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We report structural and magnetic properties of the spin-$\frac12$ quantumantiferromagnet Cu[C$_6$H$_2$(COO)$_4$][C$_2$H$_5$NH$_3$]$_2$ by means ofsingle-crystal x-ray diffraction, magnetization, heat capacity, and electronspin resonance (ESR) measurements on polycrystalline samples, as well asband-structure calculations. The triclinic crystal structure of this compoundfeatures CuO$_4$ plaquette units connected into a two-dimensional frameworkthrough anions of the pyromellitic acid [C$_6$H$_2$(COO)$_4$]$^{4-}$. Theethylamine cations [C$_2$H$_5$NH$_3]^+$ are located between the layers and actas spacers. Magnetic susceptibility and heat capacity measurements establish aquasi-two-dimensional, weakly anisotropic and non-frustrated spin-$\frac12$square lattice with the ratio of the couplings $J_a/J_c\simeq 0.7$ along the$a$ and $c$ directions, respectively. No clear signatures of the long-rangemagnetic order are seen in thermodynamic measurements down to 1.8\,K. However,the gradual broadening of the ESR line suggests that magnetic ordering occursat lower temperatures. Leading magnetic couplings are mediated by the organicanion of the pyromellitic acid and exhibit a non-trivial dependence on theCu--Cu distance, with the stronger coupling between those Cu atoms that arefurther apart.

Quasi-two-dimensional $S=1/2$ magnetism of Cu[C$_6$H$_2$(COO)$_4$][C$_2$H$_5$NH$_3$]$_2$