Magnetism and chemical ordering in binary transition metal clusters

Binary $XY$ clusters, with $X,Y∊\left\{\text{Mn},\text{Fe},\text{Co},\text{Ni}\right\}$, are investigated within first-principles simulations in the framework of density-functional theory. In the case of Co-Mn, the increase in magnetic moment with Mn concentration, which is in contrast to the bulk behavior and was also observed experimentally, is explained on the basis of the electronic structure of the clusters. For Co-Fe, Ni-Mn, Ni-Fe, and Ni-Co, due to the ferromagnetic couplings between the local moments, the same dependence is found, i.e., moments increasing with the concentration of the element with the lower value of atomic number. For Fe-Mn (as well as Co-Mn and Ni-Mn clusters containing many Mn atoms), the situation appears to be more complex with antiferromagnetic tendencies resulting in a nonmonotonic change of the cluster moment with Mn concentration.

Figure 1

(Color online) Magnetic moments (top panel) and relative energies (bottom panel) for the 164 isomers of icosahedral 13-atom Co-Mn clusters. Isomers with a Mn atom at the center are represented by circles (magenta), clusters with a Co atom at the center with squares (green). The black lines mark the lowest-energy isomers found for each composition.

Figure 2

(Color online) Change of the site-projected electronic density of states of 13-atom Co-Mn clusters with Mn concentration. Occupied Mn states are shaded. The $\delta$ peaks of the energy levels have been smeared using a value of 50 meV. The scale of the bottom panel has been changed in favor of better readability of the figure.

Figure 3

(Color) Magnetic moments (top panel) and relative energies (bottom panel) for various isomers of icosahedral 55-atom Co-Mn clusters. Different kinds of isomers are distinguished by color; the lowest-energy isomers are marked by a dashed line.

Figure 4

(Color online) Electronic density of states of a ${\text{Co}}_{49}{\text{Mn}}_6$ cluster, projected onto states of the central Mn atom (magenta), outer shell Mn atoms (green), and Co atoms (black).

Figure 5

(Color) Magnetic moments (top panels) and mixing energies (bottom panels) of 13-atom binary TM clusters as a function of composition. For each system, results are divided into two groups according to the element occupying the central position of the icosahedron. Black dashed lines mark the properties of the lowest-energy isomers found for each composition.

Figure 6

(Color online) Magnetic moments of 13-atom Ni-Fe clusters, calculated within GGA (blue circles), as well as $\text{GGA}+U$ with $U_{\text{Ni}}=3\text{eV}$ and $U_{\text{Fe}}=2\text{eV}$ (red squares).