Anisotropic magnetic property of single crystals $R$V${}_6$Sn${}_6$ ($R$ = Y, Gd - Tm, Lu)

$R$V${}_6$Sn${}_6$ ($R$ = Y, Gd - Tm, Lu) single crystals are synthesized by Sn-flux method and their physical properties are characterized by magnetization, resistivity, and specific heat measurements. Powder X-ray diffraction patterns of all samples can be well indexed with the hexagonal HfFe${}_6$Ge${}_6$-type structure, where rare-earth atoms form hexagonal layers and vanadium atoms form Kagome layers. At high temperatures, magnetic susceptibility measurements of moment bearing rare-earths ($R$ = Gd - Tm) follow Curie-Weiss behavior. Effective moments estimated from the polycrystalline average of magnetic susceptibility curves are consistent with the values for free $R^{3+}$ ion. Strong magnetic anisotropy due to crystalline electric field effects is observed for moment bearing rare-earths, except GdV${}_6$Sn${}_6$. The easy magnetization direction is determined to be $c$-axis for $R$ = Tb - Ho and $ab$-plane for $R$ = Er, and Tm. The vanadium ions in $R$V${}_6$Sn${}_6$ possess no magnetic moment. The compounds for $R$ = Y and Lu exhibit typical characteristics of paramagnetic metals. At low temperatures, the magnetic ordering is confirmed from magnetization, specific heat, and resistivity: the highest $T_N=4.9$~K for GdV${}_6$Sn${}_6$ and the lowest $T_N=2.3$~K for HoV${}_6$Sn${}_6$. No magnetic ordering is observed down to 1.8~K for $R$ = Er and Tm. A slight deviation of the magnetic ordering temperature from the de Gennes scaling suggests the dominant Ruderman-Kittel-Kasuya-Yosida (RKKY) exchange interaction between rare-earth moments in metallic $R$V${}_6$Sn${}_6$ compounds.