Hole-doping of Ca$_{1-x}$Na$_x$V$_2$O$_4$ ($x = 0 - 0.5$) With Zig-Zag Vanadium Chains*

CaV$_2$O$_4$ crystallizes in an orthorhombic $Pnam$ structure with $S=1$ zig-zag V chains along the $c$-axis. In this low-dimensional, insulating system the triangular arrangement of V atoms with $J_1\approx J_2$ leads to competing frustrating antiferromagnetic (AF) interactions. Our recent studies on powders and single crystals of CaV$_2$O$_4$ show long-range AF ordering at a N$\acute{\rm e}$el temperature $T_{\rm N} \sim 75 - 78$~K (with a monoclinic distortion at $\sim 145-150$~K) and signatures of partial spin-freezing below 20~K. We have tried doping CaV$_2$O$_4$ into the metallic state by substitution at the Ca site to drive V into fractional valence states. We have succeeded in replacing Ca upto 50\% by Na at 1200~$^{\circ}$C. Powder XRD patterns of our Na-substituted samples are nearly single-phase CaV$_2$O$_4$-type, while the $c$-axis lattice parameter decreases sharply - Thus Na indeed substitutes for Ca instead of occupying interstitial positions. The room temperature resistance of Na-doped sintered pellets decreases significantly. High field ($H$ = 1 T) dc magnetization measurements show a steep fall in $T_{\rm N}$ while low field ($H$ = 100 Oe) data suggest onset of spin-glass like behavior as the Na content increases. We shall present our results and discuss the evolution from a partially disordered AF insulator to a spin-glass.