  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.
