  We apply neutron diffraction, high-resolution synchrotron x-ray diffraction,
magnetization measurements, electronic structure calculations, and quantum
Monte-Carlo simulations to unravel the structure and magnetism of
(CuCl)LaTa2O7. Despite the pseudo-tetragonal crystallographic unit cell, this
compound features an orthorhombic superstructure, similar to the Nb-containing
(CuX)LaNb2O7 with X = Cl and Br. The spin lattice entails dimers formed by the
antiferromagnetic fourth-neighbor coupling J4, as well as a large number of
nonequivalent interdimer couplings quantified by an effective exchange
parameter Jeff. In (CuCl)LaTa2O7, the interdimer couplings are sufficiently
strong to induce the long-range magnetic order with the Neel temperature TN~7 K
and the ordered magnetic moment of 0.53 mu_B, as measured with neutron
diffraction. This magnetic behavior can be accounted for by Jeff/J4~1.6 and
J4~16 K. We further propose a general magnetic phase diagram for the
(CuCl)LaNb2O7-type compounds, and explain the transition from the gapped
spin-singlet (dimer) ground state in (CuCl)LaNb2O7 to the long-range
antiferromagnetic order in (CuCl)LaTa2O7 and (CuBr)LaNb2O7 by an increase in
the magnitude of the interdimer couplings Jeff/J_4, with the (CuCl)LaM2O7 (M =
Nb, Ta) compounds lying on different sides of the quantum critical point that
separates the singlet and long-range-ordered magnetic ground states.
