1998/04/24 by Carsten Timm, S. M. Girvin, H. A. Fertig
Physics and Astronomy · #Antiferromagnetism #Classical XY model #Condensed matter physics #Lattice (music) #Magnetic field #Phase (matter) #Phase diagram #Phase transition #Physics #Physics of Superconductivity and Magnetism #Quantum Hall effect #Quantum and electron transport phenomena #Quantum mechanics #Renormalization group #Skyrmion #Theoretical and Computational Physics #cond-mat.mes-hall
paper · pdf · doi:10.1103/physrevb.58.10634
published as Phys. Rev. B 58, 10 634 (1998) · 15 pages with 5 figures. Minor revisions. Important reference to M. Rao, S. Sengupta, and R. Shankar, Phys. Rev. Lett. 79, 3998 (1997) added
arxiv created 1998/04/24 · openalex publication_date 1998/10/15 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The melting and magnetic disordering of the Skyrmion lattice in the quantum Hall system at filling factor \ensuremathν\ensuremath≈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=0 phase diagram. We propose that the triangular and square Skyrmion lattices are generically separated by a centered rectangular phase in the quantum Hall system.