Effect of confinement on spin polarization and magnetism of Co$_{2}$Si nanoclusters*

Size-modified electronic structure and surface effects can lead to unusual magnetic ordering, modified ordering temperatures, and different spin structures in nanoclusters as compared to the corresponding bulk alloys. Thus nanoclusters can be used as building blocks to create new complex magnetic nanostructures for potential applications.\footnote{B. Balamurugan, D.J. Sellmyer et al. \textit{Sci. Rep}. \textbf{4}, 6265 (2014); \textit{Adv. Mater.} \textbf{25}, 6089, (2013); \textit{Appl. Phys. Lett.} \textbf{101}, 122407 (2012).} We show room-temperature ferromagnetic ordering in Co$_{2}$Si nanoclusters with relatively large magnetic moments (0.49 $\mu_{\mathrm{B}}$/Co at 300 K and 0.70 $\mu_{\mathrm{B}}$/Co at 10 K) and magnetocrystalline anisotropy ($K_{1} \approx $ 4 Mergs/cm$^{3}$ at 10 K), as contrasted to very weak itinerant magnetism in bulk Co$_{2}$Si (0.001 $\mu_{\mathrm{B}}$/Co at 300 K and 0.072 $\mu_{\mathrm{B}}$/Co at 10 K). The DFT and analytical model calculations explain the size-dependence of the observed magnetic moments on the size of Co$_{2}$Si nanoclusters, which vary from 0.6 to 30 nm, by a surface-induced spin polarization of nanoclusters.