Ca$_{2}$Ru$_{1-x}$Cr$_{x}$O$_{4 }$(0 $<$ x $<$ 0.13): Negative volume thermal expansion via orbital and magnetic orders

Ca$_{2}$RuO$_{4}$ undergoes a metal-insulator transition at T$_{MI}$= 357 K, followed by a well-separated transition to antiferromagnetic order at T$_{N }$= 110 K. Dilute Cr doping for Ru reduces the temperature of the orthorhombic distortion at T$_{MI}$ and induces ferromagnetic behavior at T$_{C}$. The lattice volume V of Ca$_{2}$Ru$_{1-x}$Cr$_{x}$O$_{4}$ (0 $<$ x $<$ 0.13) abruptly expands with cooling at both T$_{MI}$ and T$_{C}$, giving rise to a total volume expansion $\Delta $V/V $\approx $ 1 {\%}, which sharply contrasts the smooth temperature dependence of the few known examples of negative volume thermal expansion driven by anharmonic phonon modes. In addition, the near absence of volume thermal expansion between T$_{C}$ and T$_{MI}$ represents an Invar effect. The two phase transitions, which surprisingly mimic the classic freezing transition of water, suggest an exotic ground state driven by an extraordinary coupling between spin, orbit and lattice degrees of freedom.