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Dynamics and polarization of superparamagnetic chiral nanomotors in a rotating magnetic field

Externally powered magnetic nanomotors are of particular interest due to the potential use for \emph{in vivo} biomedical applications. Here we develop a theory for dynamics and polarization of recently fabricated superparamagnetic chiral nanomotors powered by a rotating magnetic field. We study in detail various experimentally observed regimes of the nanomotor dynamic orientation and propulsion and establish the dependence of these properties on polarization and geometry of the propellers. Based on the proposed theory we introduce a novel "steerability" parameter $γ$ that can be used to rank polarizable nanomotors by their propulsive capability. The theoretical predictions of the nanomotor orientation and propulsion speed are in excellent agreement with available experimental results. Lastly, we apply slender-body approximation to estimate polarization anisotropy and orientation of the easy-axis of superparamagnetic helical propellers.