Microphotoluminescence mapping experiments were performed on a modulation
doped (Cd,Mn)Te quantum well exhibiting carrier induced ferromagnetism. The
zero field splitting that reveals the presence of a spontaneous magnetization
in the low-temperature phase, is measured locally; its fluctuations are
compared to those of the spin content and of the carrier density, also measured
spectroscopically in the same run. We show that the fluctuations of the carrier
density are the main mechanism responsible for the fluctuations of the
spontaneous magnetization in the ferromagnetic phase, while those of the Mn
spin density have no detectable effect at this scale of observation.Comment: 4 pages, 3 figure
