  Strongly correlated electrons in layered perovskite structures have been the
birthplace of high-temperature superconductivity, spin liquid, and quantum
criticality. Specifically, the cuprate materials with layered structures made
of corner sharing square planar CuO$_4$ units have been intensely studied due
to their Mott insulating grounds state which leads to high-temperature
superconductivity upon doping. Identifying new compounds with similar lattice
and electronic structures has become a challenge in solid state chemistry.
Here, we report the hydrothermal crystal growth of a new copper tellurite
sulfate Cu$_3$(TeO$_4$)(SO$_4$)$\cdot$H$_2$O, a promising alternative to
layered perovskites. The orthorhombic phase (space group $Pnma$) is made of
corrugated layers of corner-sharing CuO$_4$ square-planar units that are
edge-shared with TeO$_4$ units. The layers are linked by slabs of
corner-sharing CuO$_4$ and SO$_4$. Using both the bond valence sum analysis and
magnetization data, we find purely Cu$^{2+}$ ions within the layers, but a
mixed valence of Cu$^{2+}$/Cu${^+}$ between the layers.
Cu$_3$(TeO$_4$)(SO$_4$)$\cdot$H$_2$O undergoes an antiferromagnetic transition
at $T_N$=67 K marked by a peak in the magnetic susceptibility. Upon further
cooling, a spin-canting transition occurs at $T^{\star}$=12 K evidenced by a
kink in the heat capacity. The spin-canting transition is explained based on a
$J_1$-$J_2$ model of magnetic interactions, which is consistent with the
slightly different in-plane super-exchange paths. We present
Cu$_3$(TeO$_4$)(SO$_4$)$\cdot$H$_2$O as a promising platform for the future
doping and strain experiments that could tune the Mott insulating ground state
into superconducting or spin liquid states.
