Orbital altermagnetism on the kagome lattice and possible application to $A$V$_3$Sb$_5$

Abstract

Altermagnets, which encompass a broad landscape of materials, are compensated collinear magnetic phases in which the antiparallel magnetic moments are related by a crystalline rotation. Here, we argue that collinear altermagnetic-like states can also be realized in lattices with an odd number of sublattices, provided that the electronic interactions promote non-uniform magnetic moments. We demonstrate this idea for a kagome metal whose band filling places the Fermi level close to the van Hove singularity. Combining phenomenological and microscopic modeling, we show that the intertwined charge density-wave and loop-current instabilities of this model lead to a wide parameter range in which orbital ferromagnetic, antiferromagnetic, and altermagnetic phases emerge inside the charge-ordered state. In the presence of spin-orbit coupling, their electronic structures display the usual spin-split fingerprints associated with the three types of collinear magnetic order. We discuss the possible realization of orbital altermagnetic phases in the $A$V$_3$Sb$_5$ family of kagome metals.

Figures (3)

• Figure 1: (a) The kagome lattice vectors $\textbf{a}_{1,2,3}$ and the sublattices $1$ (red), $2$ (green), and $3$ (blue). (b) Brillouin zone with reciprocal vectors $\textbf{b}_{1,2,3}$ and the high-symmetry points $\Gamma$ (black), K (green), and M (red). The smaller hexagon is the Brillouin zone in the CDW phase; note that the M points of the larger BZ are folded onto the $\Gamma$ point.
• Figure 2: Bond dimerization and loop current patterns from the CDW-LC configurations associated with the ferromagnetic (FM) (a), $d$-wave altermagnetic (AM) (b), and antiferromagnetic (AFM) states (c).The direction of the magnetic moment of a plaquette is determined by its net current circulation. Different colors indicate different magnitudes of the moments. (d): Mean field phase diagram obtained from minimizing $\mathcal{F}(\textbf{W},\boldsymbol{\Phi})$ as a function of $T$ and $\gamma$. The phase boundaries are interpolated along discrete points (block dots) and the parameters used are listed in the SM.
• Figure 3: Electronic spectrum of the FM (a), AFM (b), and AM (c) phases shown in Fig. \ref{['fig:LC_states']} obtained by diagonalizing $\mathcal{H}_\text{tot}$. Red and blue denote spin-up and spin-down bands. The $\textbf{k}$-space points refer to the smaller BZ of the $2\times2$ unit cell (Fig. \ref{['fig:lattice']}(b)). The parameters used are listed in the SM. (d) Spin-splitting $\Delta E(\textbf{k})\equiv E_\uparrow - E_\downarrow$ of the highest-energy band of the AM phase plotted along the entire BZ.