Opportunities and utilization of branching and step-out behavior in magnetic microswimmers with a nonlinear response

Microswimmers are smart devices with potential applications in medicine and biotechnology at the micrometer-scale. Magnetic micropropellers with their remote control via rotating magnetic fields are especially auspicious. Helicoidal propellers with a linear velocity-frequency dependence emerged as the standard propulsion mechanism over the last decade. However, with their functions becoming more pivotal on the way to practical uses, deviations in shape and swimming behavior are inevitable. Consequently, propellers with nonlinear velocity-frequency relationships arise that not only pose different challenges but also offer advanced possibilities. The most critical nonlinearities are the wobbling behavior with its solution branching that has potential for bimodal swimming and the swimming characteristics in the step-out regime that are essential for selection and swarm control. Here, we show experimentally and with numerical calculations how the previously unpredictable branching can be controlled and, thus, becomes utilizable with an example 3D-printed swimmer device. Additionally, we report how two step-out modes arise for propellers with a nonlinear velocity-frequency dependence that have the potential to accelerate future microswimmer sorting procedures.