Magnetic fluctuations driven by quantum geometry

Using quantum distance, magnetic susceptibility in the noninteracting limit can be rigorously split into two contributions: one arises solely from band dispersion while the other stems from quantum geometric contributions. In this paper, we apply this decomposition to two materials, LaFeAsO and Pb$_9$Cu(PO$_4$)$_6$O, and demonstrate that their dominant magnetic fluctuations originate from the geometric contribution. In LaFeAsO, stripe-type antiferromagnetic fluctuations arise primarily from quantum geometry, while in Pb$_9$Cu(PO$_4$)$_6$O the geometric term suppresses antiferromagnetic fluctuations and stabilizes ferromagnetic fluctuations. Our findings highlight the essential role of quantum geometry in governing magnetic fluctuations in multiband systems, and provide a unique and quantitative framework to disentangle band-structure and wave-function-geometry effects that have often been discussed collectively as multiorbital effects.