Shape-morphing systems, which can perform complex tasks through morphological transformations, are of great interest for future applications in minimally invasive medicine1,2, soft robotics3,4,5,6, active metamaterials7 and smart surfaces8. With current fabrication methods, shape-morphing configurations have been embedded into structural design by, for example, spatial distribution of heterogeneous materials9,10,11,12,13,14, which cannot be altered once fabricated. The systems are therefore restricted to a single type of transformation that is predetermined by their geometry. Here we develop a strategy to encode multiple shape-morphing instructions into a micromachine by programming the magnetic configurations of arrays of single-domain nanomagnets on connected panels. This programming is achieved by applying a specific sequence of magnetic fields to nanomagnets with suitably tailored switching fields, and results in specific shape transformations of the customized micromachines under an applied magnetic field. Using this concept, we have built an assembly of modular units that can be programmed to morph into letters of the alphabet, and we have constructed a microscale ‘bird’ capable of complex behaviours, including ‘flapping’, ‘hovering’, ‘turning’ and ‘side-slipping’. This establishes a route for the creation of future intelligent microsystems that are reconfigurable and reprogrammable in situ, and that can therefore adapt to complex situations.
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All data generated or analysed during this study are included in the published article and its Supplementary Information, and are available from the corresponding authors on reasonable request.
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J.C. received support from the European Union’s Horizon 2020 Research and Innovation Programme under the Marie Skłodowska Curie Grant Agreement (number 701647). This work was financially supported by the European Research Council Advanced Grant–Soft MicroRobots (SOMBOT, number 743217), the Swiss National Science Foundation (number 200021_165564) and the National Natural Science Foundation of China (number 11702003). We thank A. Weber and V. Guzenko for helping with the development of the fabrication process. The sample fabrication was performed using the cleanroom facilities at the Laboratory for Micro- and Nanotechnology at the Paul Scherrer Institute, Switzerland.
The authors declare no competing interests.
Peer review information Nature thanks Je-Sung Koh, Xuanhe Zhao, and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Extended data figures and tables
a, Overview. b, Enlarged image corresponding to the dashed box in a. Shown are arrays of nanomagnets: in the array at top right, the lateral dimension of each nanomagnet is 520 nm × 60 nm; at bottom left, the lateral dimension of each nanomagnet is 398 nm × 80 nm. Scale bars: a, 4 µm; b, 2 µm.
a, Schematic of a stadium-shaped nanomagnet with length L, width d and thickness t. b, Schematic of the layout of the nanomagnet arrays with vertical separation s, and horizontal separation d/2. c, Relationship between d and L for nanomagnets with the same volume V0 and thickness t = 60 nm. Six nanomagnets with different aspect ratios are indicated on the curve (the dimensions of each magnet are indicated in nm); the colour of the points corresponds to colour of the hysteresis loops in Fig. 1c. Arrows indicate the four types of nanomagnet used in the micromachines (I–IV). d, Magneto-optical Kerr effect curves for the six differently sized nanomagnets in the field region where they switch (top panel) and the derivative with the switching region highlighted with shaded boxes (bottom panel). As the six switching regions do not overlap, all six nanomagnets can be individually programmed. e, SEM images of fabricated arrays of nanomagnets with lateral dimensions given in nanometres, corresponding to the six coloured points in c. Scale bar at bottom right (1 µm) applies to all six images.
a, Schematic of a single section of a spring. See Methods for nomenclature. b, SEM image of a two-panel device with an 8-turn spring. c, Schematic of two-panel devices with 2-, 4-, 6- and 8-turn spring designs. The turquoise and orange arrows represent the magnetization direction of the panels. d, Schematic of a two-panel device that folds when applying a controlling magnetic field B. See Methods for nomenclature. e, Optical microscope images of four fabricated devices with different numbers of turns in the spring design on application of a 5 mT controlling field. f, Predicted panel rotating angle versus applied magnetic field based on theoretical calculations of the two-panel devices with different numbers of turns. g, Measured panel rotating angle versus applied magnetic field for the fabricated devices with different numbers of hinge spring turns. Each data point corresponds to the average of three measurements of the angle using image analysis software. Error bars, ±1 s.d. Scale bars: b, 2 µm; e (applies to all images in e), 5 µm.
