  It is shown that incompressible spin quantum Hall magnetohydrodynamics allows
an exact solution for the propagation of a circularly polarized electromagnetic
wave. The solution is obtained assuming a condition between the fluid velocity
and the magnetic field which eliminates the nonlinear terms in Maxwell
equations. As a result of the coupling with spin, the propagation mode depends
on the amplitude of the magnetic field. From the full solution, the limits of
small and large wavenumber are studied obtaining linear and a nonlinear
spin-modified modes.
