First order transition and phase separation in pyrochlores with colossal-magnetoresistance

Tl$_{2}$Mn$_{2}$O$_{7}$ pyrochlores present colossal magnetoresistance (CMR) around the long range ferromagnetic ordering temperature (T$_{C}$). The character of this magnetic phase transition has been determined to be first order, by purely magnetic methods, in contrast to the second order character previously reported by Zhao et al. (Phys. Rev. Lett. 83, 219 (1999)). The highest CMR effect, as in Tl$_{1.8}$Cd$_{0.2}$Mn$_{2}$O$_{7}$, corresponds to a stronger first order character. This character implies a second type of magnetic interaction, besides the direct superexchange between the Mn$^{4+}$ ions, as well as a phase coexistence. A model is proposed, with a complete Hamiltonian (including superexchange and an indirect interaction), which reproduce the observed phenomenology.