Noncollinear magnetism of Cr and Mn nanoclusters on Ni(111): Changing the magnetic configuration atom by atom

The Korringa-Kohn-Rostoker Green-function method for noncollinear magnetic structures was applied on Mn and Cr nanoclusters deposited on the Ni(111) surface. We consider various dimers, trimers, and tetramers. We obtain collinear and noncollinear magnetic solutions, brought about by the competition of antiferromagnetic interactions. It is found that the triangular geometry of the Ni(111) substrate, together with the intracluster antiferromagnetic interactions, is the main cause of the noncollinear states, which are secondarily affected by the cluster-substrate exchange interactions. The stabilization energy of the noncollinear, compared to the collinear, states is calculated to be typically of the order of $100\mathrm{meV}∕\text{atom}$, while multiple local-energy minima are found, corresponding to different noncollinear states, differing typically by $1–10\mathrm{meV}∕\text{atom}$. Open structures exhibit sizable total moments, while compact clusters tend to have very small total moments, resulting from the complex frustration mechanisms in these systems.

Figure 1

(Color online) Different magnetic configurations of Mn dimer on Ni(001). The Mn atoms are labeled by A and B; unlabeled atoms (in blue or light gray) correspond to the Ni substrate. The configurations correspond to FM in (a), AF in (b), Ferri in (c) which is the ground state, and the noncollinear additional local minimum in (d). See text for the discussion.

Figure 2

(Color online) Different geometrical configurations considered for trimers and tetramers at the surface of Ni(111).

Figure 3

(Color online) Side view (a) and top view (b) are shown for the most stable configuration of Cr compact trimer on Ni(111); this corresponds also to the NCOL1 configuration of the Mn compact trimer. (c) and (d) represent the side view and top view of the ground state (NCOL2) of Mn compact trimer on Ni(111) while (e) and (f) depict an almost degenerate state (NCOL3) of the same Mn trimer. Finally, the side view (g) and top view (h) are shown for the most stable configuration of Mn corner trimer on Ni(111). The adatoms are labeled by A, B, and C. Unlabeled atoms (in blue or light gray) correspond to the Ni substrate. See text for more details.

Figure 4

(Color online) Top view of the collinear most stable solution (a) and the noncollinear metastable configuration (b) of compact Cr tetramer on Ni(111). In (c) is depicted the Cr tetramer-$b$ magnetic ground state on Ni(111), which basically consists of the noncollinear trimer state of Fig. 3a coupled antiferromagnetically to the fourth adatom. The adatoms are labeled by A, B, C, and D. Unlabeled atoms (in blue or light gray) correspond to the Ni substrate.