Heisenberg magnets with short-range order and spin dynamics of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6+\mathit{x}}$

We use the Schwinger-boson mean-field theory to study the spin dynamics of Heisenberg magnets in which quantum (finite S) fluctuations have destroyed the classical Néel long-range order. The low-temperature physics is dominated by the zone-center gap Δ(T) which remains finite as T->0. The effect of this T-dependent low-energy cutoff on the magnetic response functions (susceptibilty, structure factor, relaxation rates) is analyzed. We use this model to discuss the validity of a description of antiferromagnetic fluctuations in ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{6+\mathit{x}}$ in terms of local moments.