Electromagnetic Interactions in the Quantum Hall Ferromagnet

Abstract

The $ν=1$ quantum Hall ground state in samples like GaAs is well known to be ferromagnetic. The global SU(2) spin symmetry of the microscopic action is broken down to a U(1) symmetry by the ground state. The Goldstone bosons corresponding to this spontaneous breaking of symmetry are the ferromagnetic magnons which are neutral spin waves. In addition, there are topologically nontrivial, electrically charged spin excitations known as spin skyrmions, which in these samples are the favoured charge carriers. In this letter, we look into the electromagnetic coupling of these spin excitations. The discrete symmetries P and T are also broken by the ground state and we find that to the leading order, the electromagnetic interaction of the spin waves occurs through a nonminimal coupling given by a Chern-Simons like term containing both the electromagnetic potentials and the two Euler angles that specify the coset SU(2)/U(1) and thereby, the Goldstone bosons.