Correlation-Driven Orbital Order Realizes 2D Metallic Altermagnetism

Abstract

Two-dimensional metallic altermagnets are rare, and no correlated 2D material has been established to host large nonrelativistic spin splitting. Here we show that spontaneous orbital order, driven by electronic correlations and Fermi surface nesting, provides a general microscopic route to two-dimensional metallic altermagnetism. Antiferro-orbital ordering between the d$_{xz}$ and d$_{yz}$ orbitals breaks the equivalence of magnetic sublattices with opposite spins and generates a symmetry-enforced altermagnetic spin texture. As a concrete realization, we identify monolayer YbMn$_2$Ge$_2$ as a stable correlated metallic altermagnet exhibiting giant nonrelativistic spin splitting of order 1 eV. The resulting phase supports an exceptionally large and gate-tunable transverse spin conductivity. These results establish correlation-driven orbital order as a robust and general mechanism for designing correlated altermagnets with large spin splitting.

Figures (5)

• Figure 1: Spontaneous altermagnetic spin splitting induced by antiferro-orbital ordering (AFO) in a collinear antiferromagnet (AFM). (a) In the absence of orbital order, sublattice symmetry enforces Kramers-degenerate bands for both spin sectors. (b) Antiferro-orbital order breaks the equivalence of magnetic sublattices, leading to orbital-spin locking and a momentum-dependent spin splitting characteristic of altermagnetism.
• Figure 2: Monolayer YbMn$_2$Ge$_2$ as a correlated two-dimensional platform for altermagnetism. (a) Bulk crystal structure showing stacking of quadrupole layers (QLs) along the $z$ direction, with adjacent layers related by inversion symmetry. (b) Exfoliated two-dimensional unit cell consisting of a single QL, with four Mn atoms forming an $xy$-plane antiferromagnet (red and blue denote opposite spins). (c) Phonon spectrum without imaginary modes, confirming dynamical stability of the AFM phase. (d) Top view of the monolayer structure. The system preserves $C_{4z}\mathcal{T}$ symmetry and diagonal mirror-time-reversal symmetries, which connect the magnetic sublattices. (e) Electronic band structure showing large nonrelativistic spin splitting along the $\mathrm{X}\Gamma\mathrm{Y}$ path, exceeding $1$ eV near the Fermi energy. (f) Fermi contours exhibiting a characteristic $d$-wave-like spin-split structure, with red (blue) indicating up-spin (down-spin) polarization.
• Figure 3: Correlation-driven orbital order induces altermagnetism in monolayer YbMn$_2$Ge$_2$. (a) Orbital-projected band structure along the X–$\Gamma$–Y path, showing sublattice resolved d$_{xz}$ and d$_{yz}$ orbital polarization from DFT+$U$ calculations. (b) Orbital-ordered configuration of the two Mn sublattices: correlation-driven antiferro-orbital order breaks their equivalence, with the spin-up (spin-down) sublattice predominantly occupying the d$_{xz}$ (d$_{yz}$) orbital, producing anisotropic charge distributions in orthogonal planes. (c) Fermi contours exhibiting $(\pi,\pi)$ nesting, with dominant d$_{xz}$ (top) and d$_{yz}$ (bottom) orbital character. (d) Orbital pseudospin susceptibility showing a pronounced peak at $(\pi,\pi)$, indicating an instability toward antiferro-orbital order. (e) Spin and orbital structure factors from semiclassical Monte Carlo simulations of the two-orbital Hubbard model ($U \simeq 1$ eV, $J_H = U/4$, $U' = U - 2J_H$), demonstrating robust $(\pi,\pi)$ antiferromagnetic and antiferro-orbital order. The inset density-of-states plot confirms that the resulting orbital-ordered altermagnetic phase remains metallic.
• Figure 4: Giant and anisotropic transverse spin response in monolayer YbMn$_2$Ge$_2$. (a) Schematic device geometry with an in-plane electric field applied at an angle $\phi$ to the $x$ axis. The orbital-order-driven altermagnetic band structure generates a transverse spin current perpendicular to the applied field. (b) Fermi-surface contribution to the transverse spin conductivity shown as a polar color map. The radial axis denotes chemical potential $\mu$, and the polar angle represents the direction of the applied electric field. The response has a characteristic $d$-wave angular dependence. (c) Angular dependence of the transverse spin conductivity at $\mu = -1$ eV, showing the same $d$-wave symmetry. The Fermi-sea contribution is negligible compared to the Fermi-surface contribution. (d) Chemical-potential dependence of the transverse spin conductivity at $\phi = 45^\circ$. The Fermi-surface contribution changes sign near the Fermi energy.
• Figure 5: Minimal model for orbital-ordered altermagnetism in monolayer YMG. (a) Effective antiferromagnetic lattice with d$_{xz}$ and d$_{yz}$ orbitals on each site. Same-spin sites form two intertwined square lattices, indicated by dashed lines. (b) Downfolded AFM band dispersion in the low-energy basis $\{\ket{1,xz,\uparrow}, \ket{1,yz,\uparrow}, \ket{2,xz,\downarrow}, \ket{2,yz,\downarrow}\}$. (c) Schematic orbital-ordered configuration. (d) Downfolded band dispersion of the altermagnetic state in the same basis, with spin-up and spin-down bands shown in red and blue, respectively.