Skyrmion lattice melting in the quantum Hall system

The melting and magnetic disordering of the Skyrmion lattice in the quantum Hall system at filling factor n'1 are studied. A Berezinskii-Kosterlitz-Thouless renormalization-group theory is employed to describe the coupled magnetic and translational degrees of freedom. The nontrivial magnetic properties of the Skyrmion system stem from the in-plane components of the noncollinear magnetization in the vicinity of Skyrmions, which are described by an antiferromagnetic XY model. In a Coulomb gas formulation the ‘‘particles’’ are the topological defects of the XY model ~vortices! and of the lattice ~dislocations and disclinations!. The latter frustrate the antiferromagnetic order and acquire fractional vorticity in order to minimize their energy. We find a number of melting/disordering scenarios for various lattice types. While these results do not depend on a particular model, we also consider a simple classical model for the Skyrmion system. It results in a rich T 50 phase diagram. We propose that the triangular and square Skyrmion lattices are generically separated by a centered rectangular phase in the quantum Hall system. @S0163-1829~98!01740-8#