We predict the existence of chiral spin waves-collective modes in a two-dimensional Fermi liquid with the Rashba or Dresselhaus spin-orbit coupling. Starting from the phenomenological Landau theory, we show that the long-wavelength dynamics of magnetization is governed by the KleinGordon equations. The standing-wave solutions of these equations describe "particles" with effective masses, whose magnitudes and signs depend on the strength of the electron-electron interaction. The spectrum of the spin-chiral modes for arbitrary wavelengths is determined from the Dyson equation for the interaction vertex. We propose to observe spin-chiral modes via microwave absorption of standing waves confined by an in-plane profile of the spin-orbit splitting.Introduction.-The rapidly developing field of spintronics aims to manipulate electron spins by electric rather than magnetic fields. Since spin-orbit (SO) interaction allows for such a coupling, electron systems with SO interaction have been under intense study. A particularly interesting issue is the role of the electronelectron interaction in such systems [1,2]. SO-coupled Fermi liquids (FLs) are expected to exhibit a rich variety of effects, which arise only from a combination of the electron-electron and SO interactions, such as spinsplit and Rashba phases [3,4], unusual Friedel oscillations [5,6], and spin textures [7], to name just a few. The focus of this Letter is on the collective excitations in a SO-coupled FL.

We extend the Fermi-liquid (FL) theory to include spin-orbit (SO) splitting of the energy bands, focusing on the Rashba SO coupling as an example. We construct the phenomenological Landau interaction function for such a system using the symmetry arguments and verify this construction by an explicit perturbative calculation. The Landau function is used to obtain the effective mass, compressibility, and stability conditions of the FL. It is shown that although the charge-sector properties, such as the effective mass and compressibility, are determined solely by well-defined quasiparticles, the spin-sector properties, such as the spin susceptibility, contain a contribution from damped states between the spin-split Fermi surfaces and thus cannot be fully described by the FL theory, except for the case of weak SO coupling. We derive some specific properties of a chiral FL and show, in particular, that for contact interaction spin-splitting of the Fermi velocities of Rashba subbands occurs because of the Kohn anomaly, also modified by SO coupling.

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