A spin Hamiltonian for BaCdVO(PO$_4$)$_2$.

Single crystal inelastic neutron scattering is used to study spin wave excitations in the fully polarized state of the frustrated quantum ferro-antiferromagnet BaCdVO(PO$_4$)$_2$. The data analysis is based on a Heisenberg spin Hamiltonian that includes as many distinct nearest-neighbor and next-nearest neighbor interactions as allowed by crystal symmetry. All 8 such exchange constants are obtained in a simultaneous fit to over 150 scans across the dispersion manifold. This establishes a definitive quantitative model of this material. It turns out to be substantially different from the one assumed in numerous previous studies based on powder experiments.