# Encoding magnetic anisotropies in digital light processing 3D printing

Eléonore Aïdonidis, Andrea Cosola, Pierre Bourdon, Hichem Dammak, Marco Sangermano, Frédéric Demoly, Marco Faustini, Amélie Pérot, Didier Lairez, Rakine Mouhoubi, et al.

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Eléonore Aïdonidis, Andrea Cosola, Pierre Bourdon, Hichem Dammak, Marco Sangermano, et al. "Encoding magnetic anisotropies in digital light processing 3D printing." Advanced Functional Materials, 2025, 2025, pp.e23995. 10.1002/adfm.202523995. hal-05384939

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Submitted on 27 Nov 2025

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WILEY-VCH

Encoding Magnetic Anisotropies in Digital Light Processing 3D Printing

Eléonore Aïdonidis, Andrea Cosola, Pierre Bourdon, Hichem Dammak, Marco Sangermano, Frédéric Demoly, Marco Faustini, Amélie Pérot, Didier Lairez, Rakine Mouhoubi, Sébastien Blanquer, and Giancarlo Rizza*

E. Aïdonidis, A. Cosola, P. Bourdon, Didier Lairez, G. Rizza,
Laboratoire des Solides Irradies (LSI)
CEA/DRF/IRAMIS
Ecole Polytechnique
Institut Polytechnique de Paris
Palaiseau 91128, France

E-mail: giancarlo.rizza@polytechnique.edu

A. Cosola, M. Sangermano
Department of Applied Science and Technology
Politecnico di Torino
Corso Duca degli Abruzzi 24,
Torino 10129, Italy

H. Dammak
Laboratoire Structures Propriétés et Modélisation des Solides (SPMS),
Université Paris-Saclay, CentraleSupélec, CNRS
Gif-sur-Yvette F 91190, France

F. Demoly
Université Marie et Louis Pasteur, UTBM, CNRS, ICB UMR 6303, 90010 Belfort, France

F. Demoly
Université Bourgogne Europe, CNRS, Laboratoire Interdisciplinaire Carnot de Bourgogne ICB
UMR 6303, 21000 Dijon, France

M. Faustini, A Pérot
Sorbonne Université, CNRS, UMR 7574
Chimie de la Matière Condensée de Paris
Paris F-75005, France

M. Faustini, F. Demoly
Institut Universitaire de France
Paris 75231, France

Rakine Mouhoubi, Sébastien Blanquer
CNRS, Université de Montpellier
ENSCM
Montpellier, France
**Funding:** This work has been funded by the National Research Agency (ANR) through the France 2030 program PEPR DIADEM Artemis (ANR-22-PEXD-0016), and by the Commissariat a l'Energie Atomique et aux Energies Alternatives (CEA) through the project Functional-DLP of the Program Transversal de Competences (PTC). Simulations were made possible through the support of "Mésocentre" computing center of CentraleSupélec and Ecole Normale Supérieure Paris-Saclay supported by CNRS and Région Ile-de-France (http://mesocentre.centralesupelec.fr/). This research benefited from the support of the École Polytechnique fundraising initiative, Smart Environments: Nanosensors and Nanoreliability, through the use of the PLATINE platform. The WAXS measurements were made possible thanks to the support of the SWAXS platform, part of the PEPR DIADEM program (ANR-22- PEXD-0001). The magnetic device, designed for integration with additive manufacturing systems to enable magnetically-assisted 3D printing, has been patented under No. WO2025073835A1. [1]

**Keywords:** (Digital Light Processing, Magnetic 3D printing, 4D Printing, Liquid Crystal Elastomers (LCE), Thermal Actuation, Magnetic Actuation, Thermo-magnetic Actuation)

**Abstract text.** Magnetic fields are increasingly used in 4D printing to program matter across multiple length scales, enabling control over both macroscopic structures and nanoscale particle organization. However, their integration into additive manufacturing remains limited by compatibility constraints—such as interference with extrusion or optical access—and the inherent challenge of generating spatially resolved, dynamic magnetic fields. In this work, we introduce a digital light processing 3D printing method that directly encodes programmable magnetic anisotropy during fabrication. By formulating a photocurable resin with magnetic nanoparticles and liquid crystal monomers, we fabricate composite structures that respond to both magnetic and thermal stimuli. A hybrid magnetic system—combining a nested Halbach array with a coaxial coil placed in its inner cavity—enables real-time, 3D control of magnetic fields (in both direction and intensity) during the printing process. This approach enables the alignment of liquid crystal mesogens, magnetic fillers, and the formation of vertically oriented nanoparticle chains. The resulting materials exhibit direction-dependent actuation, shape reconfiguration, and selective conductivity, demonstrating a versatile platform for creating multifunctional and multi-stimuli-responsive devices.

