Hierarchical structures and magnetism of Co clusters: a perspective from integration of deep learning and a hybrid differential evolution algorithm

, were discovered by the energetic analyses. Furthermore, the magnetic stability of the clusters was verified, and a competition between the coordination number and bond length in affecting the magnetic moment was observed. Our study provides high-accuracy and high-efficiency prediction of the optimal structures of clusters and sheds light on the growth trend of Co clusters containing tens of atoms, contributing to advancing the global optimization algorithms for effective determination of cluster structures.