Extended Data Fig. 4 The 16 magnetization configurations of a four-panel micromachine and their corresponding shape transformation after applying a vertical controlling field.
The four background colours highlight the family of four distinct conformations demonstrated in Fig. 1c.
Extended Data Fig. 5 Four conformations of a micromachine consisting of a 3 × 3 assembly of four-panel modular units.
Shown in the middle and right panels are schematics and experimental demonstrations of the actuated micromachines. The units in a given micromachine all have the same conformation (left panel) corresponding to one of the 16 different magnetization configurations. Scale bars in the optical microscope images, 30 µm.
Extended Data Fig. 6 Four different modes, ‘P’, ‘X’, ‘O’ and ‘9’, encoded in the same micromachine design.
In the conjugate pairs (‘P’ and ‘9’, or ‘X’ and ‘O’), the ‘up’ and ‘down’ states of each unit are reversed. With a different nanomagnet encoding, a single micromachine with this design can transform between these four modes. See main text and Methods for details.
Extended Data Fig. 7 Possibilities for the total magnetic moments of the wing tip in the microscale ‘bird’.
a, SEM image of the wing tip of the microscale bird. Turquoise vertical bar, type II nanomagnets (398 nm × 80 nm); blue horizontal bar, type III nanomagnets (358 nm × 90 nm); purple bar (horizontal and vertical), type IV nanomagnets (300 nm × 110 nm). Each of the arrays has the same number of magnets (1,040) with the same magnetic moment m. b, Nine possible total magnetic moment magnitudes and directions. c, Schematics of 16 possible magnetic configurations of the wing tip. Each of the arrays of different types of nanomagnets (types II, III and IV) have different switching fields, and there are two out of the four arrays that have the same type IV magnets but with orthogonal orientation. Therefore, with the orientation of the nanomagnets in two of the arrays along the x direction and in the two other arrays along the y direction, there are in total 22 × 22 = 16 possible magnetic configurations that can be encoded into the wing tip. d, Schematics showing the magnitudes and directions of the total magnetic moment of the wing tip, corresponding to the 16 magnetic configurations shown in c. Scale bar in a, 4 µm.
The nanomagnets are fabricated using electron beam lithography, including patterning of a spin-coated polymer resist, thermal evaporation of a cobalt thin film and lift off. See Methods section ‘Sample fabrication’ for more details about the individual steps.
Extended Data Fig. 9 Optical microscope images of a four-panel micromachine, demonstrating operation in water and manipulation of polystyrene microbeads.
The micromachine is released in acetone and then a substitution of water for acetone is performed. The magnetization of all four panels points towards the centre. a, Micromachine in water without a magnetic field. b, The micromachine panels fold up in an applied out-of-plane magnetic field B of 10 mT. c, d, On application of a rotating magnetic field B (10 mT, 5 Hz), the micromachine rolls across the surface of a silicon wafer, and the rolling motion generates a vortex in the water surrounding it (highlighted with blue arrows). Polystyrene microbeads of 6 μm diameter (highlighted with red arrows) are trapped in the vortex and are transported to a new location. Two snapshots of the motion, separated by a time interval of 14 seconds, are shown. Scale bars, 40 µm.
Two rows of single-panel micromachines are shown, each suspended within a D-shaped ‘cutout’ in the silicon nitride membrane frame, and connected to it on the left side by hinge springs with two turns. Each panel is 10 µm × 10 µm in size. a, After fabrication, the panels are somewhat out-of-focus. This is because they are slightly tilted above the plane of the in-focus silicon nitride frame, which may be due to the residual stress in the hinge springs. The white arrows indicate the magnetization direction of the single-panel micromachines pointing left (top row) and right (bottom row). b, c, On slowly increasing the applied out-of-plane magnetic field, the panels tilt downwards (top row) or upwards (bottom row), with the tilt angle increasing as the field magnitude is increased. In the optical images, the panels with magnetization pointing to the left (top row) first become sharper (b), and they almost disappear at a tilt angle close to 90° at 35 mT (c). The panels with magnetization direction pointing to the right (bottom row) tilt upwards in the applied magnetic field, becoming less visible as the field is increased (b), until finally disappearing when the tilt angle is close to 90° at 35 mT (c). Scale bar (for a–c), 20 µm.
