In-plane ferromagnetic instability in a two-dimensional electron liquid in the presence of Rashba spin-orbit coupling

We show that due to the peculiar structure of the non-interacting energy spectrum, the Coulomb interaction leads for all densities to an in-plane ferromagnetic instability in a two-dimensional electron liquid in the presence of sufficiently strong Rashba spin-orbit coupling. This non perturbative phenomenon is characterized by an interesting anisotropic momentum space repopulation and is in nature quite different from the already identified out-of-plane ferromagnetic instability.