Static and dynamic properties of the frustrated spin- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> </mml:math> depleted kagome antiferromagnet <mml:math xmlns:mml="http://www

The structural and magnetic properties of the two-dimensional spin-$1/2$ depleted-kagome compound ${\mathrm{Cu}}_{7}{({\mathrm{TeO}}_{3})}_{2}{({\mathrm{SO}}_{4})}_{2}{(\mathrm{OH})}_{6}$ are investigated using x-ray diffraction, magnetization, heat capacity, and $^{1}\mathrm{H}$ Nuclear Magnetic Resonance (NMR) measurements. From the analysis of magnetic susceptibility, we found a large Curie-Weiss temperature $[{\ensuremath{\theta}}_{\mathrm{CW}}=\ensuremath{-}50(2)\phantom{\rule{0.28em}{0ex}}\mathrm{K}]$ and the coexistence of antiferromagnetic and ferromagnetic interactions. The value of ${\ensuremath{\theta}}_{\mathrm{CW}}$ gives an estimate of the average nearest-neighbor antiferromagnetic interaction of $J/{k}_{\mathrm{B}}\ensuremath{\simeq}66\phantom{\rule{0.28em}{0ex}}\mathrm{K}$. The NMR relaxation rates ($1/{T}_{1}$ and $1/{T}_{2}$) exhibit a peak, providing evidence for a magnetic long-range order at ${T}^{*}\ensuremath{\simeq}4\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ which appears to be canted antiferromagnetic type. Heat capacity also features a broad maximum at ${T}^{*}$ that moves towards higher temperatures with increasing magnetic field, reflecting defect induced Schottky anomaly. The frustration parameter ${f}_{r}=|{\ensuremath{\theta}}_{\mathrm{CW}}|/{T}^{*}\ensuremath{\simeq}12.5$ renders the compound a highly frustrated low-dimensional magnet.