Engineering the magnetic properties of the Mn${}_{13}$ cluster by doping

With a goal to produce a giant magnetic moment in a Mn${}_{13}$ cluster that will be useful for practical applications, we have considered the structure and magnetic properties of a pure Mn${}_{13}$ cluster and substitutionally doped it with $X=\text{Ti}$, V, Cr, Fe, Co, Ni atom respectively to produce Mn${}_{12}X$ clusters. We find that Ti and V substitutions in a Mn${}_{13}$ cluster are the most promising in terms of gaining substantial binding energy as well as achieving a higher magnetic moment through ferromagnetic alignment of the atom-centered magnetic moments. This has been demonstrated in terms of energetics and electronic properties of the clusters. For comparison, we have also studied the effect of N capping of Mn${}_{13}$ cluster, predicted in an earlier work [Phys. Rev. Lett. 89, 185504 (2002)], as a means of producing stable giant magnetic moments in Mn clusters up to cluster sizes of five Mn atoms.

Figure 1

Plot of total binding energies for icosahedral, hexagonal-close-packed, and cuboctahedral structures of the Mn${}_{13}$ cluster as a function of total magnetic moment ($M$), which is the difference between the number of electrons in the up (i.e., $N\uparrow$) and down (i.e., $N\downarrow$) spin components. The data point corresponding to the minimum energy Mn${}_{13}$ cluster has been encircled.

Figure 2

Atomic spin configurations for the minimum energy structure of a pure Mn${}_{13}$ cluster. The cyan (light gray) colored balls correspond to atoms with positive magnetic moment and blue (dark gray) colored balls correspond to atoms with negative magnetic moment. The convention for numbering the atoms is shown, which is used in Fig. 7.

Figure 3

Plot of total binding energies of icosahedral Mn${}_{12}X$ clusters as a function of total magnetic moment ($M$). The total binding energies are plotted with respect to the binding energy of the MES of an icosahedral Mn${}_{13}$ cluster. (a) and (b) correspond to the substitutions by the elements to the left and to the right of Mn in the Periodic Table, respectively. The dotted lines through zero in (a) and (b) correspond to the binding energy of MES for a pure Mn${}_{13}$ cluster. The data points corresponding to the minimum energy structure of each Mn${}_{12}X$ cluster are marked in the zoomed plots, shown as insets in (a) and (b).

Figure 4

(a) Binding energies [$E_{\text{diff}}=E_B({\text{Mn}}_{12}X){}_{\text{MES}}-E_B({\text{Mn}}_{13}){}_{\text{MES}}$] and (b) magnetic moments [$M_{\text{diff}}=M({\text{Mn}}_{12}X){}_{\text{MES}}-M({\text{Mn}}_{13}){}_{\text{MES}}$] of the minimum energy structures of Mn${}_{12}X$ clusters with respect to those of the minimum energy pure Mn${}_{13}$ cluster, respectively. The straight lines through zero in (a) and (b) are the reference fixed at the binding energy and total magnetic moment, respectively, of the MES of a pure Mn${}_{13}$ cluster.

Figure 5

Plot of total density of states (left-hand panel) and center-atom projected total density of states (right-hand panel) of the minimum energy icosahedral structures of Mn${}_{12}X$ clusters. Black curves correspond to the results for the majority-spin channel and dashed red curves for the minority-spin channel. The dotted line through zero parallel to the $y$ axis in each system corresponds to the Fermi energy of that system. Gaussian smearing (0.1 eV) has been used.

Figure 6

Plot of spin gaps [as defined in Eq. (2)] of the MESs of Mn${}_{12}X$ clusters.

Figure 7

Individual atomic magnetic moments ($m$) of the MESs of Mn${}_{12}$Ti, Mn${}_{12}$V, Mn${}_{12}$Cr, Mn${}_{13}$, Mn${}_{12}$Fe, Mn${}_{12}$Co, and Mn${}_{12}$Ni clusters. The atomic indices 1–12 correspond to the surface atoms (the same for each Mn${}_{12}X$ cluster), while index 13 corresponds to the central atom, as shown in Fig. 2. Lengths of the bars correspond to the magnitude of atomic moments. Red colored (dark) bars in the positive direction correspond to $+\mathit{ve}$ magnetic moments and green colored (gray) bars in the negative direction for $-\mathit{ve}$ magnetic moments. The central site is the most coordinated site and therefore has a very small magnetic moment for all the clusters.

Figure 8

Plot of center-to-surface average bond lengths ($\langle r\rangle$) of the MESs of Mn${}_{12}X$ clusters.

Figure 9

Variation of energy gain $\Delta$, as defined in the text, as a function of total magnetic moments of the Mn${}_{13}$N cluster. The insets show the atomic spin orientation of the minimum energy icosahedral structure and the first isomer of the Mn${}_{13}$N cluster. The cyan (light gray) colored balls correspond to atoms with a positive magnetic moment and blue (dark gray) colored balls correspond to atoms with a negative magnetic moment. The N atom [represented by the smaller-sized red (dark gray) colored ball] in the case for both structures of inset have a negative magnetic moment. The numbers in the parentheses for the insets correspond to the total magnetic moment and the relative energy to the MES of the Mn${}_{13}$N cluster, respectively.