Enhanced Spin-polarization via Partial Ge1-dimerization as the Driving Force of the 2$\times$2$\times$2 CDW in FeGe

A $2\times 2\times 2$ charge density wave (CDW) was recently observed deep inside the antiferromagnetic phase of a Kagome metal FeGe. A key question is whether the CDW in FeGe is driven by its electronic correlation and magnetism. Here, we address this problem using density functional theory and its combination with $U$ as well as dynamical mean-field theory. Our calculations show that large dimerization ($\sim 1.3$) of Ge1-sites along $c$-axis will enhance electronic correlation of the Fe-$3d$ orbitals and, as a result, it enhances the spin-polarization and saves more magnetic exchange energies. We find that the balance between magnetic energy saving and structural energy cost via partially dimerizing Ge1-sites in an enlarged superstructure, could induce a new local minimum in total energies. The response to the large partial Ge1-dimerization will induce additional small modulations ($<0.05$) of other sites in the Kagome and honeycomb layers, which further reduces the total energy and leads to a stable $2\times 2\times 2$ CDW ground state in FeGe. Our results are in good agreement with the existing experiments and reveal a novel CDW mechanism driven by the interplay of structure, electronic correlation and magnetism.