Negative Volume Thermal Expansion Via Orbital and Magnetic Orders in ${\mathrm{Ca}}_2{\mathrm{Ru}}_{1-x}{\mathrm{Cr}}_x{\mathrm{O}}_4(0<x<0.13)$

${\mathrm{Ca}}_2{\mathrm{RuO}}_4$ undergoes a metal-insulator transition at $T_{\mathrm{MI}}=357\mathrm{K}$, followed by a well-separated transition to antiferromagnetic order at $T_N=110\mathrm{K}$. Dilute Cr doping for Ru reduces the temperature of the orthorhombic distortion at $T_{\mathrm{MI}}$ and induces ferromagnetic behavior at $T_C$. The lattice volume $V$ of ${\mathrm{Ca}}_2{\mathrm{Ru}}_{1-x}{\mathrm{Cr}}_x{\mathrm{O}}_4$ ($0<x<0.13$) abruptly expands with cooling at both $T_{\mathrm{MI}}$ 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 $T_{\mathrm{MI}}$ 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.

Figure 1

(a) Temperature dependence of the $a$ and $b$ axis lattice parameters, and the ab-plane resistivity ${\rho }_{ab}$ (right scale) for $x=0$. Inset: Schematics of orbital order and disorder. (b) Cr concentration ($x$) dependence of the $a$, $b$ and $c$ axis lattice parameters (right scale) for $T=90\mathrm{K}$. (c) Ru-O1-Ru bond angle and the Ru-O2 bond distance (right scale) for $T=90\mathrm{K}$. Inset: Schematics of the distorted Ru-O1-Ru bond angle $\theta$ and a ${\mathrm{RuO}}_6$ octahedron. (d) Unit cell volume $V$ for $T=90\mathrm{K}$ and 295 K, and thermal expansion ratio $[V(295\mathrm{K})-V(90\mathrm{K})]/V(295\mathrm{K})$ (right scale) for $0\le x\le 0.135$.

Figure 2

Temperature dependences of (a) the ab-plane resistivity ${\rho }_{ab}$, (b) the magnetic susceptibility ${\chi }_{ab}$ at applied field ${\mu }_{0}H=0.5\mathrm{T}$ for $0\le x\le 0.135$, and (c) the isothermal magnetization $M(H)$ at 100 K for representative compositions $x=0$ and 0.032. Inset: $T_N$, $T_C$ and Curie-Weiss temperature ${\theta }_{\mathrm{CW}}$ vs $x$.

Figure 3

For $x=0.067$, temperature dependences of: (a) lattice parameters $a$, $b$ and $c$ axis (right scale), (b) unit cell volume $V$ and thermal expansion ratio $\Delta V/V$ (right scale), and (c) ab-plane resistivity ${\rho }_{ab}$ and magnetic susceptibility ${\chi }_{ab}$ at ${\mu }_{0}H=0.5\mathrm{T}$. The shaded area indicates a region where the structural phase transition and first-order MI transition occur.

Figure 4

The $T\mathrm{\text{−}}x$ phase diagram summarizing observed phase transitions and phase types. Right scale shows the Cr concentration ($x$) dependence of the thermal expansion ratio $\Delta V/V$. Note that the hatched region represents negative volume thermal expansion.