  Excitation with a massive spin reversal of the individual
skyrmion/antiskyrmion type is theoretically studied in a quantum Hall
ferromagnet, where the zero and first Landau levels are completely occupied
only by electrons with spins aligned strictly in the direction determined by
the magnetic field. The Wigner-Seitz parameter is not necessarily considered to
be small. The microscopic model in use is based on a reduced basic set of
quantum states [the so-called ''single-mode (single-exciton) approximation''],
which allows proper account to be taken for mixing of Landau levels, and
substantiating the equations of the classical $O(3)$ nonlinear $\sigma$ model.
The calculated ''spin stiffness'' determines the exchange gap for creating a
pair of skyrmion and antiskyrmion. This gap is significantly smaller than the
doubled cyclotron energy and the characteristic electron-electron correlation
energy. Besides, the skyrmion--antiskyrmion creation gap is much smaller than
the energy of creation of a separated electron--exchange-hole pair calculated
in the limit case of a spin magnetoexciton corresponding to an infinitely large
2D momentum. At a certain magnetic field (related to the 2D electron density in
the case of fixed filling factor $\nu$), the gap vanishes, which presumably
points to a Stoner transition of the quantum Hall ferromagnet to a paramagnetic
phase.
