Antiferromagnetic ordering in arrays of superconducting π-rings

Abstract

We report experiments in which continuous YBa2Cu3O7-δ-Nb junctions with internal sign changes in the Josephson coupling, as well as one-dimensional (1D) and two-dimensional (2D) arrays of YBa2Cu3O7-δ-Nb π-rings, are cooled through the superconducting transition temperature of the Nb in various magnetic fields. These systems have degenerate ground states with either clockwise or counter-clockwise spontaneous circulating supercurrents. The final flux state of each facet corner in the junctions and each ring in the arrays was determined using scanning superconducting quantum interference device (SQUID) microscopy. In the continuous junctions, fabricated with facets alternating between alignment parallel to a [100] axis of the YBCO and rotated 90° to that axis, half-fluxon Josephson vortices order strongly into an arrangement with alternating signs of their magnetic flux. We demonstrate that this ordering is driven by phase coupling and model the cooling process with a numerical solution of the Sine-Gordon equation. The 2D ring arrays couple to each other through the magnetic flux generated by the spontaneous supercurrents. Using π-rings for the 2D flux coupling experiments eliminates one source of static disorder seen in similar experiments using conventional superconducting rings [Davidovic, Phys. Rev. Lett. 76, 815 (1996)], since π-rings have doubly degenerate ground states in the absence of an applied field. Although anti-ferromagnetic ordering occurs, with larger negative bond orders than previously reported for arrays of conventional rings, ordering over more than a few lattice spacings is never observed in the 2D arrays, even in geometries without geometric frustration. Monte Carlo simulations of the 2D array cooling process are presented and compared with the experiment. © 2005 The American Physical Society.