E. Aïdonidis and A. Cosola contributed equally to the paper
# 1. Introduction

The functional properties of a material refer to its capacity to interact with the surrounding environment and respond dynamically to external stimuli, such as temperature, light, [2] pH, [3] mechanical forces, [4] or even electric[5,6] and magnetic fields. [7] Integrating such materials into additive manufacturing —especially within the scope of 4D printing— opens the path to constructing structures capable of shape change or property modulation over time in response to specific triggers. [8–17] Among the various classes of smart materials for 3D printing, polymers are the most commonly employed. Their processability through extrusion-based (e.g., fused filament fabrication -FDM, direct ink writing -DIW) and vat photopolymerization (e.g., stereolithography -SLA, digital light processing -DLP, two-photon polymerization –2PP) methods makes them suitable for fabricating complex architectures. [18–20] However, the performance of 4D-printed polymer structures is often constrained by limited mechanical strength or functional responsiveness. [21–25] A widely adopted strategy to overcome these limitations and improve the material’s properties involves incorporating fillers —such as nanoparticles, fibers, or platelets— into the polymeric matrix to create nanocomposite systems.

[26–29] The potential of these materials is further enhanced if embedded fillers can be manipulated to create well-ordered and/or anisotropic structures within the 3D-printed construct. In particular, this task can be accomplished by applying external forces or energies to drive the micro-to-nanoscale arrangement of nanomaterials within the printed structures. [30-45] Beyond the addition of fillers, however, an equally crucial strategy to improve the polymer physicochemical, mechanical, and functional properties involves the structuring and anisotropic organization of the polymer matrix itself. In this context, external fields can also be employed to align mesophases, liquid crystal domains, or polymer chains within the host matrix. [46-48] Such control at the molecular or supramolecular level can impart directional mechanical and actuation properties to the 4D-printed object. In particular, magnetic fields show great potential in this dual role, as they can drive the self-assembly of magneto-responsive particles (e.g., Fe₃O₄ nanoparticles), as well as orient domains within a magneto-sensitive polymeric matrix, such as a liquid crystal elastomer (LCE). [49-51]

This enables the programming of bulk anisotropy and facilitates the fabrication of structures with spatially varying mechanical or actuation responses.

Liquid Crystal Elastomers (LCEs) are a pivotal class of smart polymers, valued because their precise, programmable shape changes depend entirely on controlling the internal mesogen alignment. Historically, conventional methods like mechanical, surface, and rheological
alignment [52–55] struggle to impose this molecular order reliably within complex 3D printed architectures. The breakthrough lies in leveraging the material's magneto-responsiveness. LCE precursors possess an intrinsic diamagnetic susceptibility due to their aromatic structure, meaning their mesogens naturally align parallel to an applied magnetic field. [47] This magnetic field alignment is uniquely effective because it allows for the precise tuning of the molecular director throughout the material's bulk, without physically constraining the final part's geometry.

[56] By integrating this magnetic control with vat photopolymerization (DLP), researchers can now create complex, highly functional magneto-responsive 3D structures. This synergy offers unprecedented spatial resolution and versatility, opening new frontiers for stimuli-responsive materials. [57–59]

On this basis, by combining field-assisted alignment of both the fillers and the matrix, one can adopt a multiscale design approach that bridges molecular orientation and macroscopic geometry. This unlocks new possibilities for the creation of highly heterogeneous, multifunctional devices—from soft robots to adaptive optics and tissue scaffolds—where local structure governs global function. Recently, a first attempt to encode both micro- and macro-structural anisotropies has been reported using extrusion-based DIW 3D printing of LCE matrices containing $Fe_3O_4$ nanoparticles. [60,61] However, the alignment relied on two distinct stimuli: shear forces during extrusion were used to orient the mesogens of the LCE matrix, while an external magnetic field directed the alignment of the magnetic fillers. In this work, we demonstrate that a single stimulus, such as —the applied magnetic field— can be used to program both micro- and macro-scale anisotropies by selectively tuning its parameters to control the orientation of either the matrix or the embedded fillers.

