Evidence of frustration in the S$=$1/2 square-lattice antiferromagnet Sr$_{\mathrm{2}}$CuTe$_{\mathrm{1-}}_{x}$W$_{x}$O$_{\mathrm{6}}$

The S$=$1/2 Heisenberg frustrated square-lattice model, or J$_{\mathrm{1}}$-J$_{\mathrm{2}}$ model, describes systems with competing antiferromagnetic interactions. Magnetic order is N\'{e}el type when J$_{\mathrm{1}}\gg $ J$_{\mathrm{2}}$ and columnar when J$_{\mathrm{2}}\gg $ J$_{\mathrm{1}}$. The nature of the ground state in the highly frustrated J$_{\mathrm{2}}$/J$_{\mathrm{1}}\approx $ 0.5 region is under debate with proposals including different valence bond solids and spin liquids. We report experimental evidence of frustration in a tunable J$_{\mathrm{1}}$-J$_{\mathrm{2}}$ model system. Recent neutron scattering experiments by us [1] and ref. [2] have shown the Cu$^{\mathrm{2+}}$ square-lattice double perovskites Sr$_{\mathrm{2}}$CuTeO$_{\mathrm{6}}$ and Sr$_{\mathrm{2}}$CuWO$_{\mathrm{6}}$ to be highly two-dimensional antiferromagnets with J$_{\mathrm{2}}$/J$_{\mathrm{1}}=$ 0.03 (N\'{e}el order) and J$_{\mathrm{2}}$/J$_{\mathrm{1}}=$ 7.92 (columnar order), respectively. We have synthesized the solid solution series Sr$_{\mathrm{2}}$CuTe$_{\mathrm{1-}}_{x}$W$_{x}$O$_{\mathrm{6}}$ 0 $\le $ $x\le $ 1, and report the magnetic properties. Magnetic susceptibility $\chi $(T) shows a broad maximum at T$_{\mathrm{max}}=$ 73 K and 83 K in Sr$_{\mathrm{2}}$CuTeO$_{\mathrm{6}}$ and Sr$_{\mathrm{2}}$CuWO$_{\mathrm{6}}$, respectively. T$_{\mathrm{max}}$ reaches a minimum of $\approx $50 K in the vicinity of $x\approx $ 0.5 coinciding with a maximum in $\chi_{\mathrm{max}}$. This suggests the realization of the highly frustrated J$_{\mathrm{1}}$-J$_{\mathrm{2}}$ antiferromagnet near $x\approx $ 0.5. [1] H. Walker et al., Phys. Rev. B 94 64411. [2] P. Babkevich et al., arXiv:1605.09714.