  The spin-1/2 Heisenberg antiferromagnet on an anisotropic triangular lattice
(ATL) is an archetypal spin system hosting exotic quantum magnetism and
dimensional crossover. However, the progress in experimental research on this
field has been limited due to the scarcity of ideal model materials. Here, we
show that rhenium oxyhalides $A_{3}$ReO$_{5}X_{2}$, where spin-1/2 Re$^{6+}$
ions form a layered structure of ATLs, allow for flexible chemical substitution
in both cation $A^{2+}$ ($A$ = Ca, Sr, Ba, Pb) and anion $X^{-}$ ($X$ = Cl, Br)
sites, leading to seven synthesizable compounds. By combining magnetic
susceptibility and high-field magnetization measurements with theoretical
calculations using the orthogonalized finite-temperature Lanczos method, we
find that the anisotropy $J'/J$ ranges from 0.25 to 0.45 depending on the
chemical composition. Our findings demonstrate that $A_{3}$ReO$_{5}X_{2}$ is an
excellent platform for realizing diverse effective spin Hamiltonians that
differ in the strength of the anisotropy $J'/J$ as well as the relevance of
perturbation terms such as the Dzyaloshinskii-Moriya interaction and interlayer
exchange coupling.
