Magnetism in small bimetallic Mn-Co clusters

Effects of alloying on the electronic and magnetic properties of ${\text{Mn}}_x{\text{Co}}_y$ $\left(x+y=n=2-5;x=0-n\right)$ and ${\text{Mn}}_2{\text{Co}}_{11}$ nanoalloy clusters are investigated using the density-functional theory. Unlike the bulk alloy, the Co-rich clusters are found to be ferromagnetic and the magnetic moment increases with Mn concentration and is larger than the moment of pure ${\text{Co}}_n$ clusters of same size. For a particular sized cluster the magnetic moment increases by $2{\mu }_B/\text{Mn}$-substitution, which is found to be independent of the size and composition. All these results are in good agreement with recent Stern-Gerlach experiments [Phys. Rev. B 75, 014401 (2007) and Phys. Rev. Lett. 98, 113401 (2007)]. Likewise in bulk ${\text{Mn}}_x{\text{Co}}_{1-x}$ alloy, the local Co moment decreases with increasing Mn concentration.

Figure 1

(Color online) Ground-state structures and significant isomers of ${\text{Mn}}_x{\text{Co}}_y\left(x+y=3\right)$ clusters. The lighter (magenta) shades represent Co atoms and darker (blue) shades represent Mn atoms. The bond lengths are quoted in $\text{Å}$. The numbers in the parenthesis represent the number of Co atoms $\left(y\right)$, difference in total energy from the corresponding ground state $\left(\Delta E\right)$, and total magnetic moment, respectively. The down arrow represents the atom with antiparallel moment.

Figure 2

(Color online) Ground-state structures and significant isomers of ${\text{Mn}}_x{\text{Co}}_y\left(x+y=4\right)$ nanoalloy clusters. The same conventions are followed as in Fig. 1.

Figure 3

(Color online) Ground-state structures and significant isomers of ${\text{Mn}}_x{\text{Co}}_y\left(x+y=5\right)$ nanoalloy clusters. The same conventions are followed as in Fig. 1.

Figure 4

(Color online) Binding energy of ${\text{Mn}}_x{\text{Co}}_y$ alloy clusters as a function of Mn atoms.

Figure 5

(Color online) (a) Relative stability and (b) different (Mn-Mn, Mn-Co, and Co-Co) bond lengths of $n=5$ cluster as a function of Mn atoms.

Figure 6

(Color online) Calculated magnetic moment per atom as a function of Mn atoms.

Figure 7

(a) Co-Co bond length and (b) average local Co moment $\left({\mu }_{\text{Co}}\right)$ in ${\text{Mn}}_x{\text{Co}}_2$ clusters as a function of $x$.

Figure 8

(Color online) Isosurfaces of magnetization density for (a) ${\text{Mn}}_2\text{Co}$, (b) ${\text{Mn}}_3\text{Co}$, and (c) ${\text{Mn}}_4\text{Co}$ corresponding to 0.02, 0.03, and $0.04e/{\text{Å}}^3$, respectively. The dark (blue) and light (magenta) colors represent Mn and Co atoms, respectively. The ${\text{Mn}}_{\downarrow }$ is marked by down arrow. The blue (red) surface indicates positive (negative) magnetization density.

Figure 9

(Color online) Magnetic moment of pure ${\text{Co}}_n$ and ${\text{Mn}}_{0.5}{\text{Co}}_{0.5}$ clusters. For cluster sizes $n=3$ and 5, the cobalt rich clusters (${\text{MnCo}}_2$ and ${\text{Mn}}_2{\text{Co}}_3$, respectively) are considered (see the text).

Figure 10

(Color online) Average local Co moment $\left({\mu }_{\text{Co}}\right)$ as a function of Mn atoms for different cluster sizes.

Figure 11

(Color online) (a) The ground state, (b) first, and (c) second isomers for ${\text{Co}}_{11}{\text{Mn}}_2$ nanoalloy cluster. The same color conventions are used as in Fig. 1. The numbers in the parenthesis represent the total moment and relative energy to the ground state, $\Delta E$, respectively.

Figure 12

(Color online) The $d$-projected density of states for the (a) central, and (b) surface Mn atom of ${\text{Mn}}_2{\text{Co}}_{11}$ cluster in its ground state [marked as 1 and 2, respectively, in Fig. 11a]. A Gaussian broadening of 0.1 eV has been used. Corresponding integrated density of states up to the Fermi level, $E_F$, is also shown for the (c) central and (d) surface Mn atoms.

Figure 13

(Color online) The charge-density isosurfaces of the six down electrons in the deepest energy levels for ${\text{Mn}}_4\text{Co}$ cluster. They are shown at (a) 0.04, (b) 0.01, (c) 0.01, (d) 0.01, (e) 0.01, and (f) $0.03e/{\text{Å}}^3$, respectively. The dark (blue) and light (magenta) colors represent Mn and Co atoms, respectively, and the ${\text{Mn}}_{\downarrow }$ is marked by down arrow.

Figure 14

(Color online) The charge-density distribution for two of the majority electrons in the deep levels for ${\text{Mn}}_4\text{Co}$ cluster. The dark (blue) and light (magenta) colors represent Mn and Co atoms, respectively, and the ${\text{Mn}}_{\downarrow }$ is marked by down arrow. The isosurfaces are drawn at $0.04e/{\text{Å}}^3$ density.

Figure 15

(Color online) The charge-density distribution for (a) the minority electron at $0.01e/{\text{Å}}^3$ isodensity and (b) for one of the majority electrons at $0.03e/{\text{Å}}^3$ isodensity in the deep levels of ${\text{Mn}}_3\text{Co}$ cluster. The dark (blue) and light (magenta) colors represent Mn and Co atoms, respectively.