Birchite Cd2Cu2(PO4)2SO4·5H2…

$S=1/2$ Heisenberg ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ chain antiferromagnets have been investigated extensively due to their exotic magnetic states. Here, we report the magnetic behavior of birchite ${\mathrm{Cd}}_{2}{\mathrm{Cu}}_{2}{({\mathrm{PO}}_{4})}_{2}{\mathrm{SO}}_{4}\ifmmode\cdot\else\textperiodcentered\fi{}5{\mathrm{H}}_{2}\mathrm{O}$ and its effective spin model. Experimental studies by magnetic susceptibility, magnetization, heat capacity, and $\ensuremath{\mu}\mathrm{SR}$ measurements indicate the absence of long-range order down to 0.4 K. Theoretical studies reveal that birchite is a model compound for the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ antiferromagnetic chain: the intrachain interactions ${J}_{1}$ and ${J}_{2}$ are antiferromagnetic and their magnitude is about 100 times larger than the interchain interactions. The magnitude of ${J}_{2}$ is two to three times larger than that of ${J}_{1}$, thus the spin gap is expected to be only a few percent of that of ${J}_{1}$. The temperature dependence of the specific heat shows a broad peak at about 1 K ($\ensuremath{\simeq}0.036{J}_{1}$), which suggests the presence of a spin gap.