  We perform a magneto-optical study of a two-dimensional electron systems
(2DES) in the regime of the Stoner ferromagnetic instability for even quantum
Hall filling factors on Mg$_x$Zn$_{1-x}$O/ZnO heterostructures. Under
conditions of Landau-level crossing, caused by enhanced spin susceptibility in
combination with the tilting of the magnetic field, the transition between two
rivaling phases- paramagnetic and ferromagnetic- is traced in terms of optical
spectra reconstruction. Synchronous sharp transformations are observed both in
the photoluminescence structure and parameters of collective excitations upon
transition from paramagnetic to ferromagnetic ordering. Based on these
measurements, a phase diagram is constructed in terms of the 2D electron
density and tilt angle of the magnetic field. Apart from stable paramagnetic
and ferromagnetic phases, an instability region is found at intermediate
parameters with the Stoner transition occurring at $\nu\approx 2$. The spin
configuration in all cases is unambiguously determined by means of inelastic
light scattering by spin-sensitive collective excitations. One indicator of the
spin ordering is the intra-Landau-level spin exciton, which acquires a large
spectral weight in the ferromagnetic phases. The other - is an abrupt energy
shift of the intersubband charge density excitation due to change in the
many-particle energy contribution upon spin rearrangement. From our analysis of
photoluminescence and light scattering data, we estimate the ratio of surface
areas occupied by the domains of the two phases in the vicinity of a transition
point. In addition, the thermal smearing of a phase transition is
characterized.
