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We report single crystal growth, electrical resistivity $\rho$, anisotropicmagnetic susceptibiltiy $\chi$, and heat capacity $C_p$ measurements on theone-dimensional spin-chain ruthenate Na$_2$RuO$_4$. We observe variable rangehopping (VRH) behaviour in $\rho(T)$. The magnetic susceptibility with magneticfield perpendicular ($\chi_\perp$) and parallel ($\chi_\parallel$) to thespin-chains is reported. The magnetic properties are anisotropic with$\chi_\perp > \chi_\parallel$ in the temperature range of measurements T$\approx 2$ to $305$ K with $\chi_\perp / \chi_\parallel$ $\approx 1.4$ at$305$ K. Analysis of the $\chi(T)$ data reveals an anisotropy in the $g$-factorand Van-Vleck paramagnetic contribution. An anomaly in $\chi(T)$ and acorresponding lambda-like anomaly in $C_p$ at $T_N = 37$ K confirms long-rangeantiferromagnetic ordering. This temperature is an order of magnitude smallerthan the Weiss temperature $\theta \sim -250$ K and points to suppression oflong range magnetic order due to low dimensionality. However, we were unable toget a satisfactory fit of the experimental $\chi(T)$ by an isolatedone-dimensional spin-chain model, suggesting the importance of inter-chaininteractions in Na$_2$RuO$_4$.

Crystal growth and magnetic anisotropy in the spin-chain ruthenate Na$_2$RuO$_4$