  Coulomb exchange interactions of electrons in the nu=3 quantum Hall state are
determined from two inter-Landau level spin-flip excitations measured by
resonant inelastic light scattering. The two coupled collective excitations are
linked to inter-Landau level spin-flip transitions arising from the N=0 and N=1
Landau levels. The strong repulsion between the two spin-flip modes in the
long-wave limit is clearly manifested in spectra displaying Coulomb exchange
contributions that are comparable to the exchange energy for the quantum Hall
state at nu=1. Theoretical calculations within the Hartree-Fock approximation
are in a good agreement with measured energies of spin-flip collective
excitations.
