Spin dynamics in a frustrated magnet with short-range order

We analyze the stability of Néel and collinear orders for the frustrated ${\mathit{J}}_1$-${\mathit{J}}_2$ model on a square lattice as a function of S and ${\mathit{J}}_2$/${\mathit{J}}_1$ within the Schwinger-boson mean-field theory. For Néel order and finite S, the domain of stability extends beyond the classical boundary ${\mathit{J}}_2$/${\mathit{J}}_1$=1/2, suggesting the possibility of stabilizing (with the help of quantum fluctuations) a state that is classically forbidden. We use the solution with short-range Néel order as an effective model for the magnetic properties of high-${\mathit{T}}_{\mathit{c}}$ Cu oxides. Predictions are made for the static susceptibility, the dynamical structure factor, and the nuclear relaxation rates (all observable experimentally) at all temperatures. We show that the spin waves are overdamped even at low T and that a gap opens in the spin-fluctuation spectrum. The susceptibility is nearly linear on a wide intermediate temperature range and obeys a Curie law at high temperature in agreement with 1/N fermionic expansion.