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Using a combination of density functional theory calculations with an on-siteCoulomb repulsion term (DFT+$U$) and Boltzmann transport theory within theconstant relaxation time approximation, we explore the effect of oxygenvacancies on the electronic, magnetic, and thermoelectric properties inultrathin (LaNiO$_{3-\delta}$)$_1$/(LaAlO$_{3}$)$_1$(001) superlattices (SLs).For the pristine SL, an antiferromagnetic charge-disproportionated (AFM-CD)($d^{8}${$\underline L$}$^{2}$)$_{S=0}$($d^{8}$)$_{S=1}$ phase is stabilized,irrespective of strain. At $\delta$ = 0.125 and 0.25, the localization ofelectrons released from the oxygen defects in the NiO$_{2}$ plane triggers acharge-disproportionation, leading to a ferrimagnetic insulator both at$a_{\mathrm{STO}}$ (tensile strain) and $a_{\mathrm{LSAO}}$ (compressivestrain). At $\delta$ = 0.5, an insulating phase emerges with alternatingstripes of Ni$^{2+}$ (high-spin) and Ni$^{2+}$ (low-spin) and oxygen vacanciesordered along the [110] direction (S-AFM), irrespective of strain. This resultsin a robust $n$-type in-plane power factor of 24~$\mu$W/K$^2$ cm at$a_{\mathrm{STO}}$ and 14~$\mu$W/K$^2$ cm at $a_{\mathrm{LSAO}}$ at 300~K(assuming relaxation time $\tau = 4$~fs). Additionally, the pristine and$\delta$ = 0.5 SLs are shown to be dynamically stable. This demonstrates thefine tunability of electronic, magnetic, and thermoelectric properties ofultrathin nickelate superlattices by oxygen vacancies.

Tuning of the carrier localization, magnetic and thermoelectric  properties in ultrathin (LaNiO$_{3-\delta}$)$_1$/(LaAlO$_{3}$)$_1$(001)  superlattices by oxygen vacancies