Rotationally induced magnetic chirality in clusters of single-domain permalloy islands and gapped nanorings*

We have studied magnetic moment configurations of clusters of single-domain ferromagnetic islands in different geometries.\footnote{J. Li , S. Zhang, J. Bartell, C. Nisoli, X. Ke, Paul E. Lammert, Vincent H. Crespi, and P. Schiffer, Physical Review B \textbf{82}, 134407 (2010).} The magnetic moments of these clusters are imaged by MFM after rotational demagnetization, following our previous protocols.\footnote{R. F. Wang, C. Nisoli, R. S. Freitas, J. Li, W. McConville, B. J. Cooley, M. S. Lund, N. Samarth, C. Leighton, V. H. Crespi, P. Schiffer, Nature \textbf{439}, 303 (2006).} We observed that two types of the clusters showed a significant imbalance of their two-fold degenerate ground states after demagnetization, and this inequality is correlated to the rotational direction of the demagnetization. A similar imbalance was also found in nano-scale rings with a small gap: the chirality of their magnetic state can be precisely controlled by the rotational direction during demagnetization.