\textbf{Atomic structure prediction of Zr-Co and Hf-Co nanoclusters using the evolutionary algorithm}

Nanostructures of Hf-Co and Zr-Co rare earth free magnetic material that exhibit a high room-temperature energy product. In our study, the evolutionary algorithm coupled with density functional (DFT) method is used to identify the global energy minimum atomic structure of Zr-Co and Hf-Co clusters. Using evolutionary crystal structure optimization algorithm, as implemented in USPEX, we studied the atomic structure, binding energies, magnetic properties, and anisotropy of Zr$_{\mathrm{x}}$Co$_{\mathrm{y}}$ and Hf$_{\mathrm{x}}$Co$_{\mathrm{y}}$ (x$=$1,2 and y$=$5,7,11) clusters. A set of metastable and global minimum atomic structures are identified. Several new lower energy configurations were identified for Zr$_{\mathrm{2}}$Co$_{\mathrm{11}}$, Zr$_{\mathrm{1}}$Co$_{\mathrm{5}}$, Zr$_{\mathrm{1}}$Co$_{\mathrm{7}}$, Hf$_{\mathrm{2}}$Co$_{\mathrm{11}}$, Hf$_{\mathrm{1}}$Co$_{\mathrm{5}}$ and Hf$_{\mathrm{1}}$Co$_{\mathrm{7\thinspace }}$clusters by our calculations. We discussed the magnetic interaction between the atoms of the clusters which is critical in finding the lowest energy structure. Our calculation show that Zr-Co and Hf-Co have ferromagnetic coupling and large magnetization. We will also discuss the magnetocrystalline anisotropy (MAE) variation in these clusters.