Experimental Details

The particle preparation and experimental setup has been described in detail previously³⁹. In short, silica spheres with a diameter of d = (4.54 ± 0.45) μm have been coated on one hemisphere with a magnetic thin film according to an established recipe⁵⁶. The coating consists a multilayer stack of Ta(3.0 nm)/Pd(3.0 nm) [Co(0.28 nm)/Pd(0.9 nm)]₈/Pd(1.1 nm). This stacking is known to exhibit strong magnetic anisotropy where the easy axis points perpendicular to the film surface⁶¹. When depositing such a film on a spherical particle, the anisotropy axis points perpendicular to the particle surface. After magnetic saturation, the film becomes single domain⁶², which results in a radially symmetric anisotropy orientation across the particle surface⁵⁶. This anisotropy distribution has been confirmed also theoretically⁶³. Such a particle exhibits a stray field with dipolar characteristic, and the net dipole moment points perpendicular to the magnetic cap. A dilute suspension of such magnetically capped particles in distilled water is studied via transmission light microscopy. Following the density mismatch, the particles sediment on the bottom of the sample cell, which had been treated by plasma cleaning prior to sample preparation. To optimize the recording quality for digital image analysis, the microscopy illumination has been adjusted for homogeneous illumination via a condenser lense, and the sample has been aligned perpendicular to the light path using an adjustable stage. In addition, we have used a Lica objective (HC PL FL L 63x/0.70 CORR PH2) with an adjustable collar to correct for spherical aberration artifacts caused by the presence of the substrate glass. The attached digital camera (Leica DFC295) has a video resolution of 864 px × 648 px. An electromagnetic coil is mounted above the sample cell, providing perpendicular low-frequency fields. An additional set of two pairs of coils attached beneath the sample provide constant fields parallel to the sample plane. The microscopy recordings of single particles have been analyzed by optical image analysis using the open-source software ImageJ and the included plugin ‘particle analysis’. After converting the recordings into black-white threshold bitmaps, the ImageJ plugin measures the projected area of the transparent hemisphere of a particle over several oscillation cycles. Due to the stroboscopic microscopy recording with low frame rate (20 fps), one obtains an overlaid beat of the oscillating curve area vs. time. The minimum value of the area is extracted and, using a calibration curve, this value is correlated with an oscillation amplitude θ_A.