Itinerant magnetic phases and quantum Lifshitz transitions in a three-dimensional repulsively interacting Fermi gas with spin-orbit coupling

Magnetic phenomena in itinerant electron systems have been at the forefront of materials science. Here we show that the Weyl spin-orbit coupling (SOC) in three-dimensional repulsively interacting itinerant Fermi systems opens up a platform to host new itinerant magnetic phases, excitations, and phase transitions. A putative ferromagnetic state (FM) is always unstable against a stripe spiral spin density wave (S-SDW) or a stripe longitudinal SDW (LSDW) at small or large SOC strengths, respectively. The stripe-ordering wave vector is given by the nesting momentum of the two SOC-split Fermi surfaces with the same or opposite helicities at small or large SOC strengths, respectively. The LSDW is accompanied by a charge density wave (CDW) with half of its pitch. The transition from the paramagnet to the SSDW or LSDW+CDW is described by quantum Lifshitz-type actions, in sharp contrast to the Hertz-Millis types for itinerant electron systems without SOC. The collective excitations and Fermi surface reconstructions inside the SSDW and LSDW+CDW are also studied. The effects of a harmonic trap in cold-atom experiments are briefly discussed. In view of recent ground-breaking experimental advances in generating two-dimensional SOC in cold atoms, these phenomena can be observed in current or near-future cold-atom experiments even at very weak interactions. They may also be relevant to some itinerant magnetic materials with a strong SOC.