Section S1- Fabrication method
In this section, we would first elaborate on the fabrication process of
our proposed soft MMR (section S1A). Subsequently, we discussed about
the experiments that evaluated the proposed MMR’s material properties
(section S1B).
A. Fabrication of six-DOF soft MMR
The detailed dimensions of our six-DOF MMR could be found in Fig. S1. To
fabricate the proposed MMR, we first constructed its magnetic soft beam
component. This soft component was molded by embedding hard magnetic
microparticles (NdFeB, average diameter: 5 µm) into the liquid polymer
matrix (Ecoflex 00-10) with a 4:1 mass ratio. The mixture was then cured
in an oven for two hours at 80 °C. Once the beam was molded (Fig.
S2A), it was rolled in a cylindrical jig and subsequently magnetized by
a strong, uniform magnetic field of 1.1 T (Fig. S2B). After this
magnetization process, the magnetized beam would be endowed with its
desired harmonic magnetization profile (\(\vec{M}\), \(\varphi=\) 90° ) after it recovered to its original configuration
(Fig. S2C). Two identical buoyant components, made from Styrofoam and
cut to their desired geometry, were each adhesively bonded to the free
ends of the magnetic soft beam to form the proposed MMR (Fig. S1). For
the experiment in Fig. 6D, the buoyant components were also coated with
a thin layer of Ecoflex 00-10 to make their surfaces hydrophobic.
B. Characterization of the magnetic soft beam’s material properties
Here we conducted a simple experiment to evaluate the\(\left|\vec{M}\right|\) of our magnetic soft beam. Five
cuboid samples were constructed by the same material used for
fabricating our magnetic soft beam, and these samples had the following
dimensions: 6 mm length (\(L_{\text{sp}}\)), 4 mm width
(\(w_{\text{sp}}\)) and 1 mm thickness (\(t_{\text{sp}}\)) (Fig. S3A).
The samples were magnetized by a strong, uniform magnetic field of 1.1 T along their length, and their weights (\(W\)) were
measured by a high-precision weighing scale (A&D GH-120). Different
rotary equilibrium states could be established when the samples were
subjected to a \(\vec{B}\), which was inclined at 45° from
the horizontal plane, with varying magnitudes from 4 mT to 6 mT (Fig. S3B). As the rigid-body torque induced by the
samples’ weight would make the net magnetic moment of the samples
(\({\vec{m}}_{\text{sp}}\)) misalign with the applied \(\vec{B}\), we could use a camera to record the misalignment
angle, \(\varnothing\), between \({\vec{m}}_{\text{sp}}\) and \(\vec{B}\) (Fig. S3B). By performing a torque equilibrium
analysis on the samples (Fig. S3B), the following governing equation
could be obtained:
\[\begin{equation}
\left|{\vec{m}}_{\text{sp}}\right|\left|\vec{B}\right|\sin\varnothing=Wr_{0}\cos{\Gamma,}\nonumber \\
\end{equation}\]
where
\[\begin{equation}
\begin{matrix}r_{0}=\frac{\sqrt{{L_{\text{sp}}}^{2}+{t_{\text{sp}}}^{2}}}{2}\ .\left(S1.1\right)\\
\end{matrix}\nonumber \\
\end{equation}\]
The parameter \(r_{0}\) represented the distance between the samples’
center of mass and anchor point, and \(\Gamma\) represented the angle
between the inclined samples and the substrate (Fig. S3B). Since the
samples’ \(\left|\vec{M}\right|\) could be computed as \(\frac{\left|{\vec{m}}_{\text{sp}}\right|}{V_{\text{sp}}}\),
where \(V_{\text{sp}}\) represented the volume of the cuboid samples, we
could rearrange Eq. (S1.1) to evaluate\(\left|\vec{M}\right|\):
\[\begin{equation}
\begin{matrix}\frac{Wr_{0}\cos\Gamma}{V_{\text{sp}}\sin\varnothing}=\left|\vec{M}\right|\left|\vec{B}\right|.\left(S1.2\right)\\
\end{matrix}\nonumber \\
\end{equation}\]
Using Eq. (S1.2), we plotted \(\frac{Wr_{0}\cos\Gamma}{V_{\text{sp}}\sin\varnothing}\) against\(\left|\vec{B}\right|\) to determine the experimentally
obtained \(\left|\vec{M}\right|\) via the gradient of the
best fit line of these data (Fig. S3C). Using this analysis, we
evaluated the \(\left|\vec{M}\right|\) of our material to
be 9.40\(\times\)104 A m-1 when it was magnetized by a 1.1 T magnetic field.
In addition, we also evaluated the Young’s modulus of the magnetic soft
beam to be 271 \(\pm\) 11.7 kPa via a standard compression test
(SHIMADZU AG-X plus, 10 kN).