Supplementary Figure 1 Representative sample of DW spin textures in a Fe/Ni/W(110) film. (a) to (d) Compound SPLEEM images of the Fe/Ni/W(110) sample. As in Fig. 2 in the main text, Fe thickness is 1.5 monolayer and Ni thickness is 10 monolayer. The colour wheel represents the direction of in-plane magnetization in each image pixel. White arrows highlight the in-plane spin orientations in the DWs. Scale bar is 1 µm.
Supplementary Figure 2 Chirality as a function of strength of DMI, D ij. (a) dependent chirality derived from the Monte Carlo simulations, -1 corresponds to right-handed and +1 corresponds to left-handed. The values of parameters are,,, and the values of are shown in the inset. (b) Comparison between experimentally determined dependence of on and the best-fit simulated result with.
Supplementary Figure 3 Real-space images of the Fe/Ni/W(110) sample. (a) - (c) SPLEEM images of the 1.5ML Fe/10ML Ni/W(110) sample, mapping (a), (b), (c). Top right symbols define x, y, z axis and spin directions. (d) Compound image constructed from the SPLEEM images in (a)-(c), highlighting the orientation of the magnetization vector within the DWs. The colour wheel represents the direction of inplane magnetization in each image pixel. White arrows in (d) highlight the in-plane spin orientations in the DWs. Scale bar is 1 µm.
Supplementary Note 1 Estimating the DMI strength from dependent chirality For interfacial DMI systems without in-plane uniaxial anisotropy, the interplay between dipolar energy and DM energy determines the domain wall structure and, as we showed previously [1,2], the strength of the DMI can be estimated by experimentally testing the transition of domain wall type between chiral Néel wall and non-chiral Bloch wall. Extending this approach to the Fe/Ni/W(110) system is not straight forward because, as a function of increasing film thickness, we find that the easy magnetization rotates from out-of plane to in-plane prior to the DW spin structure transition. Moreover, the presence of significant in-plane uniaxial anisotropy complicates this approach. In addition to dipolar energy and DM energy, anisotropy also influences the domain wall type, so that the transition from chiral Néel wall to non-chiral Bloch wall due to competition between the DM interaction and dipolar interaction can be suppressed. For instance, when the dipolar energy difference between Néel wall and Bloch wall is larger than the DM energy, non-chiral Bloch walls are expected in isotropic DMI systems. But in the presence of in-plane anisotropy, Néel wall structure remains favourable in DWs oriented near. Therefore we use a Monte Carlo model to elucidate the balance of energies in the anisotropic system Fe/Ni/W(110). For the Monte Carlo simulations we adapted the two-dimensional model described in Refs. 1, 3 and 4 by adding a term to include in-plane uniaxial anisotropy, so that total energy is expressed as equation 1: ( ) ( ) where and are the position vectors of the atoms in sites and in a twodimensional plane, and are spin moments located on those sites, and,,, and correspond to exchange interaction, uniaxial out-of-plane anisotropy, uniaxial in-plane anisotropy, dipole interaction and Dzyaloshinskii-Moriya interaction, respectively. To model DWs we used arrays of 600 by 10 spin blocks bounded by an up domain and a down domain along the long boundaries and periodic boundary conditions connecting the short boundaries. As described in Ref. 4, system temperature is represented by allowing spins to fluctuate according to Boltzmann statistics. Each trial starts from random starting configurations which are allowed to relax by gradually
dropping the temperature from well above the Curie point to zero; iterations are repeated until the total energy is stabilized. Expressing the relative strengths of dipolar, anisotropy, and DM terms as fractions of the exchange interaction, this model can predict the DW spin textures. For example, assuming values of the out-of-plane anisotropy constant, inplane anisotropy constant, dipolar interaction constant, the model captures the essential magnetic structure of the Fe/Ni/W(110) system, and we can systematically vary to determine best-fit with the experimentally measured dependence of chirality on DW orientation. As plotted in supplementary figure 3a, simulated data are similar to the experimental measurements: follows a negative sin curve for small values of and drops to zero as approaches. The deviation from the sin curve is more/less pronounced for weaker/stronger, respectively. A best-fit of the value can be determined by comparing the experimentally measured dependence of chirality on DW orientations and the simulated results. We use root-mean-square deviations where is the deviation between experimental data and simulations. Figure 3b compares the experimental result with a best-fit simulation where. (Mean-square deviations R for the simulations reproduced in figure 3a are:, ;, ;,.) Figure 5a in the main text shows 100 by 10 spin block sections from the best-fit simulation, cut from final minimum-energy states individual trials arrived at. For each angle, 32 trials were simulated and the average chiralities including all trials are plotted in Fig. 5b. The value of the dipolar energy of Fe/Ni bilayers can be calculated from [1,2]; with A we find per atom. In our best-fit simulation the ration is approximately 1.4, this suggests that the strength of the interfacial DMI in the Fe/Ni/W(110) system is of the order per atom. We note that the chirality also depends on the value of, which is not known precisely. Although the best-fit value changes slightly as a function of, this Monte Carlo model clarifies how relative magnitudes of the magnetic parameters affect the DW spin structures and the best-fit value of reported here is at least a reasonable estimate.
Supplementary References [1] Chen, G. et al. Novel Chiral Magnetic Domain Wall Structure in Fe/Ni/Cu(001) Films. Phys. Rev. Lett. 110, 177204 (2013). [2] Chen, G. et al. Tailoring the chirality of magnetic domain walls by interface engineering. Nat. Commun. 4, 2671 (2013). [3] Kwon, H. Y. & Won, C. Effects of Dzyaloshinskii Moriya interaction on magnetic stripe domains. J. Magn. Magn. Mater. 351, 8 15 (2014). [4] Kwon, H. Y. et al. A Study of the stripe domain phase at the spin reorientation transition of two-dimensional magnetic system. J. Magn. Magn. Mater. 322, 2742-2748 (2010).