Soft materials capable of transforming between three-dimensional (3D) shapes in response to stimuli such as light, heat, solvent, electric and magnetic fields have applications in diverse areas such as flexible electronics1,2, soft robotics3,4 and biomedicine5-7. In particular, magnetic fields offer a safe and effective manipulation method for biomedical applications, which typically require remote actuation in enclosed and confined spaces8-10. With advances in magnetic field control 11 , magnetically responsive soft materials have also evolved from embedding discrete magnets 12 or incorporating magnetic particles 13 into soft compounds to generating nonuniform magnetization profiles in polymeric sheets14,15. Here we report 3D printing of programmed ferromagnetic domains in soft materials that enable fast transformations between complex 3D shapes via magnetic actuation. Our approach is based on direct ink writing 16 of an elastomer composite containing ferromagnetic microparticles. By applying a magnetic field to the dispensing nozzle while printing 17 , we reorient particles along the applied field to impart patterned magnetic polarity to printed filaments. This method allows us to program ferromagnetic domains in complex 3D-printed soft materials, enabling a set of previously inaccessible modes of transformation, such as remotely controlled auxetic behaviours of mechanical metamaterials with negative Poisson's ratios. The actuation speed and power density of our printed soft materials with programmed ferromagnetic domains are orders of magnitude greater than existing 3D-printed active materials. We further demonstrate diverse functions derived from complex shape changes, including reconfigurable soft electronics, a mechanical metamaterial that can jump and a soft robot that crawls, rolls, catches fast-moving objects and transports a pharmaceutical dose.
