Magnetic Susceptibility and Heat Capacity of Single Crystal CaV$_2$O$_4$ Containing $S=1$ $J_1$-$J_2$ Antiferromagnetic Spin Chains

The compound CaV$_2$O$_4$ has an orthorhombic $Pnam$ structure and contains spin $S=1$ zig-zag ($J_1$-$J_2$) chains running along the crystallographic $b$-axis. Structural considerations suggest that $J_1\approx J_2$, which would result in competing frustrating antiferromagnetic (AF) interactions in this low-dimensional system. Previous studies on powders have suggested collinear spin models, a gapless chiral phase, or spin freezing below 20~K\@. We have grown single crystals of CaV$_2$O$_4$ for the first time and carried out magnetization and heat capacity measurements down to 1.8~K\@. We observe long-range AF ordering at $T_{\rm N} = 54$~K with the easy axis being the $c$-axis, as reflected by anisotropic susceptibility $\chi$ below $T_{\rm N}$. The magnetic specific heat $C_{\rm p}^{\rm mag}(T)$ up to 100 K, obtained after subtracting the lattice contribution of nonmagnetic isostructural ${\rm CaSc_2O_4}$, shows a clear signature of long-range magnetic order at $T_{\rm N}$. However, the molar entropy attains only $\approx 1/4$ of its maximum value 2Rln(3) by 100~K, indicating strong short range order above $T_{\rm N}$ and large values $J_1,\ J_2 > 100$ K\@. This is consistent with our estimates $J_1 \approx J_2 \sim$ 150--300 K obtained by comparison of our $\chi(T)$ data with exact diagonalization calculations of $\chi(T)$.