Spin excitations in the low-temperature phase of Tm

The rare-earth metal thulium has the ferrimagnetic-antiphase-domain spin arrangement at low temperatures. We show that the spin excitations in this magnetic structure are nearly localized and largely dispersionless modes. There are seven such modes between 8 and 10 meV, and they have not been resolved by neutron scattering experiments. On the other hand, these modes have different neutron scattering cross sections in different magnetic superzones, and this gives rise to what appears as a dispersion in the spin excitation peak in the extended Brillouin zone of the crystal.