Altermagnetism in MnF$_2$: Band Splitting and Its Physical Consequences

Abstract

MnF$_2$ is widely regarded as a candidate altermagnet, but the magnitude and implications of its altermagnetic band splitting remain debated. Using electronic-structure calculations, we construct minimal models that capture the magnetic and electronic properties of MnF$_2$. These models show that the parameters governing the chiral magnon splitting and the spin splitting of the electronic bands are relatively small. Moreover, the electronic system lies in the strong-coupling regime, where most magnetic properties are controlled by the ratio $t/U$ between the characteristic hopping amplitude $t$ and the large on-site Coulomb repulsion $U$. Consequently, all exchange interactions scale as $1/U$, so a small altermagnetic hopping $δt$ produces only a proportionally small exchange term. Upon doping, the altermagnetic contribution to the anomalous Hall effect is likewise suppressed, being smaller than the conventional (non-altermagnetic) contribution by a factor of order $δt/U$. In contrast, the behavior of the conductivity tensor $\hatσ(ω)$ at $\hbar ω\sim U$ differs qualitatively, because $δt$ enters the energies of interband optical transitions \emph{directly} rather than through the reduced ratio $δt/U$. This contribution strongly reshapes $\hatσ(ω)$, leading to a dramatic enhancement of the magneto-optical response.