Recent advances in magnetically-driven 3D printing have introduced various methods for controlling magnetic fields during fabrication. These approaches fall into two main categories: systems using permanent magnets and those based on electromagnets —each offering trade-offs in cost, flexibility, and integration. The simplest setup uses a single permanent magnet, providing a compact and low-cost solution that can generate strong static fields (often >1 T). However, it only allows binary orientation (north/south) and suffers from non-uniform field distribution beyond the magnet's surface, where the field decays rapidly ($\propto r^{-3}$). This creates undesirable gradients, leading to uneven filler distribution and unpredictable forces in printed objects. Additionally, adjusting the field strength requires physically repositioning the magnet —a challenge in setups like DLP printers, where magnets can block light if placed above the vat. These limitations restrict permanent magnets mainly to configurations below the vat with top-down illumination. [62,63] To address spatial limitations, multi-magnet systems have been
introduced. Configurations such as coaxial N–S magnet pairs, often coupled with motorized
rotation stages, produce more uniform fields and allow directional control. The use of this
approach has been recently reported for the magnetic alignment of LCE mesogens using DLP
printers, [59]. Electromagnets, by contrast, allow tunable field direction and strength via electric
currents. Though typically limited to ~20 mT due to power constraints, they are easy to integrate
into 3D printers. Kim *et al* used a single-coil setup in DIW to reorient magnetic particles near
the nozzle. [64] More advanced systems include Helmholtz coils, where two identical coils
generate a uniform central field. Martin *et al* used a three-axis Helmholtz-DLP system for
dynamic alignment of iron oxide-coated alumina microparticles [65] while Nakamoto *et al*
employed five coils in SLA to align fibers vertically. [66] Emerging non-orthogonal
electromagnet configurations offer more complex field geometries. Dai et al. demonstrated this
in a robotic actuator with three magnetically controlled legs. [67] Finally, Halbach arrays have
been recently used. [68] This principle traces back to John C. Mallison, who, in 1973, introduced
the idea of single-sided flux for a planar magnetic arrangement with a constant-amplitude
rotating vector magnetization.[69] This principle was later extended by Halbach to permanent
multipole magnets by implementing the system for a loop configuration. [70]

Based on the insights from the preceding critical reviews that assessed the potential and
limitations of current approaches to encoding magnetic anisotropies during 3D printing —we
present a novel hybrid magnetic device designed to overcome key challenges, as illustrated in
**Figure 1a,c**. This device combines the advantages of nested Halbach arrays and magnetic coils,
enabling precise control over the homogeneity, spatial orientation, and intensity of the magnetic
field, offering the unique opportunity to turn the field on and off at will at any time during the
printing process. [1] It is robust, cost-effective, and fully compatible with vat
photopolymerization-based additive manufacturing. Details of the experimental setup,
numerical simulations, and integration of the device into a commercial DLP printer are provided
in the Supplementary Information (SI). As a proof of concept, we demonstrate its use in
fabricating programmable magneto-responsive structures, including multimodal actuators with
multifunctional tunable directional response (**Figure 1d-f**, **Figure 3**, and **Figure 4**), and
vertically stacked, electrically conductive nanostructures (**Figure 5**).
<figure><img src="image_2.png" /><figcaption>**Figure 1.** Hybrid magnetic device to fabricate programmable 4D-printed structures. (a) schematic of the DLP printer integrating the device, allowing (b) the magnetic field control in the horizontal plane using a nested Halbach array (in red), and (c) in the vertical direction using a coaxial coil (in red) within the central region of the nested Halbach array. The direction of the field is indicated by the arrows. (d-f) Designs of the printed structures, their relative orientation within the Halbach arrays and the expected deformations. (d1-4) cross-shaped. (e1-4) Y-shaped tripod with arms positioned at 90° and 135°, and (e5-6) all three arms spaced at 120° angle. (f1-3) hexapod shaped where all arms are spaced at 60°. M1 to M9 represent the activation modes resulting from the combination of printed structures (cross, Y-shaped tripod, and hexapod) with different Halbach array configurations (dipolar, quadrupolar, and hexapolar).</figcaption></figure>

