Superexchange interactions between spin-orbit-coupled $j\text{\hspace{0.17em}⁣}\approx \text{\hspace{0.17em}⁣}1\mathrm{/}2$ ions in oxides with face-sharing ligand octahedra

Using ab initio wave-function-based calculations, we provide valuable insights with regard to the magnetic exchange in 5$d$ and 4$d$ oxides with face-sharing ligand octahedra, BaIrO${}_3$ and BaRhO${}_3$. Surprisingly strong antiferromagnetic Heisenberg interactions as large as 400 meV are computed for idealized iridate structures with 90${}^{\circ }$ Ir-O-Ir bond angles and in the range of 125 meV for angles of 80${}^{\circ }$ as measured experimentally in BaIrO${}_3$. These estimates exceed the values derived so far for corner-sharing and edge-sharing systems and motivate more detailed experimental investigations of quantum magnets with extended 5$d$/4$d$ orbitals and networks of face-sharing ligand cages. The strong electron-lattice couplings evidenced by our calculations suggest rich phase diagrams as function of strain and pressure, a research direction with much potential for materials of this type.