Torque-driven superparamagnetic microbots

Actuation powered by a rotating magnetic field is a promising method of controlled steering of micro(nano)metric synthetic propellers through fluids. Such actuation relies on a magnetic torque, which is a product of the driving field and a dipolar magnetic moment possessed by the micro-/nanopropeller of nontrivial shape allowing for rotation-translation coupling. While ferromagnetic (permanently magnetized) microbots have been studied extensively, superparamagnetic (susceptible to magnetization, not possessing remanent magnetization) did not get as much focus. Here, we present a general theory of torque-driven actuation and steering of magnetically polarizable micropropellers. The steady torque-driven rotation regimes and their stability are considered for microbots assuming cylindrical rotational anisotropy and for arbitrary geometry and orientation of the magnetization easy axis. Furthermore, we study in detail the dynamics of planar microbots made of isotropic superparamagnetic material, for which the magnetic anisotropy is being controlled entirely by the geometry. Planar geometry is interesting from a fundamental point of view (i.e., to establish the minimal requirements for steering of polarizable microbots) and for practical reasons due to easy of microfabrication via standard photolithography. It is demonstrated that stable torque-driven rotation resulting in net propulsion would require high degree of geometric and magnetic asymmetry, e.g., the L-shaped planar propeller with unequal arms, with a shorter arm made of superparamagnetic material, can be efficiently steered by a rotating magnetic field.