Magnetic phase diagram of a two-orbital model for bilayer nickelates with varying doping

Motivated by the recently discovered high-T_c bilayer nickelate superconductor La_3⁢Ni₂⁢O₇, we comprehensively research a bilayer 2×2×2 cluster for different electronic densities n 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 n. Based on the spin structure factor S(q), we have obtained a rich magnetic phase diagram in the plane defined by n and U/W, at fixed Hund coupling, where U is the Hubbard strength and W the bandwidth. We have observed numerous states, such as A-AFM, Stripes, G-AFM, and C-AFM. At half-filling, n=2 (two electrons per Ni site, corresponding to N=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 “half-empty” and “half-full” 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 n=1.5 (or N=12), density corresponding to La₃⁢Ni₂⁢O₇, we obtained the “Stripe 2” ground state (antiferromagnetic coupling in one in-plane direction, ferromagnetic coupling in the other, and antiferromagnetic coupling along the z axis) in the 2×2×2 cluster. In addition, we obtained a much stronger AFM coupling along the z axis than the magnetic coupling in the xy plane. The random-phase approximation calculations with varying n give very similar results as Lanczos, even though both techniques are based on quite different procedures. Additionally, a state with q/π=(0.6,0.6,1) close to the E-phase wavevector is found in our RPA calculations by slightly reducing the filling to n=1.25, possibly responsible for the E-phase SDW recently observe. Authors: Lin, Ling-Fang [University of Tennessee, Knoxville, TN (United States)] (ORCID:0000000300456537); Zhang, Yang [University of Tennessee, Knoxville, TN (United States)] (ORCID:0000000336235883); Kaushal, Nitin [University of British Columbia, Vancouver, BC (Canada)] (ORCID:0000000317239547); Alvarez, Gonzalo [Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)] (ORCID:0000000214968261); Maier, Thomas A. [Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)] (ORCID:0000000214249996). DOE Contract: AC05-00OR22725. Subjects: 36 MATERIALS SCIENCE; Hubbard model; Magnetism; Many-body techniques; Strongly correlated systems; Unconventional superconductors