We demonstrate magnetophoretic conductor tracks that can transport single
magnetized beads and magnetically labeled single cells in a 3-dimensional
time-varying magnetic field. The vertical field bias, in addition to the
in-plane rotating field, has the advantage of reducing the attraction between
particles, which inhibits the formation of particle clusters. However, the
inclusion of a vertical field requires the re-design of magnetic track
geometries which can transport magnetized objects across the substrate.
Following insights from magnetic bubble technology, we found that successful
magnetic conductor geometries defined in soft magnetic materials must be
composed of alternating sections of positive and negative curvature. In addition
to the previously studied magnetic tracks taken from the magnetic bubble
literature, a drop-shape pattern was found to be even more adept at transporting
small magnetic beads and single cells. Symmetric patterns are shown to achieve
bi-directional conduction, whereas asymmetric patterns achieve unidirectional
conduction. These designs represent the electrical circuit corollaries of the
conductor and diode, respectively. Finally, we demonstrate biological
applications in transporting single cells and in the size based separation of
magnetic particles.