Mechanism of MRPs and their magnetically induced buckling. (a) Schematics to show the geometry of a Mie resonator pillar. (b) Numerically simulated acoustic pressure around an MRP at 9100 Hz. (c) Numerically calculated effective bulk modulus and density of an MRP in functions of the acoustic frequency. The shaded area indicates a regime with negative modulus and positive density. (d, e) Schematic and sample for an MRP array with a small spacing (). (f) Numerically simulated pressure of an acoustic wave moving through the MRP array with a small spacing (). (g) The experimentally measured and numerically simulated acoustic transmission of the MRP array with a small space in functions of the frequency. The shadowed area indicates the Mie resonance frequency regime. (h, i) Schematic and sample for an MRP array with a large spacing (). (j) Numerically simulated pressure of an acoustic wave moving through the MRP array with a large spacing (). (k) The experimentally measured and numerically simulated acoustic transmission of the MRP array with a large spacing in functions of the frequency. (l) Image sequence to show the magnetically induced bending of an MRP with increasing magnetic fields. The inset shows a schematic for the application of the magnetic field to the MRP. (m) Bending angles of MRPs with various volume fractions of the iron particle in functions of the magnetic field. The shaded area indicates the critical magnetic field . (n) The experimentally measured critical magnetic fields for various volume fractions of the iron particle in a function of , where is Young’s modulus of the elastomer and is the effective magnetic susceptibility difference. The error bars indicate the variation of the magnetic field within the shaded area in (m). Scale bars in (e) and (i) denote 1 cm.