  We present a microscopic model of the spin-gap quantum magnet (CuCl)LaNb2O7
that was previously suggested as a realization of the spin-1/2 frustrated
square lattice. Taking advantage of the precise atomic positions from recent
crystal structure refinement, we evaluate individual exchange integrals and
construct a minimum model that naturally explains all the available
experimental data. Surprisingly, the deviation from tetragonal symmetry leads
to the formation of spin dimers between fourth neighbors due to a Cu-Cl-Cl-Cu
pathway with a leading antiferromagnetic exchange J4 ~ 25 K. The total
interdimer exchange amounts to 12 - 15 K. Our model is in agreement with
inelastic neutron scattering results and is further confirmed by quantum
Monte-Carlo simulations of the magnetic susceptibility and the high-field
magnetization. Our results establish (CuCl)LaNb2O7 as a non-frustrated system
of coupled spin dimers with predominant antiferromagnetic interactions and
provide a general perspective for related materials with unusual
low-temperature magnetic properties.
