We consider the two-dimensional electron gas confined laterally to a narrow channel by a harmonic potential. As the Zeeman splitting matches the intersubband separation the nonlocal spin polarization develops a minimum as reported by Frolov et al. [Nature (London) 458, 868 (2009)]. This phenomenon termed Ballistic Spin Resonance is due to the degeneracy between the nearest oppositely polarized subbands that is lifted by spin-orbit coupling. We showed that the resonance survives the weak and short-range interaction. The latter detunes it and as a result shifts the Zeeman splitting at which the minimum in spin polarization occurs. Here this shift is attributed to the absence of Kohn theorem for the spin sloshing collective mode. We characterized the shift due to weak interaction qualitatively by analyzing the spin sloshing mode within the Fermi liquid phenomenology.
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