Enhanced spin-polarization via partial Ge-dimerization as the driving force of the charge density wave in FeGe

A $2\ifmmode\times\else\texttimes\fi{}2\ifmmode\times\else\texttimes\fi{}2$ charge density wave (CDW) was recently observed deep inside the antiferromagnetic phase of a kagome metal FeGe, which significantly enhances its spin-polarization. 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 ($\ensuremath{\sim}1.3$ \AA{}) of Ge1 sites along the $c$ 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 ($<0.05$ \AA{}) of other sites in the kagome and honeycomb layers, which further reduces the total energy and leads to a stable $2\ifmmode\times\else\texttimes\fi{}2\ifmmode\times\else\texttimes\fi{}2$ CDW ground state in FeGe. Our results are in good agreement with the existing experiments and reveal a different unconventional CDW mechanism driven by primarily saving magnetic energies via the interplay of structure, electronic correlation, and magnetism.