  We present a Hartree-Fock study that incorporates the effects of Landau level
mixing and screening due to filled levels into the computation of energies and
states of quasiparticles in quantum Hall ferromagnets.
  We use it to construct a phase diagram for skyrmion stability as a function
of magnetic field and Zeeman coupling strengths. We find that Landau level
mixing tends to favor spin-polarized quasiparticles, while finite thickness
corrections favor skyrmions. Our studies show that skyrmion stability in high
Landau levels is very sensitive to the way in which electron-electron
interactions are modified by finite thickness, and indicate that it is crucial
to use models with realistic short distance behavior to get qualitatively
correct results.
  We find that recent experimental evidence for skyrmions in higher Landau
levels cannot be explained within our model.
