High-resolution thermal expansion measurements of BaCuSi$_4$O$_{10}$ and BaCuSi$_2$O$_6$

BaCuSi$_4$O$_{10}$ and BaCuSi$_2$O$_6$ were used in many ancient Chinese artifacts as synthetic pigments, and recently named as Han Blue and Han Purple, respectively.\footnote{E. W. FitzHugh \emph{et al}., Stud. Conserv. \textbf{37}, 145 (1992).} Besides being important synthetic pigments of ancient and modern times, these compounds have attracted scientific and technological interest due to their luminescent properties.\footnote{S. M. Borisov \emph{et al}., Anal. Chim. Acta \textbf{787}, 219 (2003); G. Pozza \emph{et al}., J. Cult. Herit. \textbf{1}, 393 (2000); S. M. Borisov \emph{et al}., Anal. Chem. \textbf{85}, 9371 (2013).} Moreover, Han Purple is a spin-dimer compound with an interesting phase diagram and a potential solid state device for exploring quantum effects in magnetic field induced Bose-Einstein condensation.\footnote{M. Jaime \emph{et al}., Phys. Rev. Lett. \textbf{93}, 087203 (2004).} In this work, we study BaCuSi$_2$O$_6$ and BaCuSi$_4$O$_{10}$ single crystals grown by floating zone method and flux growth technique, respectively. The results of thermal expansion, specific heat, and magnetization measurements of these compounds will be presented in detail.