Extend NdJ relationship with the size, multiple exchanges and Dzyaloshinskii-Moriya interaction for Néel skyrmions in hexagonal magnetic interfaces
For the integration with other parts of spintronic devices, it is desired to minimize the size of skyrmions to a nanometer scale. To provide a theoretical guidance for this endeavour, we established an extended NdJ relationship between the skyrmion size and fundamental magnetic properties of two-dimensional hexagonal ferromagnetic lattices, including multiple exchanges between different neighbors (J 1 -J 4 ), Dzyaloshinskii-Moriya interactions (d 1 and d 2 ) and on-site magnetic anisotropy energy. We demonstrated the applicability of this approach through density functional theory and spin spiral calculations for several interface, e.g., Co/Gra, Rh/Gra, Co/Pt 3 and MgO/Co/Pt 3 , and showed that the size of Néel skyrmions can be effectively reduced by either enhancing d or more conveniently reducing J through cancelation of J i s.