Altermagnetic polarons: the fate of alter magnetic band splittings at strong coupling

TL;DR

The paper tackles how altermagnetic band splittings behave in strongly correlated Mott altermagnets, where conventional band pictures fail. It combines self-consistent Born approximation (SCBA) and variational cluster approximation (VCA) to study hole motion and spin-polaron formation in checkerboard and $t_{2g}$-orbital models. A key finding is that spin-dependent spectral-weight transfer dominates, producing altermagnetic polarons with spin-momentum locking rather than simply spin-split bands, with one spin projection becoming incoherent in many regimes. The results have implications for ARPES measurements and suggest rich interplay between altermagnetism, polaron dynamics, and potential superconducting tendencies in correlated altermagnets.

Abstract

While a spin-dependent band splitting is one of the characteristic features of altermagnets, the conventional band picture itself breaks down in the many altermagnets that are correlated Mott materials. We employ two numerical many-body methods, the self-consistent Born approximation and variational cluster approach, to explore this strongly correlated regime and investigate hole motion in Mott altermagnets. Our results reveal that spin-dependent spectral-weight transfer is the dominant signature of Mott altermagnetism. This pronounced spin-momentum locking of the quasiparticle spectral weight arises from the formation of altermagnetic polarons, whose dynamics are governed by the interplay between free hole motion and the coupling of the hole to magnon excitations in the altermagnet. We demonstrate this effect by calculating ARPES spectra for three canonical altermagnetic systems: the checkerboard $J$-$J'$ model, a variant describing the transition-metal--ion sites of the inverse Lieb lattice, and the Kugel-Khomskii spin-orbital altermagnet based on cubic vanadates RVO$_3$ (R=La, Pr, Nd, Y).

Figures (8)

• Figure 1: (a) Cartoon for hole propagation in the (generalized) checkerboard model: The hole has moved from its original position (dashed empty circle) to the current one (filled circle) via two NN hoppings (black dashed horizontal and vertical line) and two NNN hopping processes (blue dashed diagonal lines). The NN processes have disturbed the AF background and thus created magnons, the NNN hopping left it intact. Adding (different) couplings along the dotted lines as well descibes the transition-metal sublattice of the inverse Lieb lattice (ILL) 2025arXiv250804839C. (b) Cartoon for the spin-orbital model based on LaVO$_3$. The $xy$ orbital is half filled and superexchange leads to AF order, indicated by red and blue color. Additionally, the $xz$/$yz$ orbitals share one electron, which can only hop along one direction (indicated by the fat arrows) and whose spin is aligned to the $xy$ spin on the same site. Superexchange processes due to $xz$/$yz$ hopping induce Ising spin coupling.
• Figure 2: One-particle spectral density obtained with SCBA for the checkerboard model with $J=0.4\;t$, NNN $J'=0.15\;t$ and $t'=-0.5\;t$ and (a) spin up, (b) spin down. Momenta are here given in terms of a one-site unit cell; peaks were broadened with a Lorentzian of width $0.02\;t$ for plotting. For comparison to the usual square-lattice antiferromagnet, momenta $\mathbf{q}$ here correspond to a one-site unit cell. They can be obtained from momenta $\mathbf{k}$ of the two-site unit cell as $q_{x/y} = (k_{a} \pm k _{b})/2$. The lines in the floor correspond to the mean-field (MF) bands for a Hubbard model with $t=1$, $t'=-0.5\;t$, and $U=10t$. Panel (c) shows the spectral density for spin up (blue) and down (red) at momentum $\mathbf{q}=(\pi/2,\pi/2)$ and compares the MF approximation (plotted upwards) to the SCBA (plotted downwards).
• Figure 3: QP weights SM at momentum $(\tfrac{\pi}{2},\tfrac{\pi}{2})$ for (a) $J'=0.15\;t$ and variable $t'$ and (b) $t'=0$ and variable $J'$.
• Figure 4: One-particle spectral density obtained with SCBA for spin down on the generalized checkerboard (representing transition-metal ions on the ILL) with $J = 10\;\textrm{meV}$, $J' = 2.5\;\textrm{meV} \approx J'_b = 3\;\textrm{meV}$, and $|S|=\tfrac{5}{2}$. In (a), NN hopping $t=300\;\textrm{meV}$, $t' = 150\;\textrm{meV} = \tfrac{t}{2}$, and $t'_b=10\;\textrm{meV}$ describe an $xy$ orbital. (b) is for the $3z^2-r^2$ orbital with $t=t'=60\;\textrm{meV}$ and $t'_b=180\;\textrm{meV} = 3t$2025arXiv250621661G. Lines on the floor correspond to the large-$U$ limit of MF, where the hole only hops on the spin-down sublattice.
• Figure 5: Occupied states obtained with VCA for the three-orbital $t_{2g}$ model with $t=1$, $U=14 t$, $J_H=2 t$, $\Delta=-0.5\;t$ in the AF and AO state illustrated in Fig. \ref{['fig:cartoon_LaVO3']}. (a) gives the energy- and momentum dependent spectrum for spin up and (b) for spin down. Weight in red comes from the $xy$ orbital, while the combined $xz$ and $yz$ weight is shown in blue. (c) and (d) show the weight of up. resp. down states integrated over the energy range $-1.2 t< \omega < -0.5 t$, all orbitals.