DFT+U and Quantum Monte Carlo study of electronic and optical properties of AgNiO$_2$ and AgNi$_{1-x}$Co$_{x}$O$_2$ delafossite

The delafossite 2H-AgNiO$_2$ has received a great deal of attention because of its unique semi-metallic nature, which only AgNiO$_2$ exhibits among the $d^{10}$-based delafossites, and its antiferromagnetism in the NiO$_2$ coupled with a lattice distortion. In contrast, AgCoO$_2$ is insulating, and we predict that substitutional doping of Co on magnetic Ni sites will induce a metal-insulator transition. The electronic and magnetic structure of AgNiO$_2$ have been widely studied using Density Functional Theory (DFT), but earlier studies have not included corrections for strong on-site Coulomb interactions. Using Quantum Monte Carlo (QMC) simulations, we obtain accurate estimates for the electronic and magnetic properties of AgNiO$_2$. We also conclude that the rather strong electron correlations in AgNiO$_2$ are underestimated in DFT unless on-site Coulomb interactions are accounted for beyond typical mean-field DFT approaches. We also study various phases of AgNi$_x$Co$_{1-x}$O$_2$ and estimate their formation energies and gap openings under Co substitutional doping in order to investigate the electronic properties and phase stability of the intermetallics.