Magnetic fluctuations driven by quantum geometry

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.

Figures (5)

• Figure 1: Band structure (left) and Fermi surface (right) of LaFeAsO. Colors show the orbital weights of Fe $3d_{xy}$ (red), $3d_{yz}$ (green), $3d_{z^2}$ (blue), $3d_{xz}$ (navy) and $3d_{x^2-y^2}$ (yellow).
• Figure 2: (a) The static spin susceptibility, (b) the band term and (c) the geometric term for LaFeAsO at $T = 116\mathrm{\;K}$.
• Figure 3: Band structure (left) and Fermi surface (right) of Pb9Cu(PO4)6O. The Fermi surface is displayed for the chemical potential, $\mu = 10 \mathrm{\;meV}$. Orange (blue) indicates high (low) Fermi velocity as determined by the FPLO calculation.
• Figure 4: Static irreducible susceptibility of electron doped Pb9Cu(PO4)6O ($\mu = 10\mathrm{\;meV}$) at $T = 116\mathrm{\;K}$. Total susceptibility $\chi^0$ (left), the band term $\chi^0_\mathrm{band}$ (middle) and the geometric term $\chi^0_\mathrm{geom}$ (right) are plotted. Cuts through $q_z = 0$ (top), $q_z = \pi/2c$ (middle) and $q_z = \pi/c$ (bottom) are shown.
• Figure 5: Static spin susceptibility $\chi^\mathrm{s}(\bm{q})$ calculated within RPA. (a) LaFeAsO for onsite Coulomb interaction parameters $U = 0.8\mathrm{\;eV}$, $V = U/2$, and $J = J' = U/4$ at $T = 116\mathrm{\;K}$, showing a pronounced peak at $\bm{Q} = (\frac{1}{2}, 0)$. (b-d) Pb9Cu(PO4)6O ($\mu = 10\mathrm{\;meV}$) for $U = 100\mathrm{\;meV}$, $V = U/2$, and $J = J' = U/4$ at $T = 116\mathrm{\;K}$, showing $\chi^\mathrm{s}(\bm{q})$ for $q_z =0$, $\pi/2c$, and $\pi/c$, respectively. A ferromagnetic peak at $\bm{Q} = (0, 0, 0)$ is enhanced, while antiferromagnetic fluctuations are suppressed.