SPATIAL SPIN DISTRIBUTION OF A SKYRMION IN A 2-DIMENSIONAL ELECTRON-GAS AT A SMALL G-FACTOR

The effect of a weak Zeeman spin splitting on the spatial distribution and the energy of an isolated skyrmion in a 2D electron gas under a s trong magnetic field at filling factor nu = 1 is studied within the fr amework of the Hartree-Fock approximation. Finite Zeeman splitting int roduces two different characteristic lengths into the problem, corresp onding to the tail and the core of the spin distribution. The non-line ar differential equation for the macroscopic spin density associated w ith the skyrmion is solved in the limit of very small g-factor, for wh ich the tail of the skyrmion is much longer than its core radius. In t his limit the Coulomb repulsion energy of the skyrmion, which determin es the core radius, does not affect the shape of the spin distribution .