First-principles calculation of the Dzyaloshinskii-Moriya interaction: A Green's function approach

We present a Green's function approach to calculate the Dzyaloshinskii-Moriya interactions (DMIs) from first-principles electronic structure calculations that is computationally more efficient and accurate than the most commonly employed supercell and generalized Bloch-based approaches. The method is applied to the (111) Co/Pt bilayer where the Co and/or Pt thickness dependence of the DMI coefficients is calculated. Overall, the calculated DMIs are in relatively good agreement with the corresponding values reported experimentally. Furthermore, we investigate the effect of strain in the DMI tensor elements and show that the isotropic N\'eel DMI can be significantly modulated by the normal strains ${\ensuremath{\epsilon}}_xx$ and ${\ensuremath{\epsilon}}_yy$ and is relatively insensitive to the shear strain ${\ensuremath{\epsilon}}_xy$. Moreover, we show that anisotropic strains, $({\ensuremath{\epsilon}}_xx\ensuremath{-}{\ensuremath{\epsilon}}_yy)$ and ${\ensuremath{\epsilon}}_xy$, result in the emergence of anisotropic N\'eel- and Bloch-type DMIs, respectively.