  We present a study of the magnetic order and the structural stability of
two-dimensional quantum spin systems in the presence of spin-lattice coupling.
For a square lattice it is shown that the plaquette formation is the most
favourable form of static two-dimensional dimerization. We also demonstrate
that such distortions may coexist with long range magnetic order, in contrast
to the one-dimensional case. Similarly, the coupling to Einstein phonons is
found to reduce, but not to eliminate the staggered magnetic moment. In
addition, we consider the renormalization of the square lattice phonon spectrum
due to spin-phonon coupling in the adiabatic approximation. Towards low
temperatures significant softening mainly of zone boundary phonons is found,
especially around the $(\pi,0)$ point of the Brillouin zone. This result is
compatible with the tendency to plaquette formation in the static limit. We
also point out the importance of a "magnetic pressure" on the lattice due to
spin-phonon coupling. At low temperatures, this results in a tendency towards
shear instabilities of the lattice.
