  We report a neutron scattering study on the tetragonal compound
Sr_2Cu_3O_4Cl_2, which has two-dimensional (2D) interpenetrating Cu_I and
Cu_{II} subsystems, each forming a S=1/2 square lattice quantum Heisenberg
antiferromagnet (SLQHA). The mean-field ground state is degenerate, since the
inter-subsystem interactions are geometrically frustrated. Magnetic neutron
scattering experiments show that quantum fluctuations lift the degeneracy and
cause a 2D Ising ordering of the Cu_{II} subsystem. Due to quantum fluctuations
a dramatic increase of the Cu_I out-of-plane spin-wave gap is also observed.
The temperature dependence and the dispersion of the spin-wave energy are
quantitatively explained by spin-wave calculations which include quantum
fluctuations explicitly. The values for the nearest-neighbor superexchange
interactions between the Cu_I and Cu_{II} ions and between the Cu_{II} ions are
determined experimentally to be J_{I-II} = -10(2)meV and J_{II}= 10.5(5)meV,
respectively. Due to its small exchange interaction, J_{II}, the 2D dispersion
of the Cu_{II} SLQHA can be measured over the whole Brillouin zone with thermal
neutrons, and a novel dispersion at the zone boundary, predicted by theory, is
confirmed. The instantaneous magnetic correlation length of the Cu_{II} SLQHA
is obtained up to a very high temperature, T/J_{II}\approx 0.75. This result is
compared with several theoretical predictions as well as recent experiments on
the S=1/2 SLQHA.
