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. 2025 Oct 17;15:36387. doi: 10.1038/s41598-025-20466-z

Table 1.

Average distance Inline graphic (in a.u.) from the graphene overlayer on Ni(111) (GR/Ni), and between the graphene overlayer and the Ni surface, f-electron occupation Inline graphic, spin Inline graphic, orbital Inline graphic, and the total Inline graphic + Inline graphic moments (in Inline graphic) for the Dy-atom. The non-f spin and the orbital magnetic moments, together with the total non-f magnetic moment m in the Dy@GR/Ni unit cell. The non-zero CF parameters [Inline graphic], and the exchange field Inline graphic for Dy adatom on GR/Ni(111) (in meV). The magnetic anisotropy constants K, and the corresponding magnetic anisotropy energy (MAE, meV) for the Dy adatom on GR/Ni(111) (in meV).

Dy@GR/Ni Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic+Inline graphic
Dy 4.145 9.94 3.38 5.26 8.64
GR/Ni 4.136 -18.03 -1.80 -19.83
CEF Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic
(meV) 14.20 -4.19 -0.36 -8.50 11.0
MAE Inline graphic Inline graphic Inline graphic Inline graphic Inline graphic[010]-Inline graphic[001]
(meV) -8.39 11.80 -0.60 0.66 2.15
Inline graphic[100]-Inline graphic[010]
1.32