By means of first principles schemes based on magnetically constrained density functional theory and on the band unfolding technique we study the effect of doping on the conducting behaviour of the Lifshitz magnetic insulator NaOsO3. Electron doping is treated realistically within a supercell approach by replacing sodium with magnesium at different concentrations. Our data indicate that by increasing carrier concentration the system is subjected to two types of transition: (i) insulator to bad metal at low doping and low temperature and (ii) bad metal to metal at high doping and/or high-temperature. The predicted doping-induced insulator to metal transition (MIT) has similar traits with the temperature driven MIT reported in the undoped compound. Both develops in an itinerant background and exhibit a coupled electronic and magnetic behaviour characterized by the gradual quenching of the (pseudo)-gap associated with an reduction of the local spin moment. Unlike the temperature-driven MIT, chemical doping induces substantial modifications of the band structure and the MIT cannot be fully described as a Lifshitz process.
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