Altermagnetic Ground State in Distorted Kagome Metal CsCr$_3$Sb$_5$

The CsCr$_3$Sb$_5$ exhibits superconductivity in close proximity to a density-wave (DW) like ground state at ambient pressure\cite{Liu:2024aa}, however details of the DW is still elusive. Using first-principles density-functional calculations, we found its ground state to be a $4\times2$ altermagnetic spin-density-wave (SDW) at ambient pressure, with an averaged effective moment of $\sim$1.7$\mu_B$/Cr. The magnetic long range order is coupled to the lattice, generating 4$a_0$ structural modulation. Multiple competing SDW phases are present and energetically close, suggesting strong magnetic fluctuation at finite temperature. The electronic states near Fermi level are dominated by Cr-3$d$ orbitals, and the kagome flat bands are closer to the Fermi level than those in the $A$V$_3$Sb$_5$ family in paramagnetic state. When external pressure is applied, the energy differences between competing orders and structural modulations are suppressed. Yet, the magnetic fluctuation remains present and important even at high pressure because the high-symmetry kagome lattice is unstable in nonmagnetic phase up to 30 GPa. Our results suggest the crucial role of magnetism to stabilize the crystal structure, under both ambient and high pressure.