Interplay of Hybridization and Magnetization  in Structural Stability of 3d Transition-Metal-Doped Ag₁₃  and Au₁₃...

Using the first-principles density functional theory, we perform a systematic investigation of preference between compact and open structures in 3d transition-metal-doped Ag ₁₃ and Au₁₃ clusters, considering two extreme geometrical structural patterns of icosahedral (ICO) geometry and buckled-biplanar (BBP) geometry. Interestingly, while the pristine clusters are found to favor the relatively open, low-symmetry BBP geometry, doping with a 3d transition metal atom substantially modifies this preference. Our study provides important microscopic insight on this. The general optimized structural preference for ICO of the doped cluster is explained by the gain in the hybridization overcoming the loss in magnetization energy. A remarkable exception is the Au₁₂Mn cluster which tends to favor the open BBP structure similar to the pristine counterpart, but with enhanced stability. For the Au₁₂Mn cluster, the amplified crystal field splitting of $d$ states of the doped transition metal atom due to distorted geometry together with relative positioning of Au d and Mn d levels results in significantly strengthening of the hybridization effect for the open BBP geometry, which, in resonance with magnetization energy gain, stabilizes the BBP structure over the ICO structure.