Spin excitations in ${\mathrm{La}}_2{\mathrm{CuO}}_4:$ Consistent description by inclusion of ring exchange

We consider the square lattice Heisenberg antiferromagnet with plaquette ring exchange and a finite interlayer coupling leading to a consistent description of the spin-wave excitation spectrum in ${\mathrm{La}}_2{\mathrm{CuO}}_4.$ The values of the in-plane exchange parameters, including ring exchange $J_{\square },$ are obtained consistently by an accurate fit to the experimentally observed in-plane spin-wave dispersion, while the out-of-plane exchange interaction is found from the temperature dependence of the sublattice magnetization at low temperatures. The fitted exchange interactions $J=151.9\mathrm{}\hspace{0.5em}\mathrm{meV}$ and $J_{\square }=0.24J$ give values for the spin stiffness and the Néel temperature in excellent agreement with the experimental data.