Well defined spin waves were observed when the spin dynamics of Tl2Mn2O7, the first pyrochlore compound found to exhibit colossal magnetoresistance, was measured [J.W.Lynn et al., Phys.Rev.Lett. 80,4582(1998)], in stark contrast with the experimental results on the larger family of magnetoresistive manganites with perovskite structure. In this work, we present our calculation for the spin waves in Tl2Mn2O7, which we described using the microscopic generic model proposed recently for this compound [C.I.Ventura and M.A.Gusmao, Phys.Rev.B 65, 14422(2002)]. We have employed a canonical transformation to determine perturbatively the effective spin-wave Hamiltonian, obtaining therefrom the renormalization of the ferromagnetic spin waves related to the localized Mn$^{4+}$ spins, due to their coupling with the conduction electrons present. We have calculated the magnon dispersion relations along different paths in the first Brillouin zone, comparing them with those which are obtained for an ideal isotropic ferromagnet. This comparison evidences an agreement between the ferromagnetic magnons obtained from the generic model and the bare spin waves, such as had been found in neutron scattering experiments.
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