Magnetic fluctuations driven by quantum geometry

TL;DR

This paper demonstrates that quantum geometric contributions significantly influence magnetic fluctuations in materials, providing a new framework to distinguish between band dispersion and wavefunction geometry effects.

Contribution

It introduces a rigorous decomposition of magnetic susceptibility into dispersion and geometric parts, applied to real materials, revealing the dominant role of quantum geometry in magnetic fluctuations.

Findings

Quantum geometry dominates magnetic fluctuations in LaFeAsO.

Quantum geometry influences ferromagnetic and antiferromagnetic stability.

Framework disentangles band-structure and wavefunction effects.

Abstract

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.