General trends of superconducting pairing and magnetic correlations in the Ruddlesden-Popper nickelate m-layered superconductors La_m+1Ni_mO3_m+1

We report a comprehensive theoretical analysis of the Ruddlesden-Popper layered nickelates Lam+1NimO3m+1 (m = 1 to 6) under pressure. These materials have recently received significant attention due to the discovery of superconductivity in some nickelates under pressure. Our results suggest that, while these Ruddlesden- Popper layered nickelates display many similarities, they also show noticeable differences. One of the common features of Lam+1NimO3m+1 is that the electronic states near the Fermi level are mainly contributed by Ni 3d orbitals, slightly hybridized with O 2p orbitals. The Ni d3z2−r2 orbitals display bonding-antibonding, or bonding-antibonding-nonbonding, characteristic splittings, depending on the even or odd number of stacking layers m. In addition, the ratio of the in-plane interorbital hopping between d3z2−r2 and dx2−y2 orbitals and in-plane intraorbital hopping between dx2−y2 orbitals was found to be large in Lam+1NimO3m+1 (m = 1 to 6), and this ratio increases from m = 1 to m = 6, suggesting that the in-plane hybridization will increase as the layer number m increases. In contrast to the dominant s±-wave state driven by spin fluctuations in the bilayer La3Ni2O7 and trilayer La4Ni3O10, two nearly degenerate dx2−y2-wave and s±-wave leading states were obtained in the four-layer stacking La5Ni4O13 and five-layer stacking La6Ni5O16. The leading s±-wave state was recovered in the six-layer material La7Ni6O19 with slightly higher calculated pairing strength λ than that of the dx2−y2-wave state. All this evidence suggests that both s±-wave and dx2−y2-wave channels are strongly competing in the high-order niceklates based on our random-phase approximation calculations. In general, at the level of the random-phase approximation treatment, the superconducting transition temperature Tc decreases in stoichiometric bulk systems from the bilayer La3Ni2O7 to the six-layer La7Ni6O19, despite the m-dependent dominant pairing. Both in-plane and out-of-plane magnetic correlations are found to be quite complex.Within the in-plane direction, we obtained the peak of the magnetic susceptibility at q = (0.6π, 0.6π) for La5 Ni4O13 (m = 4) and La7Ni6O19 (m = 6) and at q = (0.7π, 0.7π) for La6Ni5O16 (m = 5). Along the out-of-plane direction, four layers are coupled as ↓ − ↑ − ↑ − ↓in La5Ni4O13, five layers are coupled as↑ − ↑ − ↓ − ↑ − ↑in La6Ni5O16, and six layers are coupled as↑ − ↓ − ↓ − ↑ − ↑ − ↓in La7Ni6O19.