Neutron scattering study of ${\mathrm{Sr}}_2{\mathrm{Cu}}_3{\mathrm{O}}_4{\mathrm{Cl}}_2$

We report a neutron scattering study on the tetragonal compound ${\mathrm{Sr}}_2{\mathrm{Cu}}_3{\mathrm{O}}_4{\mathrm{Cl}}_2,$ which has two-dimensional (2D) interpenetrating ${\mathrm{Cu}}_{\mathrm{I}}$ and ${\mathrm{Cu}}_{\mathrm{II}}$ subsystems, each forming a $S=1/2\mathrm{}$ square lattice quantum Heisenberg antiferromagnet (SLQHA). The mean-field ground state is degenerate, since the intersubsystem interactions are geometrically frustrated. Magnetic neutron scattering experiments show that quantum fluctuations lift the degeneracy and cause a 2D Ising ordering of the ${\mathrm{Cu}}_{\mathrm{II}}$ subsystem. Due to quantum fluctuations a dramatic increase of the ${\mathrm{Cu}}_{\mathrm{I}}$ 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 ${\mathrm{Cu}}_{\mathrm{I}}$ and ${\mathrm{Cu}}_{\mathrm{II}}$ ions and between the ${\mathrm{Cu}}_{\mathrm{II}}$ ions are determined experimentally to be $J_{\mathrm{I}-\mathrm{I}\mathrm{I}}=-10\left(2\right)\mathrm{}$ meV and $J_{\mathrm{II}}=10.5\mathrm{}\left(5\right)\mathrm{}$ meV, respectively. Due to its small exchange interaction $J_{\mathrm{II}},$ the 2D dispersion of the ${\mathrm{Cu}}_{\mathrm{II}}$ SLQHA can be measured over the whole Brillouin zone with thermal neutrons, and a dispersion at the zone boundary, predicted by theory, is confirmed. The instantaneous magnetic correlation length of the ${\mathrm{Cu}}_{\mathrm{II}}$ SLQHA is obtained up to a very high temperature, ${T/J}_{\mathrm{II}}\approx \mathrm{0.75.}$ This result is compared with several theoretical predictions as well as recent experiments on the $S=1/2\mathrm{}$ SLQHA.