Sr_2Cu_3O_4Cl_2 is an antiferromagnet consisting of weakly coupled CuO planes
which comprise two weakly interacting antiferromagnetic subsystems, I and II,
which order at respective temperatures T_I \approx 390K and T_{II} \approx 40K.
Except asymptotically near the ordering temperature, these systems are good
representations of the two-dimensional quantum spin 1/2 Heisenberg model. For
T< T_{II} there are four low-energy modes at zero wave vector, three of whose
energies are dominated by quantum fluctuations. For T_{II} < T < T_I there are
two low energy modes. The mode with lower energy is dominated by quantum
fluctuations. Our calculations of the energies of these modes (including
dispersion for wave vectors perpendicular to the CuO planes) agree extremely
well with the experimental results of inelastic neutron scattering (in the
accompanying paper) and for modes in the sub meV range observed by electron
spin resonance. The parameters needed to describe quantum fluctuations are
either calculated here or are taken from the literature. These results show
that we have a reasonable qualitative understanding of the band structure of
the lamellar cuprates needed to calculate the anisotropic exchange constants
used here.Comment: 84 pages, 7 figure
