International audienceLow-frequency quasi-periodic oscillations, or LFQPOs, are ubiquitous in black hole X-ray binaries and provide strong constraints on the accretion-ejection processes. Although several models have been proposed, none has been proven to reproduce all observational constraints, and no consensus has emerged so far. We make the conjecture that disks in binaries are threaded by a large-scale vertical magnetic field that splits it into two radial zones. In the inner jet-emitting disk (JED), a near equipartition field allows driving powerful self-collimated jets, while beyond a transition radius, the disk magnetization is too low and a standard accretion disk (SAD) is settled. In a series of papers, this hybrid JED-SAD disk con...