Magnetic and Orbital Orders Coupled to Negative Thermal Expansion in Mott Insulators, {Ca$_{2}$Ru$_{1-x}$M$_{x}$O$_{4}$} (M = 3d transition metal ion)*

{Ca$_{2}$RuO$_{4}$} is a structurally-driven Mott insulator with a metal-insulator transition at $T _{MI}$ = 357K, followed by a well-separated antiferromagnetic order at $T _{N}$ = 110 K. Slightly substituting Ru with a 3d transition metal ion M effectively shifts $T _{MI}$ and induces exotic magnetic behavior below $T _{N}$. Moreover, M doping for Ru produces negative thermal expansion in {Ca$_{2}$Ru$_{1-x}$M$_{x}$O$_{4}$} (M = Cr, Mn, Fe or Cu); the lattice volume expands on cooling with a total volume expansion ratio, $\Delta$V/V, reaching as high as 1\%. The onset of the negative thermal expansion closely tracks $T _{MI}$ and $T _{N}$, sharply contrasting classic negative thermal expansion that shows no relevance to electronic properties. In addition, the observed negative thermal expansion occurs near room temperature and extends over a wide temperature interval [1, 2]. These findings underscores new physics driven by a complex interplay between orbital, spin and lattice degrees of freedom.\\[4pt] [1] T.F. Qi, O.B. Korneta, S. Parkin, L.E. DeLong, P. Schlottmann and G. Cao, Phys. Rev. Lett. 105 177203 (2010)\\[0pt] [2] T. F. Qi, O. B. Korneta, S. Parkin, Jianping Hu and G. Cao, Phys. Rev. B 85 165143 (2012)