Phase diagram of a quantum Hall ferromagnet edge, spin-textured edges, and collective excitations

We study the electric and magnetic properties of the edge of a two-dimensional electron gas in the presence of a magnetic field and at filling factor unity. We obtain the phase diagram of the system as a function of the smoothness of the confining potential and of the Zeeman energy. The existence of a spin-textured edge is proved as a function of these parameters. We also calculate the low-energy excitations of the spin-textured phase. We obtain that in addition to the classical edge magnetoplasmons, at small wave vectors, there is an almost dispersionless excitation, with a finite gap of energy at zero wave vector. This excitation is associated with internal excitations of the spin-textured edge phase.