Topological protected in nanomagnetism means that there are states associated to topological invariants, i.e. which don't depends of local physics as impurities or so on.
Thank you Daniel. Could you elaborate further as to why they do not depend on local physics. Are they stable energy configurations. What is the definition of impurities in the case of nano-magnetic devices ?
Zhang, Haijun, et al. Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface." Nature Physics 5, 2009, 438; Chen, Y. L., et al. Experimental realization of a three-dimensional topological insulator, Bi2Te3, Science, 325, 2009, 178. Hasan, M. Zahid, and Charles L. Kane. Colloquium: topological insulators, Reviews of Modern Physics, 82, 2010, 3045