Transformations into the four types of conformation of a four-panel micromachine, which has (1) all four panels magnetized towards the centre, (2) three panels magnetized inwards and one panel magnetized outwards, (3-4) two panels magnetized inwards and the other two magnetized outwards. The micromachine is actuated using an applied magnetic field with the field direction given by the yellow bar at the top left of the video.
Transformations into the four types of conformation of the micromachine with a 3 × 3 assembly of the four-panel units. For each of the transformations, the units of the micromachine have (1) all four panels magnetized towards the centre, (2) three panels magnetized inwards and one panel magnetized outwards, (3-4) two panels magnetized inwards and the other two magnetized outwards. The micromachine is actuated using an applied magnetic field with the field direction given by the yellow bar at the top left of the video.
Transformations into ‘P’ and ‘X’ conformations of the micromachine when encoded with the corresponding magnetic configuration. The micromachine is actuated using an applied magnetic field with the field direction given by the yellow bar at the top left of the video. The direction and the magnitude of the magnetic field is varied to best demonstrate the transformation.
Transformations of the microscale bird encoded with ‘flapping’ behaviour and actuated with a slowly varying magnetic field, as well as with high frequency magnetic fields. The slowly varying field direction is given by the yellow bar at the top left of the video. At high frequencies, the movement is recorded for two different applied magnetic fields: 1 mT and 15 mT, oscillating at 1 Hz and 3.5 Hz respectively. The applied field direction in both cases is close to the out-of-plane direction.
Transformations of the microscale bird actuated with a slowly varying magnetic field and a high frequency field, demonstrating ‘hovering’ behaviour when actuated with the high frequency field. The slowly varying field direction is given by the yellow bar at the top left of the video. For the high frequency field, the magnitude is 1.5 mT, and its direction rotates back and forth through 180° at a frequency of 1 Hz. As shown in the video, the micromachine remains ‘flat’ when actuated with a slowly varying field; the ‘hovering’ occurs when applying a dynamic field. As a result of the different dimensions of the body and the wing panels, they rotate at different frequencies resulting in the ‘hovering’ behaviour.
Transformations of the microscale bird actuated with a slowly varying magnetic field and a high frequency field, demonstrating ‘turning’ behaviour when actuated with the high frequency field. The slowly varying field is applied out-of-plane. The high frequency field is applied close to the out-of-plane direction oscillating at 24.5 Hz with a magnitude of 11.6 mT. When actuated with the slowly varying field, a ‘twisting’ behaviour can be observed at the right wing of the bird due to the parallel magnetization of the neighbouring panels, while the left wing remains still relative to the body of the bird. This asymmetric motion of the right and left wings leads to a ‘turning’ behaviour when actuated with a high frequency field.
Transformations of the microscale bird actuated with a slowly varying magnetic field and a high frequency field, demonstrating ‘side-slipping’ behaviour when actuated with the high frequency field. The slowly varying field is applied out-of-plane. The high frequency field is applied close to the out-of-plane direction oscillating at 19.5 Hz with a magnitude of 6.2 mT. For the right wing, the angle between the magnetization on neighbouring panels is 45° and, when actuated by the slowly varying field, a ‘bending and twisting’ behaviour can be observed. For the left wing, only the left wing joint panel is magnetized and the left wing tip only moves passively as the left wing joint rotates. This asymmetric motion of the right and left wings leads to ‘side-slipping’ behaviour when actuated with a high frequency field.
Manipulation of 6 μm diameter Polystyrene microbeads with a four-panel micromachine in a rotating magnetic field (10 mT, 5 Hz). The field direction is indicated by the yellow bar at the top left of the video.
Operation of single-panel micromachines in air. The applied magnetic field is along the out-of-plane direction with its magnitude varying from 0 mT to 35 mT, and then back to 0 mT.
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Cui, J., Huang, T., Luo, Z. et al. Nanomagnetic encoding of shape-morphing micromachines. Nature 575, 164–168 (2019). https://doi.org/10.1038/s41586-019-1713-2
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