Magnetic interactions in the $S=1\mathrm{/}2$ square-lattice antiferromagnets Ba${}_2$CuTeO${}_6$ and Ba${}_2$CuWO${}_6$: parent phases of a possible spin liquid

The isostructural double perovskites Ba${}_2$CuTeO${}_6$ and Ba${}_2$CuWO${}_6$ are shown by theory and experiment to be frustrated square-lattice antiferromagnets with opposing dominant magnetic interactions. This is driven by differences in orbital hybridisation of Te${}^{6+}$ and W${}^{6+}$. A spin-liquid-like ground state is predicted for Ba${}_2$Cu(Te${}_{1-x}$W${}_x$)O${}_6$ solid solution similar to recent observations in Sr${}_2$Cu(Te${}_{1-x}$W${}_x$)O${}_6$.