The ordering of spontaneous magnetization moments in large-scale two-dimensional superconducting pgr-ring arrays
Large planar arrays of Josephson junctions form two-dimensional systems with many interesting properties, especially arrays containing superconducting pgr-junctions with unconventional superconducting d-wave symmetry. Here we present an analytical investigation of spontaneous magnetization in two-dimensional superconducting pgr-ring arrays, starting from an ansatz that each of the identical pgr-rings carries a magnetic flux with the same frustration index. Our results show that the flux structure with full antiparallel spontaneous magnetization is the most favourable of all possible arrangements in both square and triangular ring arrays. In a hexagonal pgr-ring (triangular flux) array, although there is no full antiparallel flux pattern, the antiparallel bond of nearest-neighbour spontaneous magnetization fluxes is still energetically favourable. These results are in agreement with those recently observed experimentally by Hilgenkamp et al (2003 Nature 422 50-3) in a triangular flux array.