin-wave dispersion in low dimensional systems has never been measured experimentally.In this Letter we report the first experimental evidence of the influence of DM interaction on the spin-wave dispersion in a double-layer Fe. We show that in the presence of the DM interaction the spin-wave dispersion is asymmetric. By measuring the highly resolved spin polarized electron energy loss (SPEEL) spectra in both energy loss and gain regimes and by reversing the magnetization of the film, we measure the DM interaction driven asymmetry in the spin-wave dispersion of Fe double-layer grown on W(110). By using an extended Heisenberg spin Hamiltonian, the energy asymmetry is modeled giving rise to a quantitative determination of the longitudinal components of DM vectors.The iron layer was deposited onto a clean W(110) single crystal at room temperature (RT). Special care has been taken concerning the cleaning of the W crystal as described elsewhere [23]. Prior to the SPEELS measurements, the structural, chemical and magnetic properties were checked by means of low energy electron diffraction, Auger electron spectroscopy and magneto optical Kerr effect measurements. The Fe films reveal the expected structural and magnetic properties well-known from literature [24][25][26]. The SPEELS measurements were perf...