  We study theoretically the effects of f-d magnetic exchange interaction in
the R$_2$Ir$_2$O$_7$ pyrochlore iridates. The R$^{3+}$ f-electrons form
localized magnetic doublets due to the crystal field environment, while the
Ir$^{4+}$ d- electrons are more itinerant and feel a strong spin-orbit
coupling. We construct and analyze a minimal model capturing this physics,
treating the Ir subsystem using a Hubbard-type model. First neglecting the
Hubbard interaction, we find Weyl semi-metal and Axion insulator phases induced
by the f-d exchange. Next, we find that f-d exchange can cooperate with the
Hubbard interaction to stabilize the Weyl semi-metal over a larger region of
parameter space than when it is induced by d-electron correlations alone.
Applications to experiments are discussed.
