Larmors theorem holds for magnetic systems that are invariant under spin rotation. In the presence of spin-orbit coupling this invariance is lost and Larmors theorem is broken: for systems of interacting electrons, this gives rise to a subtle interplay between the spin-orbit coupling acting on individual single-particle states and Coulomb many-body effects. We consider a quasi-two-dimensional, partially spin-polarized electron gas in a semiconductor quantum well in the presence of Rashba and Dresselhaus spin-orbit coupling. Using a linear-response approach based on time-dependent density-functional theory, we calculate the dispersions of spin-flip waves. We obtain analytic results for small wave vectors and up to second order in the Rashba and Dresselhaus coupling strengths $alpha$ and $beta$. Comparison with experimental data from inelastic light scattering allows us to extract $alpha$ and $beta$ as well as the spin-wave stiffness very accurately. We find significant deviations from the local density approximation for spin-dependent electron systems.
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