Altermagnetism in an interacting model of Kagome materials

Abstract

The Hubbard model on the Kagome lattice is a widely used interacting model for describing the electronic properties of various transition metal-based Kagome materials. We find altermagnetism driven by Coulomb interaction in the Kagome Hubbard model at Dirac filling with no spin-orbit coupling nor explicit spatial symmetry breaking present. We show how this insulating altermagnet is relevant to other lattices with larger unit cells such as the Lieb-Kagome lattice. The ALM found displays a characteristic magnon splitting which can be detected in inelastic neutron scattering experiments on interacting Kagome materials.

Figures (4)

• Figure 1: Altermagnetism in the Kagome Hubbard model at Dirac filling. The $t'-U$ phase diagram at $n=2/3$ and fixed temperature $T=0.02t$ obtained from HF is shown. A paramagnetic metal (PM), an altermagnetic insulator (ALMI), a pinned metal droplet insulating (PMDI), and a possible quantum spin liquid (QSL) phase arise. In the white regions stable converged phases are not found. HF calculations on $N\times N$ cell lattices with $N=12 - 18$ and periodic boundary conditions have been used.
• Figure 2: a) Charge and spin densities in the ALM state of the Kagome Hubbard model at $n=2/3$, $U=8$ and $t'=0.7t$. Yellow (purple) sites indicate higher (lower) charge densities and arrows show mean spin vector directions; the unit cell is enclosed by blue dashed lines. b) Spin character of energy eigenvalues in the topmost band. Red and blue regions correspond to spin up and down eigenstates, respectively; the dashed white lines mark the edges of the first Brillouin Zone. c) Energy bands of the Kagome ALM along a high-symmetry path in momentum space. Again, red and blue lines indicate the spin up and down character of the bands at the corresponding momentum. The chemical potential is shown with a dashed green line, and dashed gray lines show the (spin degenerate) tight-binding band structure of the Kagome lattice.
• Figure 3: Left panels: momentum dependence of the eigenvalues of the non-interacting susceptibility matrix in the orbital basis $\chi_{ab}({\bf q},0)$ at $n=2/3$ and $T=0.01t$, for $t'$ indicated in each figure. Right panel: evolution of the ALM and AFM order parameters with temperature, for the HF ground state at $U=8t$, $t'=0.7t$, $n=2/3$ in a $12\times12$ lattice. The corresponding charge-spin configurations of the unit cell are sketched in each temperature interval.
• Figure 4: Imaginary part of the physical spin susceptibility $(\chi_{+-}+\chi_{-+})({\bf q},\omega)/2$ of the Kagome altermagnet ($U=8t$, $t'=0.7t$, $n=2/3$, $T=0.01t$) along a momentum path connecting high-symmetry points.