Theoretical justification of stable ferromagnetism in ferroelectric BiFeO3 by first-principles

•DFT study demonstrates the stability of an observed ferromagnetic order in BiFeO3.•Such a novel macroscopic ferromagnetism coexist with the ferroelectric arrangement.•Conditions to be fulfilled by crystalline structure and chemical bonding are outlined.•The ferromagnetic order is associated to covalence of the spin-up eg orbitals.•The electronic structures suggest applications as spin inverter semiconductor.