Current Density and Local Magnetic Field of Spontaneous Magnetization States in One-Dimensional Superconducting Corner Junction Arrays

Current density and local magnetic field of spontaneous magnetization states in one-dimensional superconducting connected corner-junction arrays have been analysed by solving the phase equation of the arrays. The solutions can be expressed by the Jacobian elliptic functions, which have been calculated numerically. Our results show that the corner fluxons with a fraction of half flux quantum are arranged in an antiferromagnetic fashion, which is in agreement with the recent experiments observed by Hilgenkamp et al. (Nature 422(2003)50). In addition, we present the magnetization flux of each corner junction in the array as a function of facet length.