## 2. Results and Discussion

### 2.1 Strategy for Encoding Multimodal and Multifunctional Bending Actuations

Multimodal bending refers to the ability of a structure to undergo multiple, directionally distinct bending deformations in response to external stimuli. In printed structures, this control can be achieved by choosing specific Halbach array configurations, each of which generates a distinct magnetic field pattern that determines the resulting magnetic anisotropy. As described in Supplementay Information (SI), Halbach cylinder can be segmented into *P* identical magnets having the same strength but a different planar orientation φ, set by the rule φ=(k+1)θ, where θ is the magnet's position around the cylindrical array. [68,71,72] The value of the integer number *k* controls the magnetic field shape within the cylinder: *k*=1 generates a uniform (dipolar) field, while *k*=2 and *k*=3 create more complex (quadrupolar and hexapolar) fields with increasing spatial gradients. Finally, the combination of two Halbach arrays in nested coaxial configuration, can be used to tune both the field intensity and direction in the *x*-y plane.

To exploit these tunable characteristics and highlight the system's multimodal capabilities (activation directions), four structures were designed (Figure 1). The first one is a symmetric cross, consisting of four segments (arms) of equal length (Figure 1d1), the second consists of
a tripod arranged in a Y-shape, with two possible sub-configurations: either two arms positioned at a 90° angle, or all three arms spaced at 120°, as depicted in **Figure 1e1** and **Figure 1e6**. The last one is a hexapod with six arms evenly spaced at 60° in a radial pattern, (**Figure 1f1**). **Figure 1d2** to **Figure 1f3** illustrate how the encoding of distinct deformation modes is enabled by the orientation of these structures relative to the magnetic field lines produced by Halbach arrays. For instance, three activation modes (M1, M2, and M3) would be encoded by the cross structure. Modes M1 and M2 utilize a dipolar Halbach configuration: in M1, the magnetic field lines align with the long axis of two arms and the short axis of the other two (**Figure 1d2**, Movie S10, Supporting Information); in M2, the cross is rotated so that all four arms are positioned at 45° to the field lines (**Figure 1d3**). Mode M3 employs a quadripolar Halbach configuration, aligning the magnetic field along the long axis of all four arms (**Figure 1d4**, Movie S12, Supporting Information). The Y-shaped structure has a configuration that permits greater flexibility and demonstrates four activation modes (M4, M5, M6, and M7). M4 mode uses dipolar Halbach setup to align a single arm with the field while the other two sit at 45° (**Figure 1e2**). By rotating the structure by 45°, mode M5 allows for three different alignments, where one arm is parallel (0°), one normal (90°), and one at 45° to the applied field (**Figure 1e3**). M6 is based on a quadripolar Halbach configuration where two arms are aligned with the field and the third one unaligned (**Figure 1e4**). Finally, for mode M7 all three arms are spaced at 120° and a hexapolar Halbach configuration is used such that all the arms are aligned along the field (**Figure 1e5**). The hexapod structure supports two activation modes (M8 and M9). In M8, a dipolar Halbach configuration aligns two arms with the field and the remaining four at 60° (**Figure 1f2**, Movie S11, Supporting Information), whereas M9 uses a hexapolar Halbach configuration to align all six arms with the magnetic field (**Figure 1f3**).

