Emergence of correlation-driven altermagnetism in Hubbard model on geometrically frustrated square lattice

Abstract

We investigate the emergence of altermagnetism -- a collinear magnetic phase characterized by large non-relativistic spin splitting and zero net magnetization -- driven by electronic correlations on 3x3 geometrically frustrated square lattice. Using exact diagonalization of the simple and the extended Hubbard model, we analyze the interplay between on-site repulsion U , nearest-neighbor (NN) Coulomb interaction V and geometric frustration across various filling factors (N=8,9,10). Unlike traditional models that rely on single-particle anisotropy or specific sublattice geometries, our results demonstrate that altermagnetic signatures arise from many-body fluctuations in doped Mott insulators. We find that while geometric frustration suppresses altermagnetism at half-filling (N=9), carrier doping (hole (N=8) or electron (N=10)) stabilizes robust, rotationally symmetric altermagnetic correlations. Furthermore, we identify a critical threshold for the NN interaction V at intermediate coupling (U=4) where the altermagnetic state in the electron-doped sector undergoes a first-order-like transition, whereas strong coupling (U=10) stabilizes well-formed local moments and preserves the anisotropic spin texture. This work establishes a fluctuation-mediated route to altermagnetism on symmetric geometrically frustrated lattices and identify carrier concentration and the NN Coulomb interaction as a critical tunable parameter for controlling magnetic anisotropy in strongly correlated systems.

Figures (13)

• Figure 1: Schematic representation of the frustrated square lattice with periodic boundary conditions. The red dashed lines mark the periodic wrapping in both spatial directions.
• Figure 2: Average altermagnetic spin-response measure $\langle\Delta_{\mathrm{spin}}\rangle$ as a function of on-site interaction $U$ for the simple Hubbard model on $3\times 3$ frustrated square lattice. Results are shown for half-filling ($N=9$, $S=\frac{1}{2}$) and for one-hole ($N=8$, $S=0$) and one-electron ($N=10$, $S=0$) doping.
• Figure 3: Average local moment $\bar{m}$ as a function of on-site interaction $U$ for the simple Hubbard model on $3\times 3$ frustrated square lattice. Results are shown for half-filling ($N=9$, $S=\frac{1}{2}$) and for one-hole ($N=8$, $S=0$) and one-electron ($N=10$, $S=0$) doping.
• Figure 4: Real-space heatmaps of the altermagnetic correlation matrix element $\Omega_{5j}$ for the central reference site (site 5) on the $3\times 3$ frustrated square lattice at $U=2,6,12$. Results are shown for $N=8$ (top-row), $N=9$ (middle-row) and $N=10$ (bottom-row). Doped sectors exhibit pronounced, interaction-enhanced anisotropic correlation patterns, whereas the half-filled case shows strongly suppressed and nearly uniform correlations due to geometric frustration.
• Figure 5: Anisotropy parameter $\mathcal{A}$ as a function of on-site interaction $U$ for the simple Hubbard model ($V=0$) at fillings $N=8,9,10$.