Specific Heat of Three Magnetic Linear-Chain Antiferromagnets

Abstract

The specific heat of ${\mathrm{C}\mathrm{u}[\mathrm{N}{\mathrm{H}}_{2}{(\mathrm{C}{\mathrm{H}}_{2})}_{3}\mathrm{N}{\mathrm{H}}_{2}]}_{2}$S${\mathrm{O}}_{4}$ \ifmmode\cdot\else\textperiodcentered\fi{} ${\mathrm{H}}_{2}$O ("CPDS\ifmmode\cdot\else\textperiodcentered\fi{}${\mathrm{H}}_{2}$O") and of a mixed sample of Cu${(\mathrm{N}{\mathrm{H}}_{3})}_{4}$-Se${\mathrm{O}}_{4}$ ("CTSel") and Cu${(\mathrm{N}{\mathrm{H}}_{3})}_{4}$Se${\mathrm{O}}_{4}$\ifmmode\cdot\else\textperiodcentered\fi{}${\mathrm{H}}_{2}$O ("CTSel\ifmmode\cdot\else\textperiodcentered\fi{}${\mathrm{H}}_{2}$O") have been measured from 2 to 20 K, and excellent agreement has been obtained with the Bonner-Fisher theory for infinite magnetic linear chains of spin \textonehalf{}, with an isotropic Heisenberg interaction between nearest neighbors. From the fit between experiment and theory, the following exchange constants $J$ are obtained: CPDS\ifmmode\cdot\else\textperiodcentered\fi{}${\mathrm{H}}_{2}$O, (${1.09}_{\ensuremath{-}0.08}^{+0.04}$) K; CTSel, (${0.24}_{5}$ \ifmmode\pm\else\textpm\fi{}0.03) K; and CTSel\ifmmode\cdot\else\textperiodcentered\fi{}${\mathrm{H}}_{2}$O, (2.36\ifmmode\pm\else\textpm\fi{}0.03) K. A preliminary description of the crystal structures of these compounds is also given. CTSel\ifmmode\cdot\else\textperiodcentered\fi{}${\mathrm{H}}_{2}$O is isomorphous with Cu${(\mathrm{N}{\mathrm{H}}_{3})}_{4}$S${\mathrm{O}}_{4}$\ifmmode\cdot\else\textperiodcentered\fi{}${\mathrm{H}}_{2}$O; in addition, a close structural relationship is found between these salts and CPDS\ifmmode\cdot\else\textperiodcentered\fi{}${\mathrm{H}}_{2}$O. Thus, the variation of $J$ with interionic separation $\mathcal{r}$ may be estimated for these simple linear systems. This estimate gives $N=10.9$ where $J=a{r}^{\ensuremath{-}n}$.