Vortices with antiferromagnetic cores in the SO(5) theory of high temperature superconductivity

We consider the problem of superconducting Ginzburg-Landau (G-L) vortices with antiferromagnetic cores which arise in Zhang's SO(5) model of antiferromagnetism (AF) and high temperature superconductivity (SC). This problem was previously considered by Arovas et al. who constructed approximate "variational" solutions, in the large kappa limit, to estimate the domain of stability of such vortices in the temperature-chemical potential phase diagram. By solving the G-L equations numerically for general kappa, we show that the amplitude of the antiferromagnetic component at the vortex core decreases to zero continuously at a critical value of the AF-SC anisotropy (g~0.25) which is essentially independent of kappa for large kappa. The magnetic field profile, the vortex line energy and the value of the B-field at the center of the vortex core, as functions of anisotropy are also presented.