Magnon spectrum of the helimagnetic insulator Cu$_{2}$OSeO$_{3}$

Complex low-temperature-ordered states in chiral magnets are typically governed by acompetition between multiple magnetic interactions. The chiral-lattice multiferroic Cu2OSeO3became the first insulating helimagnetic material in which a long-range order of topologicallystable spin vortices known as skyrmions was established. Here we employ state-of-the-artinelastic neutron scattering to comprehend the full three-dimensional spin-excitation spectrumof Cu2OSeO3 over a broad range of energies. Distinct types of high- and low-energydispersive magnon modes separated by an extensive energy gap are observed in excellentagreement with the previously suggested microscopic theory based on a model of entangledCu4 tetrahedra. The comparison of our neutron spectroscopy data with model spin-dynamicalcalculations based on these theoretical proposals enables an accurate quantitative verificationof the fundamental magnetic interactions in Cu2OSeO3 that are essential for understandingits abundant low-temperature magnetically ordered phases