Topological ferromagnetism in Rashba systems

We unravel a previously unexplored mechanism instigating magnetic instabilities both in three-dimensional and two-dimensional Rashba systems. These instabilities arise from the spin-dependent interactions of itinerant electrons, stemming from the Rashba spin-orbit coupling invoked by their mutual Coulomb fields. The ferromagnetic transition is associated with the rotation symmetry breaking not only in the spin, but also in the orbital spaces. The latter effect leads to deformation of the Fermi surface of the polarized itinerant electrons into the ellipsoidal or toroidal shape. It may undergo genus-changing topological Lifshitz transition between these shapes as a function of the spin-orbit coupling magnitude or interactions strength. The transition may have a number of observable manifestations in thermodynamic and and transport properties, as well as in spectra of Friedel and Shubnikov-de Haas oscillations.