After establishing the strategy to introduce directional magnetic anisotropies, the next objective is to demonstrate multifunctionality. Specifically, this involves showing that directional (multimodal) deformations can be triggered by various stimuli. This is done by using photocurable LCs. Notably, LCEs exhibit distinct phases based on the ordering of their mesogens. [47,73] In the nematic phase, the mesogens align to produce long-range orientational order and anisotropic properties, which is defined as nematic monodomain state; whereas in the isotropic phase, the mesogens are randomly oriented, resulting in isotropic behavior of the material. LCE actuate by undergoing a reversible shape change when their mesogens transition from an ordered nematic phase to a disordered isotropic phase, causing the polymer network to deform. Multifunctionality can be achieved by appropriately tuning the formulation so that the LC resin can be printed in either the nematic or the isotropic phase, as illustrated in **Figure 2**.
When printed in the nematic phase (Figure 2b), actuation is driven by thermal stimuli that induce nematic-to-isotropic phase transitions. Conversely, when printed in the isotropic phase in presence of toluene, the mesogens are not aligned in monodomain state and thermal actuation is not possible (Figure 2c). In this case, the LC resin serves simply as a soft, inert matrix for dispersing nanofillers. If these nanofillers are magnetic nanoparticles, the resulting elastomeric material becomes magneto-active. Finally, the application of a specific magnetic field is required to achieve either thermal or magnetic responsiveness in a multimodal construct, which can be generated by appropriately rotating two nested Halbach arrays (Figure 2d).

<figure><img src="image_3.png" /><figcaption>**Figure 2.** Phase diagram of liquid crystal organization showing the two photocurable resins used to create (a) thermally (RM257+EDDET+E7+BAPO) and (b) magnetically (RM257+EDDET+BHT+Toluene+BAPO) responsive 3D-printed features. (c) Nested Halbach cylinder configuration with co-aligned magnetic fields,</figcaption></figure>
generating a field intensity of 100 mT, used for fabricating thermo-responsive features. B₀ = 50 mT represents the maximum magnetic field generated by each Halbach array. The nested configuration, in which the arrays are rotated by ±θ respectively, produces a total field B = 2B₀ cos θ. (d) Nested configuration with two co-aligned Halbach arrays (θ =0°) generates a field intensity of 100 mT, while when they are rotated by 84° in clockwise and anticlockwise directions, a field intensity of 10 mT is produced. The former configuration is used to produce thermo-magnetic element, whereas the latter for fabricating magneto-responsive features

**2.2 Multimodal Thermo-Responsive LCE Actuations**

To fabricate the nematic LCE networks, we employed a photopolymerization process based on
acrylate–thiol chain transfer [74] (Figure 2b). The mesogenic diacrylate RM257 (1,4-Bis[4-(3-
acryloyloxypropyloxy)benzoyloxy]-2-methylbenzene) was used as the primary monomer, and
EDDET (2,2'-(ethylenedioxy)diethanethiol) served as the dithiol chain extender. Since RM257
alone does not exhibit a nematic phase below its melting point (Tm~69 °C), we added a non-
reactive mesogenic solvent E7 (4-cyano-4'-pentylbiphenyl) at a 1:1.5 weight ratio to obtain a
stable nematic phase at room temperature. The presence of this nematic phase at room
temperature is essential for aligning the mesogens under an external magnetic field during
printing — an effect supported by previous work, [47] and experimentally confirmed by
polarized optical microscopy (POM) and wide-angle X-ray scattering (WAXS), as shown in
Figures S10, S20. Moreover, differential scanning calorimetry (DSC) analysis showed a
decrease in the nematic–isotropic transition temperature of the mixture to Tni = 68.8 °C,
compared to Tni~126 °C for pure RM257 (Figure S9, Supporting Information).

Recent studies have shown that a field strength of approximately 100 mT is necessary to achieve effective nematic alignment. [57,75] However, as the magnetic field strength decreases with distance (B~r⁻³), where r is the inner radius of the Halbach array, achieving high field intensities with a Halbach array requires reducing its inner diameter, which in turn limits the printable surface area. To address this point, concentric Halbach arrays in nested configuration were designed and for the first time implemented in a DLP printer (Figure 2b,d and Section S.1 in SI). This design enhances the magnetic field by leveraging the principle of vectorial superposition. This approach enables reaching the required 100 mT field strength while maintaining an acceptable printing surface of approximately A=πd²/4~ 12 cm², where d=4 cm is the inner diameter for the used Halbach array. Finally, the build platform of the DLP printer (Asiga Max X27, Sydney, Australia) was also modified to make it compatible with the Halbach array configuration (Figure 1a,b). Activating the magnetic field while the LC resin is still in its liquid state allows the photopolymerization process to fix the mesogens in a specific
magnetic alignment. This results in a 3D-printed structure whose internal orientation follows
the applied field pattern, as shown in **Figure 1**.

