Massive spin-flip excitations in a $\nu = 2$ quantum Hall ferromagnet

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.