Coupling of Orbital and Magnetic Orders to Colossal Negative Thermal Expansion in Novel Mott Insulators

Ca$_{2}$RuO$_{4}$ is intimately associated with both \textbf{\textit{negative volume thermal expansion (NVTE)}} and \textbf{\textit{negative linear thermal expansion (NLTV)}} when doped by a 3d transition metal ion M for Ru. The NVTE and NLTE observed in this system constitutes a compelling and extraordinary example in that (1) the coefficient of NVTE and NLTE reaches -213 $\times $ 10$^{-6}$ K$^{-1}$ and -148 $\times $ 10$^{-6}$ K$^{-1}$, respectively, constituting \textbf{\textit{colossal negative thermal expansion (NTE)}}; (2) the NTE anomalies closely track the onset temperatures of orbital and magnetic orders, in sharp contrast to classic NTE that shows no relevance to physical properties; (3) the NTE and physical properties can be effectively tuned via varying M and x in Ca$_{2}$Ru$_{1-x}$M$_{x}$O$_{4}$; (4) the NTE occurs near room temperature and extends over a wide temperature interval ranging from 100 K to 350 K. Moreover, NTE and Invar effect commonly exist in these 4d-based ruthenates and 5d-based iridates, e.g. Sr$_{n+1}$Ir$_{n}$O$_{3n+1}$ and BaIrO$_{3}$. These novel NTE materials provide a much-needed paradigm for functional materials with anomalous thermal expansion and electronic characteristics.