Emergence of noncollinear magnetic ordering in small magnetic clusters: ${\mathrm{Mn}}_n$ and $\mathrm{As}@{\mathrm{Mn}}_n$

Using first-principles density functional calculations, we have studied the magnetic ordering in pure ${\mathrm{Mn}}_n$ $(n=2–10,13,15,19)$ and $\mathrm{As}@{\mathrm{Mn}}_n$ $(n=1–10)$ clusters. Although, for both pure and doped manganese clusters, there exists many collinear and noncollinear isomers close in energy, the smaller clusters with $n⩽5$ have collinear magnetic ground states and the emergence of noncollinear ground states is seen for $n⩾6$ clusters. Due to strong $p\text{−}d$ hybridization in $\mathrm{As}@{\mathrm{Mn}}_n$ clusters, the binding energy is substantially enhanced and the magnetic moment is reduced compared to the corresponding pure ${\mathrm{Mn}}_n$ clusters.

Figure 1

(Color online) Optimal noncollinear structures for ${\mathrm{Mn}}_n$ clusters in the size range $n=3–10$. The first line gives the number of atoms $n$ in the cluster and the energy relative to the corresponding ground state $\Delta E\left(\mathrm{meV}\right)$, whereas, the second line represents the average degree of noncollinearity ($\theta$ in degree) and the corresponding total magnetic moment $\left({\mu }_B\right)$. The optimal collinear structures are not shown here rather we refer to Kabir et al. (Ref. 21).

Figure 2

(Color online) Optimal noncollinear magnetic ordering for ${\mathrm{Mn}}_{13}$, ${\mathrm{Mn}}_{15}$, and ${\mathrm{Mn}}_{19}$.

Figure 3

(Color online) The ground state and closely lying isomers of $\mathrm{As}@{\mathrm{Mn}}_n$ clusters. The first line indicates the nature of magnetic ordering [collinear (CL) or noncollinear (NCL)] and the relative energy to the corresponding ground state (meV) and the second line indicates the average $\theta$ (in degree) for NCL case and the total magnetic moment $\left({\mu }_B\right)$. For the collinear cases, orange (blue) refers the positive (negative) Mn moment. Yellow atom refers the As atom for all the structures.

Figure 4

(Color online) Plot of binding energy for optimal collinear and noncollinear configurations as a function of Mn atoms $\left(n\right)$ in pure ${\mathrm{Mn}}_n$ and $\mathrm{As}@{\mathrm{Mn}}_n$ clusters. Binding energy is defined as $\mathrm{BE}\left({\mathrm{Mn}}_n\right)=-[E\left({\mathrm{Mn}}_n\right)-nE\left(\mathrm{Mn}\right)]∕n$ for pure ${\mathrm{Mn}}_n$ clusters and $\mathrm{BE}\left(\mathrm{As}@{\mathrm{Mn}}_n\right)=-[E\left(\mathrm{As}@{\mathrm{Mn}}_n\right)-nE\left(\mathrm{Mn}\right)-E\left(\mathrm{As}\right)]∕(n+1)$ for $\mathrm{As}@{\mathrm{Mn}}_n$ clusters, where $E\left({\mathrm{Mn}}_n\right)$ and $E\left(\mathrm{As}@{\mathrm{Mn}}_n\right)$ are the total energies of pure ${\mathrm{Mn}}_n$ and $\mathrm{As}@{\mathrm{Mn}}_n$ clusters, respectively. The ◻ (∎) represents the optimal noncollinear (collinear) structures for pure ${\mathrm{Mn}}_n$ clusters, whereas, ▵ (▴) represents the optimal noncollinear (collinear) structures for $\mathrm{As}@{\mathrm{Mn}}_n$ clusters. Inset shows the total energy difference between the optimal collinear (CL) and noncollinear (NCL) configurations $\mathbf{(}\delta E=-[E_{\mathrm{CL}}\left(n\right)-E_{\mathrm{NCL}}\left(n\right)]\mathbf{)}$ as a function of $n$. The 엯 (●) represent ${\mathrm{Mn}}_n\left(\mathrm{As}@{\mathrm{Mn}}_n\right)$ clusters.

Figure 5

(Color online) Plot of magnetic moment per atom as a function of $n$ for pure ${\mathrm{Mn}}_n$ and $\mathrm{As}@{\mathrm{Mn}}_n$ clusters. Values only for the ground states have only been shown (see Tables for isomers). The SG experimental values for pure ${\mathrm{Mn}}_n$ clusters are shown with error bars.