Ordering due to Quantum Fluctuations inSr2Cu3O4Cl2

${\mathrm{Sr}}_2{\mathrm{Cu}}_3{\mathrm{O}}_4{\mathrm{Cl}}_2$ has ${\mathrm{Cu}}_{\mathrm{I}}$ and ${\mathrm{Cu}}_{\mathrm{II}}$ subsystems, forming interpenetrating $S=1\mathrm{}/2$ square lattice Heisenberg antiferromagnets. The classical ground state is degenerate, due to frustration of the intersubsystem interactions. Magnetic neutron scattering experiments show that quantum fluctuations cause a two dimensional Ising ordering of the ${\mathrm{Cu}}_{\mathrm{II}}$'s, lifting the degeneracy, and a dramatic increase of the ${\mathrm{Cu}}_{\mathrm{I}}$ out-of-plane spin-wave gap, unique for order out of disorder. The spin-wave energies are quantitatively predicted by calculations which include quantum fluctuations.