Magnetism in AV_{3}Sb_{5} (A=Cs, Rb, and K): Origin and Consequences for the Strongly Correlated Phases.

The V-based kagome systems AV_{3}Sb_{5} (A=Cs, Rb, and K) are unique by virtue of the intricate interplay of nontrivial electronic structure, topology, and intriguing fermiology, rendering them to be a playground of many mutually dependent exotic phases like charge-order and superconductivity. Despite numerous recent studies, the interconnection of magnetism and other complex collective phenomena in these systems has yet not arrived at any conclusion. Using first-principles tools, we demonstrate that their electronic structures, complex fermiologies and phonon dispersions are strongly influenced by the interplay of dynamic electron correlations, nontrivial spin-polarization and spin-orbit coupling. An investigation of the first-principles-derived intersite magnetic exchanges with the complementary analysis of q dependence of the electronic response functions and the electron-phonon coupling indicate that the system conforms as a frustrated spin cluster, where the occurrence of the charge-order phase is intimately related to the mechanism of electron-phonon coupling, rather than the Fermi-surface nesting.