Two-dimensional zone-center spin-wave excitations in ${\mathrm{La}}_2$Cu${\mathrm{O}}_4$

We have studied the spin-wave excitations near the two-dimensional zone center at 80 K in a single crystal of ${\mathrm{La}}_2$Cu${\mathrm{O}}_4$ which orders at $T_N=195\mathrm{}$ K. In-plane and out-of-plane modes are observed at energies of 1.0±0.25 meV and 2.5±0.5 meV, respectively, The in-plane mode energy is determined primarily by the antisymmetric exchange and it measures this term directly. The out-of-plane mode energy corresponds to a planar anisotropy energy of ∼0.016 meV. We observe, in addition, the appearance of significant $E\simeq 0$ scattering below 30 K.