Strongly correlated altermagnet CaCrO$_3$

Altermagnetism, a newly discovered magnetic phase, has spurred growing research activity. Studies from a perspective of dynamical electronic correlation still remain scarce. Employing density functional theory plus dynamical mean-field theory (DFT+DMFT) that incorporates dynamical electronic correlation, we demonstrate that CaCrO$_3$ is a strongly correlated altermagnet. Our DFT+DMFT calculations successfully reproduce the correlated metallic behavior of CaCrO$_3$ and quantitatively capture the incoherent state observed experimentally. We also identify that the altermagnetic CaCrO$_3$ is a Hund's metal. The incoherent state is attributed to Hund's coupling, which gives rise to a non-Fermi liquid behavior. Moreover, we find that altermagnetism can induce flat bands, and these incipient flat bands are further promoted by the strong renormalization from Hundness, which further drives a heavy-fermion behavior. Hence, we establish CaCrO$_3$ as a strongly correlated altermagnet and propose that Hund's metals provide an ideal platform for investigating the interplay between electronic correlation and altermagnetism. Our work will promote the study of strongly correlated altermagnetism physics.