  We study the effects of electron doping in Mott insulators containing d^4
ions such as Ru4+, Os4+, Rh5+, and Ir5+ with J=0 singlet ground state.
Depending on the strength of the spin-orbit coupling, the undoped systems are
either nonmagnetic or host an unusual, excitonic magnetism arising from a
condensation of the excited J=1 triplet states of t_2g^4. We find that the
interaction between J-excitons and doped carriers strongly supports
ferromagnetism, converting both the nonmagnetic and antiferromagnetic phases of
the parent insulator into a ferromagnetic metal, and further to a nonmagnetic
metal. Close to the ferromagnetic phase, the low-energy spin response is
dominated by intense paramagnon excitations that may act as mediators of a
triplet pairing.
