Odd-parity magnetism by quantum geometry

Abstract

We uncover a geometric mechanism of odd-parity multipole magnetism driven by the quantum metric of Bloch electrons. By analyzing spin and odd-parity multipole susceptibilities in a multi-sublattice model, we demonstrate that the quantum metric directly controls the instability toward odd-parity magnetic multipole order over a wide range of parameters, which condenses under Hubbard interaction. The resulting state exhibits complex magnetic correlations, as a hallmark of quantum-geometric magnetism. These results establish a geometric design principle for odd-parity multipole magnets and provide a route toward the experimental verification of quantum-geometric magnetism.

Figures (6)

• Figure 1: Lattice structure of the bilayer Lieb lattice model. (a) Top view illustrating intra-layer hopping parameters with arrows. (b) Side view and the inter-layer hopping parameter.
• Figure 2: Band dispersion of the bilayer Lieb lattice model for $(t_1,t_2,t_3,t_4,t_{\rm p})=(1, 0.4, 0.15, 0.2, 0.1)$.
• Figure 3: Curvature of (a) spin susceptibility $\chi^{\rm{E}}_0(\bm{q})$ and (b) multipole susceptibility $\chi^{\rm{O}}_0(\bm{q})$ at ${\bm q}=0$, namely, $\partial_{q_x}^2\chi^{\rm{E/O}}_0(\bm{q})|_{{\bm q}=0}$. Blue lines represent the total curvature, while red and green lines show the contributions from band dispersion and quantum geometry, respectively.
• Figure 4: Bare susceptibility for (a) spin fluctuation $\chi^{\rm{E}}_0(\bm{q})$ and (c) multipole fluctuation $\chi^{\rm{O}}_0(\bm{q})$. We show (b) $\chi^{\rm{E}}_{0,\rm band}(\bm{q})$ and (d) $\chi^{\rm{O}}_{0,\rm band}(\bm{q})$ without quantum-geometric effects for comparison. The chemical potential is set to $\mu=0.7$.
• Figure 5: Bare spin susceptibility $\chi^{\rm{E}}_0(\bm{q})$ at (a) $\mu=0.4$ and (b) $\mu=0.8$. Bare multipole susceptibility $\chi^{\rm{O}}_0(\bm{q})$ at (c) $\mu = 0.4$ and (d) $\mu=0.8$.