Magnetic fluctuations driven by quantum geometry

Using quantum distance, magnetic susceptibility in the non-interacting limit can be rigorously split into two contributions: one arising solely from band dispersion, while the other stems from quantum geometric contributions. In this Letter, 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 multi-band systems, and provide a unique and quantitative framework to disentangle band-structure and wavefunction-geometry effects that have often been discussed collectively as multi-orbital effects.