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Chen et al. Soft Sci. 2026, 6, 9 Page 11 of 36

In addition, multiple permanent magnets can be employed to generate more complex and programmable
magnetic field profiles, thereby inducing a richer diversity of deformation modes in the MLMs. For instance,
when two separated magnets are placed opposite each other, each attracts a portion of the magnetic particles
within the MLM droplet, thereby stretching the MLM droplet [Figure 5D] . Gradually increasing the
[89]
distance between two opposing magnets elongates the MLM until it ruptures, splitting it into two smaller
droplets. Similarly, when a single MLM droplet is exposed to a critical confining magnetic field generated by
two or four cylindrical permanent magnets aligned with identical polarity, it splits into two or four smaller
sub-droplets, respectively [Figure 5E] . In both cases, the splitting behavior results from a magnetic force
[87]
that exceeds the surface tension of the MLM.

Under a static external magnetic field, prominent particle alignment-induced significant modulus variation
[Figure 5F] , and Rosensweig instability-induced spike formation can also be observed in the MLMs
[90]
[91]
[Figure 5G] . The magnetically controlled modulus variation occurs due to the field-induced
microstructural reorganization of magnetic particles within the LMs. Upon application of an external
magnetic field, the particles become magnetized and experience strong dipole-dipole interactions. These
attractions cause the particles to rapidly align along the magnetic field lines, forming chain-like structures
[Figure 5F] . These structures create a solid-like network throughout the fluid volume, dramatically
[90]
increasing its resistance to deformation. Consequently, the macroscopic modulus, such as the shear modulus,
experiences a significant orders-of-magnitude increase, as the MLM transitions from a viscous liquid to a
viscoelastic solid. This effect can be enhanced by increasing the applied magnetic field.

Rosensweig instability-induced spike formation arises from a competition between magnetic and surface
energies [91,92] . When a vertical magnetic field is applied, the MLMs become magnetized and drive the system
toward minimal total energy. Surface tension and gravity promote a flat interface to minimize surface area
and potential energy. In contrast, the magnetic field encourages morphological deformation that lowers
magnetic reluctance. Above a critical field strength, the energy benefit from expelling magnetic flux exceeds
the energy cost of increased surface area and higher gravitational potential. This flux expulsion occurs
through the growth of peaks that extend into the air, which has higher magnetic permeability. The resulting
energy imbalance causes spontaneous symmetry breaking of the flat interface. This leads to the formation of
a regular array of sharp and stationary spikes [Figure 5G] .
[93]

Electromagnet manipulation
The electromagnet is a magnet in which the magnetic field is both generated and controlled by an electric
current flowing through a coiled wire, in accordance with Ampere’s circuital law. When an electric current
passes through a solenoid wound around a ferromagnetic core (e.g., Fe), it induces a magnetic field
proportional to the current. Different from the permanent magnets, electromagnets offer dynamic tunability,
allowing both field strength and polarity to be controlled via input current. This capability enables
programmable actuation and rapid switching, although it usually comes at the cost of increased energy
consumption and bulkier hardware.

A single electromagnet can offer little functional advantage over a permanent magnet for manipulating
MLMs. Consequently, arrays consisting of multiple independently addressable electromagnets are more
commonly employed, as they enable the generation of highly controllable, dynamic, and spatially complex
magnetic fields through precise modulation of the input currents. Similar to the manipulation using multiple
permanent magnets, the electromagnetic array can also manipulate the MLMs to execute diverse behaviors
such as 2D/3D locomotion, deformation, and separation [Figure 6A and B] [50,51] . Notably, the most
fundamental distinction between them is the dynamic reconfigurability of the magnetic field. An