Abstract
Using first-principles density-functional theory, we investigate the electronic structure of a class of low-dimensional quantum spin systems of general formula ${A}_{3}B{B}^{\ensuremath{'}}{\text{O}}_{6}$, which has drawn recent interest due to their intriguing magnetic properties. In our study, we focus on three compounds, ${\text{Sr}}_{3}{\text{NiPtO}}_{6}$, ${\text{Sr}}_{3}{\text{CuPtO}}_{6}$, and ${\text{Sr}}_{3}{\text{NiIrO}}_{6}$, formed from choices of $3d$ and $5d$ elements in $B$ and ${B}^{\ensuremath{'}}$ sites. Based on our first-principles calculations, we derive the magnetic interactions and the single-ion anisotropies, which define the underlying spin models for the three compounds. Our study forms the basis for future investigations.
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