Stable rings formed by magnetization-controllable microspheres at zero field are observed and reported in this Rapid Communication. The magnetic microspheres were made by plating glass beads with a critical thickness of Ni film. We found that the ring leading to magnetic flux closure is the most stable configuration. At high concentrations, all individual rings, chains, and clusters join together to form a netlike structure. A computer simulation based on the dipole-dipole interaction, without thermal noise, has been carried out, and the results are in good agreement with the experimental observations. Based on an analytic approach we give a simple explanation of the formation and stability of rings.

• Received 5 November 1998

DOI:https://doi.org/10.1103/PhysRevE.59.R4758