Hund electronic correlation in La${}_3$Ni${}_2$O${}_7$ under high pressure

By means of density functional theory plus dynamical mean-field theory (DFT+DMFT), we investigate the correlated electronic structures of La${}_3$Ni${}_2$O${}_7$ under high pressure. Our calculations show that La${}_3$Ni${}_2$O${}_7$ is a multi-orbital Hund metal. Both the 3$d_{z^2}$ and 3$d_{x^2-y^2}$ orbitals of Ni are close to be half filled and contribute the bands across the Fermi level. Band renormalization and orbital selective electronic correlation are observed. Through imaginary-time correlation functions, the discovery of high-spin configuration, spin-frozen phase, and spin-orbital separation shows that the system is in a frozen moment phase at high temperatures above 290 K and is a Fermi liquid at low temperatures, which is further comfirmed by the calculated spin, orbital, and charge susceptibilities under high temperatures. Our study uncovers Hundness in La${}_3$Ni${}_2$O${}_7$ under high pressure.