Electronic structure and magnetic properties of higher-order layered nickelates: La$_{n+1}$Ni$_{n}$O$_{2n+2}$ ($n=4-6$)

The recent discovery of superconductivity in Sr-doped NdNiO$_2$, with a critical temperature of $10-15$ K suggests the possibility of a new family of nickel-based high-temperature superconductors (HTS). NdNiO$_{2}$ is the $n=infty$ member of a larger series of layered nickelates with chemical formula R$_{n+1}$Ni$_{n}$O$_{2n+2}$ (R $=$ La, Nd, Pr; $n = 2, 3, dots, infty$). The $n=3$ member has been experimentally and theoretically shown to be cuprate-like and a promising HTS candidate if electron doping could be achieved. The higher-order $n=4,5,$ and $6$ members of the series fall directly into the cuprate dome area of filling without the need of doping, thus making them promising materials to study, but have not been synthesized yet. Here, we perform first-principles calculations on hypothetical $n=4,5,$ and $6$ structures to study their electronic and magnetic properties and compare them with the known $n=infty$ and $n=3$ materials. From our calculations, we find that the cuprate-like character of layered nickelates increases from the $n=infty$ to the $n=3$ members as the charge transfer energy and the self-doping effect due to R-$d$ bands around the Fermi level gradually decrease.