Magnon dispersion curve of antiferromagnetic ${\mathrm{Bi}}_2$${\mathrm{CuO}}_4$

We present detailed neutron-scattering studies of the magnon dispersion curve in ${\mathrm{Bi}}_2$${\mathrm{CuO}}_4$. We show the existence of a single doubly degenerate dispersion branch. In this antiferromagnetic S=1/2 system, we found that our experimental results are totally accounted for by a model of four superexchange interactions: ${\mathit{J}}_1$=2.2±0.15; ${\mathit{J}}_2$=0.7±0.05; ${\mathit{J}}_3$=0.2±0.05; ${\mathit{J}}_4$=0.8±0.05; and anisotropy constant D=0.3±0.05 in meV. These Cu-Cu interactions are similar to those between the two ${\mathrm{CuO}}_2$ planes of the so-called bilayer of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6+\mathit{x}}$, and this work is a direct determination of such couplings in copper oxides.