High spin, low spin or gapped spins: magnetism in the bilayer nickelates

Inspired by the recent discovery of high-temperature superconductivity in bilayer nickelates, we investigate the role of magnetism emerging from a hypothetical insulating $d^8$ parent state. We demonstrate that due to the interplay of superexchange and Hund's coupling, the system can be in a high-spin, low-spin or spin-gapped state. The low-spin state has singlets across the bilayer in the $d_{z^2}$ orbital, with charge carriers in the $d_{x^2-y^2}$ orbital. Thus, at low energy scales, it behaves as an effective one band system when hole doped. By contrast, the high-spin state is a more robust, spin-1 antiferromagnet. Using Hartree-Fock methods, we find that for fixed interaction strength and doping, high-spin magnetism remains more robust than the low-spin counterpart. Whether this implies that the high spin state provides a stronger pairing glue, or more strongly competes with superconductivity remains an open question. Our analysis therefore underscores the importance of identifying the spin state for understanding superconductivity in nickelates.