Tuning the $S=1\mathrm{/}2$ square-lattice antiferromagnet Sr${}_2$Cu(Te${}_{1-x}$W${}_x$)O${}_6$ from N\'eel order to quantum disorder to columnar order

The spin-1/2 square-lattice Heisenberg model is predicted to have a quantum disordered ground state when magnetic frustration is maximized by competing nearest-neighbor $J_1$ and next-nearest-neighbor $J_2$ interactions ($J_2/J_1 \approx 0.5$)\mathrm{.}ThedoubleperovskitesSr$_2$CuTeO$_6$andSr$_2$CuWO$_6$ are isostructural spin-1/2 square-lattice antiferromagnets with N'eel ($J_1$ dominates) and columnar ($J_2$ dominates) magnetic order, respectively. Here we characterize the full isostructural solid solution series Sr${}_2$Cu(Te${}_{1-x}$W${}_x$)O${}_6$ ($0\le x\le 1$) tunable from N'eel order to quantum disorder to columnar order. A spin-liquid-like ground state was previously observed for the $x$ = 0.5 phase, but we show that the magnetic order is suppressed below 1.5 K in a much wider region of $x\approx$ 0.1-0.6. This coincides with significant $T$-linear terms in the low-temperature specific heat. However, density functional theory calculations predict most of the materials are not in the highly frustrated $J_2\mathrm{/}{J}_1\approx 0.5$ region square-lattice Heisenberg model. Thus, a combination of both magnetic frustration and quenched disorder is the likely origin of the spin-liquid-like state in $x$ = 0.5.