The chiral magnetic nanomotorsElectronic supplementary information (ESI) available: Effectiveness of the rotating magnetic field vs. the gradient field for particle propulsion, rotation matrix definition, stability analysis of the low-frequency solution, estimates of the rotational viscous resistance coefficients of helix, helical geometries, numerical algorithm of chirality calculation and remanent magnetization of helices. See DOI: 10.1039/c3nr04853e

Propulsion of chiral magnetic nanomotors powered by a rotating magnetic field is in the focus of the modern biomedical applications. This technology relies on strong interactions of dynamic and magnetic degrees of freedom of the system. Here we study in detail various experimentally observed regimes of the helical nanomotor orientation and propulsion depending on the actuation frequency, and establish the relation of these two properties to the remanent magnetization and geometry of the helical nanomotors. The theoretical predictions for the transition between the regimes and nanomotor orientation and propulsion speed are in excellent agreement with available experimental data. The proposed theory offers a few simple guidelines towards the optimal design of the magnetic nanomotors. The analytical predictions for the orientation and propulsion velocity of externally driven chiral magnetic nanomotors show excellent agreement with available experimental results.