Magnons in the colossal magnetoresistance pyrochloreTl2Mn2O7

Abstract

Well defined ferromagnetic spin waves were observed when the spin dynamics of ${\mathrm{Tl}}_{2}{\mathrm{Mn}}_{2}{\mathrm{O}}_{7}$, 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 to 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 ${\mathrm{Tl}}_{2}{\mathrm{Mn}}_{2}{\mathrm{O}}_{7}$, 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 ${\mathrm{Mn}}^{4+}$ 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, providing a simple explanation for the neutron scattering results.