First, we show that the samples printed without applying the magnetic field (Figure 3a1,b1,c1,e6, Movie S1, S2) do not undergo deformation when placed on a heated plate above 120 °C, confirming that magnetic alignment is necessary to activate the actuation of the samples. Each arm of the printed LCE features can be viewed as a cantilever—fixed at one end and free at the other— allowing their thermally induced actuation to be directly connected to the mesogen orientation. This orientation is, in turn, determined by the alignment of the structure relative to the magnetic field generated by the Halbach arrays, as illustrated in Figure 1. When mesogens are aligned along the arm’s length of the structure, a bending toward the vertical direction is observed. If the mesogens are oriented along the short axis, contraction occurs across the width, resulting in minimal deformation, whereas when the mesogens are angled at 45°, heating induces a torsional response, causing the free end of the beam to twist out of the plane. It is worth noticing that depending on the polarity *k* of the used Halbach array as well as the shape of the structure that were designed, multimodal deformations are possible within a printed structure. The actuation of the different modes (M1-M9) is shown in Figure 3. For the sake of example, for the cross structure, in mode M1 only two arms bend if dipolar Halbach configuration is used (Figure 3a2, Movie S3, Supporting Information). However, if the cross is rotated by 45°, mode M2, the same structure shows the twist of all four arms (Figure 3a3, Movie S5, Supporting Information), while in quadrupolar Halbach configuration (mode M3), all four arms exhibit bending (Figure 3a4, Movie S4, Supporting Information). For the Y-shaped structures in dipolar Halbach configuration, mode M4 features two twisted arms and one bent arm (Figure 3b2, Movie S6, Supporting Information), while mode M5 exhibits one twisted arm, one bent arm, and one inactive arm (Figure 3b3). In quadrupole Halbach configuration, mode M6 shows two bent and one inactive arm (Figure 3b4) and in hexapolar Halbach configuration, mode M7 exhibits all arms bending (Figure 3b5). Finally, for hexapod structure in dipolar Halbach configuration only two arms are active (bending) (Figure 3c2, Movie S7, Supporting Information), which increases to six when hexapolar Halbach configuration is used (Figure 3c3). Finite element (FE) simulations of the thermo-responsive LCE behavior are shown in Figure 3d-f) and described in supplementary information S.13. These FE simulations provide highly accurate predictions of the complex shape-changes upon thermal actuation. The good agreement between the predicted deformations and the experimentally printed structures validates the model’s ability to capture the underlying physics of encoded mesogen alignment.
<table><thead><tr><th colspan="5">LCE magnetic alignment B= 100 mT</th></tr><tr><th>B=0 mT</th><th>Dipolar<br>(k=1)</th><th>Quadripolar<br>(k=2)</th><th>Hexapolar<br>(k=3)</th><th>B=0 mT</th></tr></thead><tbody><tr><td>Control sample</td><td></td><td></td><td></td><td>Control sample</td></tr><tr><th colspan="5">Thermal actuation</th></tr><tr><td>a1)<br>+</td><td>a2)<br>M1</td><td>a3)<br>M2</td><td>a4)<br>M3</td><td></td></tr><tr><td>b1)<br>+</td><td>b2)<br>M4</td><td>b3)<br>M5</td><td>b4)<br>M6</td><td>b5)<br>M7</td></tr><tr><td>c1)<br>*</td><td>c2)<br>M8</td><td></td><td>c3)<br>M9</td><td>b6)<br>2 cm</td></tr><tr><th colspan="5">Finite Element Simulations</th></tr><tr><td>d1)<br>X</td><td>d2)<br>M1</td><td>d3)<br>M2</td><td>d4)<br>M3</td><td></td></tr><tr><td>e1)<br>+</td><td>e2)<br>M4</td><td>e3)<br>M5</td><td>e4)<br>M6</td><td>e5)<br>M7</td></tr><tr><td>f1)<br>*</td><td>f2)<br>M8</td><td></td><td>f3)<br>M9</td><td>e6)<br>Y</td></tr></tbody></table>

