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

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