The origin of magnetic ordering in quasi-two-dimensional quantum magnets Cu(\textit{tn})Cl$_{2}$ and Cu(\textit{en})(H$_{2}$O)$_{2}$SO$_{4}$

A comparative analysis of magnetic properties of Cu(\textit{en})(H$_{2}$O)$_{2}$SO$_{4}$ (\textit{en} $=$ C$_{2}$H$_{8}$N$_{2})$ (1) and Cu(\textit{tn})Cl$_{2}$ (\textit{tn} $=$ C$_{2}$H$_{10}$N$_{2})$ (2) has been performed to search for the origin of magnetic ordering observed in (1) at $T_{c} =$ 0.9 K while hidden in (2). Previously, both materials were approximated by a quasi-two-dimensional (2d) spin 1/2 Heisenberg model on the square lattice with effective intralayer and interlayer coupling $J$/$k_{B} =$ 3 K and $J$'$=$ 10$^{-3}J, $ respectively. The first principles calculations revealed in (1) a spatial anisotropy of exchange coupling within a layer, $J_{1}$/$J_{2} =$ 0.15, in accordance with a proximity of data to 2d behavior. Considering only effect of interlayer coupling, $T_{c} =$ 0.8 K was evaluated, while $T_{c} =$ 0.85 K, when a weak ising-like spin anisotropy, $\Delta =$ 0.015 was introduced into Heisenberg layers. The effects of spin and spatial anisotropy on the ordering of (1) and the absence of a phase transition in (2) are discussed.