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understanding and advancing magnetically manipulated liquid metals in soft robotics, offering fundamental insights
to stimulate interdisciplinary research and accelerate technological breakthroughs in this emerging field.

INTRODUCTION
Soft robots represent a transformative paradigm in robotics, leveraging compliant materials and bioinspired
architectures to achieve unprecedented adaptability in dynamic environments . Unlike rigid robots, soft
[1-5]
robots exploit continuum-body deformation and distributed actuation mechanisms to emulate biological
behaviors such as the multi-degree-of-freedom manipulation of the octopus . Moreover, their inherent
[6-8]
mechanical compliance enables safe interaction with fragile objects such as biological tissues and resilience to
collisions, while embodied intelligence allows environment-responsive motions without complex control
algorithms. Consequently, soft robots enable diverse and promising applications, including minimally
invasive surgery, confined-space search-and-rescue operations, and next-generation wearable assistive
devices [9-11] . Furthermore, soft robotics draws on advances in soft matter physics and flexible electronics to
address key challenges such as efficient actuation, scalable design, and adaptive control. Ultimately, these
developments envision robots that can integrate more naturally with living systems, particularly the human
body.

In recent years, liquid metals (LMs), particularly gallium-based alloys such as eutectic gallium-indium
(EGaIn) and gallium-indium-tin alloy (Galinstan), have emerged as a promising class of functional materials
for soft robotics [12-16] . LMs uniquely combine excellent adaptability of liquids with high electrical and thermal
conductivity of conventional metals, thereby offering a set of properties that are rarely observed in a single
material system. For instance, LMs remain fluid at or near room temperature, enabling extreme
deformability, self-healing capability, and conformability suited to complex geometries of the LM soft
robots [17,18] . The metallic-level conductivity allows their use in electrically controlled soft robots as stretchable
conductors, electrodes, and interconnects, with reliable signal transmission and efficient power delivery even
under large deformations [19-21] . Meanwhile, the high thermal conductivity makes LMs suitable for heat
dissipation and thermal management within soft robots, particularly in thermally driven modules and
high-power electronics [22,23] . Moreover, their facile processability and good compatibility further broaden
their utility, facilitating the development of multifunctional and highly integrated soft robots . Specifically,
[12]
LMs can be patterned and integrated with a wide range of soft substrates (e.g., elastomers and hydrogels)
using techniques such as direct injection, printing, or mixing [24-26] . These composite structures endow soft
robotic systems with additional capabilities such as multi-stimuli responsiveness [12,27-30] . Unlike conventional
mercury with high toxicity, gallium-based LMs show good biocompatibility potential for biomedical
applications [31-34] . Taken together, these comprehensive advantages position LMs as transformative materials
in advancing the performance, durability, and functionality of next-generation soft robotic systems.

These unique properties of LMs enable their versatile manipulation in soft robots through various
methods . For example, large deformation and directional locomotion can be achieved through
[14]
electrochemical oxidation [35-38] , Marangoni flow [39,40] , and magnetic manipulation [41-44] . Electrochemical
oxidation enables manipulation of LM by applying voltages to form surface oxidation and thus control
surface tension and morphology [35-38] . Marangoni flow drives the motion of the LM droplet, which is
generated by a surface tension gradient resulting from the asymmetric charge distribution under an applied
electric field [39,40] . Magnetic manipulation controls the movement and deformation of LM using external
magnetic fields, acting on either pre-added magnetic particles or internal currents [41-43] . Among various
manipulation methods, magnetic manipulation demonstrates unique comprehensive advantages and has
attracted significant research interest [1,41,42,45] . For instance, our previous work employed magnetic
manipulation to pattern LM to create flexible electronics, even on nonplanar substrates or within confined