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The infinite-layer structure nickelate Ba$_2$NiO$_2$(AgSe)$_2$ (BNOAS) with$d^8$ Ni ions and a peculiar susceptibility $\chi(T)$ is studied withcorrelated density functional methods. The overriding feature of thecalculations is violation of Hund's rule coupled with complete butunconventional spin-orbital polarization, leading to an unexpected low spin$^1B_1$, "off-diagonal singlet" (ODS) textured by an internal orbital structureof compensating $d_{x^2-y^2}^{\uparrow}$ and $d_{z^2}^{\downarrow}$ spins. Thisunconventional configuration has lower energy than conventional high-spin orlow-spin alternatives. An electronic transition is obtained at a critical Ni-Oseparation $d_c^{Ni-O}=$2.03 \AA, above which Ni becomes magnetic in squareplanar NiO$_2$ compounds. We propose scenarios for the signature of magneticreconstruction in $\chi(T)$ at $T_{m}$=130 K without any Curie-Weiss background(no moment) that invoke ordering of Ni $d^8$ moieties that are largely thisgeneralized Kondo singlet. The underlying physics of this system is modeled bya Kondo sieve model (2D Kondo necklace) of a "Kondo" $d_{z^2}$ spin on eachsite, coupled to a $d_{x^2-y^2}$ spin that is itself strongly coupled toneighboring like-spins within the layer. The observed magnetic order placesBNOAS below the quantum critical point of the Kondo sieve model, providing arealization of the previously unreported long-range ordered near-singlet weakantiferromagnetic phase. We propose electron doping experiments that woulddrive the system toward a $d^{9-\delta}$ configuration and possiblesuperconductivity with similarity to the recently reported Ba$_2$CuO$_{3.2}$that superconducts at 73 K.

Proposed ordering of textured spin singlets in a bulk infinite layer nickelate