under pressure*

Following the recent report of superconductivity in the bilayer nickelate La₃Ni₂O₇ under pressure, in this talk we will present an analysis of the electronic and magnetic properties of the compound as a function of pressure using density functional theory-based methods. At the bare DFT level, the electronic structure of the ambient and high-pressure phase of La₃Ni₂O₇  is qualitatively similar. Upon including local correlation effects within DFT+U and allowing for magnetic ordering, we find a delicate interplay between pressure and electronic correlations. Within the pressure-correlations phase space, we identify a region (at U values consistent with constrained RPA calculations) characterized by a spin-state transition with increasing pressure, where the ground state of the material changes from a high-spin A-type antiferromagnet to a low-spin G-type antiferromagnet with contrasting electronic structures. While the energy landscape of this material is rich, with many competing magnetic states, we find a common thread to be that all of these different states are driven by the Ni d_x2-y2 orbitals. The electronic structure of pressurized La₃Ni₂O₇ will be compared with that of other members of the family of superconducting layered nickelates, focusing on the similarities and differences with cuprate physics.