Low energy magnons in the chiral ferrimagnet $\text{Cu}_2\text{OSeO}_3$: a coarse-grained approach

We report a comprehensive neutron scattering study of low energy magnetic excitations in the breathing pyrochlore helimagnetic $\text{Cu}_2\text{OSeO}_3$. Fully documenting the four lowest energy magnetic modes that leave the ferrimagnetic configuration of the "strong tetrahedra" intact ($|\hbar\omega|<13$ meV), we find gapless quadratic dispersion at the $\Gamma$ point for energies above 0.2 meV, two doublets separated by 1.6(2) meV at the $R$ point, and a bounded continuum at the $X$ point. Our constrained rigid spin cluster model relates these features to Dzyaloshinskii-Moriya (DM) interactions and the incommensurate helical ground state. Combining conventional spin wave theory with a spin cluster form-factor accurately reproduces the measured equal time structure factor through multiple Brillouin zones. An effective spin Hamiltonian describing the complex anisotropic inter-cluster interactions is obtained.