Abstract
Motivated by the recently discovered high-ππ bilayer nickelate superconductor La3β’Ni2β’O7, we comprehensively research a bilayer 2Γ2Γ2 cluster for different electronic densities π by using the Lanczos method. We also employ the random-phase approximation to quantify the first magnetic instability with increasing Hubbard coupling strength, also varying π. Based on the spin structure factor πβ‘(π), we have obtained a rich magnetic phase diagram in the plane defined by π and π/π, at fixed Hund coupling, where π is the Hubbard strength and π the bandwidth. We have observed numerous states, such as A-AFM, Stripes, G-AFM, and C-AFM. At half-filling, π=2 (two electrons per Ni site, corresponding to π=16 electrons), the canonical superexchange interaction leads to a robust G-AFM state (π,π,π) with antiferromagnetic couplings both in-plane and between layers. By increasing or decreasing electronic densities, ferromagnetic tendencies emerge from the βhalf-emptyβ and βhalf-fullβ mechanisms, leading to many other interesting magnetic tendencies. In addition, the spin-spin correlations become weaker both in the hole or electron doping regions compared with half-filling. At π=1.5 (or π=12), density corresponding to La3β’Ni2β’O7, we obtained the βStripe 2β ground state (antiferromagnetic coupling in one in-plane direction, ferromagnetic coupling in the other, and antiferromagnetic coupling along the π§ axis) in the 2Γ2Γ2 cluster. In addition, we obtained a much stronger AFM coupling along the π§ axis than the magnetic coupling in the π₯β’π¦ plane. The random-phase approximation calculations with varying π give very similar results as Lanczos, even though both techniques are based on quite different procedures. Additionally, a state with π/π=(0.6,0.6,1) close to the E-phase wavevector is found in our RPA calculations by slightly reducing the filling to π=1.25, possibly responsible for the E-phase SDW recently observed in experiments. Our predictions can be tested by chemically doping La3β’Ni2β’O7.