In systems where electrons form both dispersive bands and small local spins, we show that changes of the spin configuration can tune the bands through a Lifshitz transition, resulting in a continuous metal-insulator transition associated with a progressive change of the Fermi surface topology. In contrast to a Mott-Hubbard and Slater pictures, this spin-driven Lifshitz transition appears in systems with small electron-electron correlation and large hybridization. We show that this situation is realized in 5d distorted perovskites with an half-filled t2g bands such as NaOsO3, where the strong p − d hybridization reduces the local moment, and spin-orbit coupling causes a large renormalization of the electronic mobility. This weakens the role of electronic correlations and drives the system towards an itinerant magnetic regime which enables spin-fluctuations.PACS numbers: 71.30.+h, 75.47.Lx, 71.27.+a Metal-to-insulator transitions (MITs) are one of the most important phenomena in solid-state physics and their fundamental understanding represents an enduring challenge in solid state theory [1,2]. Different mechanisms have been invoked to explain the formation of an insulating regime. Classical examples are realized in 3d transition metal oxides (TMOs), where the nonconducting state is typically understood within the MottHubbard model as arising from the competition between strong electron-electron interaction (U ) and the electronic mobility, associated to the (non-interacting) bandwidth (W ) [3][4][5]. When moving to the more spatially extended 4d and 5d orbitals the W increases and the U is expected to become smaller, leading to the tendency towards metallicity as in the itinerant magnet SrRuO 3 [6]. In contrast to these expectations, recent theory and experiment have revealed that in 'heavy' 5d TMOs, the enhanced spin-orbit coupling (SOC) strength [7] can lead to the formation of a variety of novel types of quantum states including unexpected insulating regimes [8][9][10][11]. In the most representative example, Sr 2 IrO 4 , the concerted action of a strong SOC and a moderate U leads to the opening of a small spectral gap [11,12] denominated relativistic Mott gap. Other and more rare types of MITs have been recently proposed for magnetic relativistic osmium oxides based on the Slater mechanism [13][14][15][16], driven by antiferromagnetic (AFM) order, where the gap is opened by exchange interactions and not by electronic correlation, [17] or Lifshitz-like processes [18,19], involving a rigid change of the Fermi surface topology [20].In this work we show that in weakly correlated (small U ) itinerant magnets the combined effect of longitudinal and rotational spin-fluctuations can cause a continu- * cesare.franchini@univie.ac.at ous MIT with Lifshitz characteristics, fundamentally different from relativistic Mott or purely Slater insulating states. The necessary conditions for the onset of this type of spin-driven Lifshitz MIT are the coexistence of a small U , a small local moment and an high degree of orbital ...