Figure 1

Obtainable magnetization orientations of a helix coil. Micromagnetic simulations carried out on planar and coiled-up magnetic strips: (a) Initial magnetization is in-plane, perpendicular-to-strip (left); hollow-bar-magnetized helix coils can be created (right). (b) Initial magnetization is in-plane, parallel-to-strip (left), results in a corkscrew-magnetized coil (right). (c) An out-of-plane magnetized strip (left) assembles into a radial-magnetized coil (right). Simulation details are given in 15.Reuse & Permissions

Figure 2

Makeup and assembly of differently magnetized hybrid coils. (a) Composition of the different layer stacks for a hard out-of-plane or in-plane magnetized active layer. (b) Self-assembled coiling process: A photolithographic step defines the SU8 pattern. The active layer is deposited on top of this. The SU8 is delaminated from the substrate in $N$-methyl-2-pyrrolidone, causing the gradient strain between the SU8 and active layer to lead to a roll-up. (c) An optical image (i) and artist rendition (ii) of a hybrid helix coil with an SU8 organic outer layer and an inorganic magnetic (active) inner layer.Reuse & Permissions

Figure 3

Tracking of coil trajectory vs magnetized film orientation. (a) Coils with in-plane magnetized films in the parallel-to-strip direction exhibit forward dancing motion. (b) Coils with in-plane magnetized films in the perpendicular-to-strip direction exhibit end-over-end tumbling. (c) Straight and deterministic forward motion of coils with out-of-plane magnetized films.Reuse & Permissions

Figure 4

Response of radial-magnetized coils to an alternating external magnetic field. (a),(c) Optical microscopy images revealing the rotation of the coil over approximately 120° when the permanent magnet is rotated the same number of degrees. A tracking of either end of the coil can be made (red dotted line). The axis of the coil is oriented perpendicular to the field lines of the permanent magnet. (b),(d) Corresponding schematic images showing the coil’s rotation angle ${\Psi }_{\mathrm{coil}}$ after a rotation of the permanent magnet over the angle ${\theta }_{\mathrm{mag}}$. The uncompensated magnetic moment is indicated in yellow. (e) Time evolution of the coil’s rotation angle ${\Psi }_{\mathrm{coil}}$ for various rotation speeds of the permanent magnet ${\omega }_{\mathrm{mag}}$. The slope $\tau$ of each curve reveals the average rotation speed of the coil for a corresponding ${\omega }_{\mathrm{mag}}$. When ${\omega }_{\mathrm{mag}}\ge {\omega }_{\mathrm{mag}}^{\mathrm{transition}}$ (here $250°{\mathrm{s}}^{-1}<{\omega }_{\mathrm{mag}}^{\mathrm{transition}}<300°{\mathrm{s}}^{-1}$), the average rotational velocity of the coil drops off. (f) A close-up view of two full rotations of the coil for values of ${\omega }_{\mathrm{mag}}<{\omega }_{\mathrm{mag}}^{\mathrm{transition}}$ shows that the motion of the coil is rotative but not linear. (g) A close-up view for ${\omega }_{\mathrm{mag}}>{\omega }_{\mathrm{mag}}^{\mathrm{transition}}$ illustrates an oscillatorylike rotative motion of the coil.Reuse & Permissions