Study of electronic correlations in Cr-based Kagome metals via slave-spin mean field

Kagome metals are materials characterized by a lattice made of corner-sharing triangles that have sparked interest in recent years due to the plethora of physical phenomena that they host, encompassing topology, electronic correlations, superconductivity, and magnetism. Among the members of the family, recent studies have suggested some Cr-based compounds as particularly strongly correlated systems, with possible magnetic phases due to the magnetic moments of Cr. This work focuses on the ab initio study of electronic correlations on two Cr-based compounds of this family: CsCr6Sb6 and CsCr3Sb5, exploiting the formalism of density functional theory and of slave-spin mean field theory to introduce many-body effects (DFT+SSMF). CsCr6Sb6 recently drew the attention of researchers for two reasons: a significantly flat band close to the Fermi level, not reproduced by DFT, and the experimental observation of Kondo effect in it, opening the way for the combination of Kagome physics with heavy-fermion physics. CsCr3Sb5, instead, is known for its rich phase diagram, hosting a competition between density wave phases and superconductivity. In addition to this, recent DFT studies have revealed that it also shows an altermagnetic ground state. In this work we first study the Fermi liquid behaviour of CsCr6Sb6 and how electronic correlations, in the framework of DFT+SSMF, renormalize its energy bands. With these results we evaluate a theoretical value of the Sommerfeld coefficient: $\gamma_{th}=63.39 mJ mol^{-1}K^{-2}$, which is in good agreement with the experimental one: $\gamma_{exp} = 75mJ mol^{-1}K^{-2}$. For CsCr3Sb5, instead, we study how electronic correlations stabilize the altermagnetic ground state, obtaining a significant increase in the magnetic moments of the Cr atoms with respect to DFT. Finally we simulate hole doping on both compounds, exploring how it affects the degree of correlation of CsCr6Sb6 and the magnetic properties of CsCr3Sb5.