Discretized Motion of Surface Walker under a Nonuniform AC Magnetic Field

The motion of peanut-shaped magnetic microrods (PSMRs) with different magnetic moment (M_s) orientations φ_M under a nonuniform AC magnetic field has been investigated systematically. When gradually changing φ_M from 90° (perpendicular to the long axis of the PSMR) to 0°, the motion of the PSMR evolves from rolling to precession, then to tumbling. Systematic investigations on the translational velocity v_p versus the magnitude of the applied magnetic field B and the angular velocity ω_B show that the overall motion of the PSMRs can be divided into four different zones: Brownian motion zone, synchronized zone, asynchronized zone, and oscillation zone. The v_p-ω_B relationship can be rescaled by a critical frequency ω_c, which is determined by M_s, B, and a hydrodynamic term. An intrinsic quality factor q_m for the translational motion of a magnetically driven micro-/nanomotor is defined and is found to range from 0.73 to 13.65 T^-1 in the literature, while the Fe PSMRs in the current work give the highest q_m (= 25.48 T^-1). High speed movies reveal that both the tumbling and precession motions of the PSMRs have a discretized nature. At the instances when the magnetic field changes direction, the PSMR performs an instantaneous rotation and the strong hydrodynamic wall effect would impose a driving force to move the PSMR translationally, and about more than 60% of the time, the PSMR neither rotates nor moves translationally. Based on this discretized motion nature, an analytic expression for q_m is found to be determined by the shape of the surface walker, the hydrodynamics near a wall, and the magnetic properties of the surface walker. This work can help us to better understand the motion of magnetic surface walkers and gain insight into designing better micro-/nanomotors.