**Figure 3.** Multimodal thermal actuation of LCs resins printed in nematic phase. (a1), (b1), (c1), and (b6) represent the control samples that are printed without applying a magnetic field (B=0 mT). Actuation modes (M1–M9) of various printed LCE structures under different Halbach magnetic field configurations. For the cross-shaped structure, (a2) dipolar fields activate two arms (M1), while (a3) a 45° rotation results in twisting of all four arms (M2); (a4) quadrupolar fields induce bending in all arms. In Y-shaped structures, (b2) dipolar configurations yield mixed actuation: two twisted and one bent arm (M4), and (b3) one twisted, one bent, and one inactive arm (M5). (b4) Quadrupolar fields cause two arms to bend (M6), and (b5) hexapolar fields actuate all arms (M7). For the hexapod structure, (c2) dipolar fields bend only two arms while twisting the other four (M8), while (c3) hexapolar fields activate all six (M9). d-f) finite element simulations of thermo-responsive LCE, see **Figure S13**, Supporting Information.
## 2.3 Multimodal Magneto-Responsive LCE Nanocomposite Actuations

As a second demonstration of the device's multimodal activation capability, we highlight its use in printing magneto-responsive composites. In this case, the main challenge lies in introducing magnetic anisotropy by aligning Fe₃O₄ nanoparticles without relying on the mesogen alignment. This approach ensures that actuation is driven purely by magnetic interactions, while the LCE matrix contributes solely through its elastomeric properties. To achieve this, the photocurable LC resin was specifically optimized to remain in the isotropic phase at room temperature throughout the printing process (Figure 2c). A mesogenic diacrylate RM257 was used as the primary monomer, and EDDET as the dithiol chain extender, while BHT (2,6-ditert-butyl-4-methylphenol, 0.5 wt%) was added as a free-radical inhibitor to improve the storage stability of the resin, and BAPO was used as the photoinitiator for subsequent light-induced polymerization. Finally, toluene was incorporated into the formulation at increasing concentrations. DSC revealed a progressive suppression of the nematic phase with higher toluene content (Figure S8, Supporting Information), such that above 50 wt% toluene, the nematic phase disappeared, and the formulation displayed an isotropic phase at room temperature, as confirmed by polarized optical microscopy (POM) and wide-angle X-ray scattering (WAXS) (Figure S10, S20 Supporting Information). Magneto-active elastomers were obtained by embedding commercially available 100 nm soft magnetic nanoparticles (Fe₃O₄) at 4 wt% into the LC formulation. As previously reported,[15] a magnetic field of approximately 10 mT is sufficient to induce the self-assembly of nanoparticles into chains oriented along the field direction. This can be achieved by appropriately rotating the two nested cylindrical Halbach cylinders by an angle of θ=84° in clockwise and counterclockwise directions via remote control, using an Arduino microcontroller (Figure 2d). Under the influence of an external magnetic field, Fe₃O₄ nanoparticles align into linear chains along the field direction through dipole-dipole interactions.[76] Owing to their elongated shape these chains display magnetic anisotropy, with a well-defined easy axis of magnetization, thereby imparting anisotropic magneto-mechanical properties to the embedding matrix.[77] In contrast to the thermally driven LCEs, magneto-active LCEs nanocomposites can be actuated by magnetic torque (τ=m×B), where m the magnetic moment vector, allowing the sample's arm to align along the applied field. Thus, only the bending effect can be experimentally observed. The actuation of the different modes (M1-M9) is shown in Figure 4 and corresponding movies are available in SI. First, we demonstrate that printed samples containing dispersed Fe₃O₄ nanoparticles —i.e., without chain formation during the printing step (B=0 mT)— do not
exhibit any deformation when exposed to an external magnetic field. Indeed, as shown in **Figure 4a1, 4b1, 4b5** and **4c1**, Movie S8, S9, no actuation occurs for any of the designed shapes when placed above a 3×3×3 cm³ cubic permanent magnet generating a 90 mT field, perpendicular to the plane of the objects. As previously reported,[77] this confirms that magnetic alignment of the nanoparticles during printing is essential to induce torque actuation under an external magnetic field. Second, we show the different actuation modes when samples are printed under magnetic field. In the case of the cross-shaped structures, two distinct actuation modes are observed: mode M1 involves the activation of two arms (**Figure 4a2**, Movie S10, Supporting Information), while mode M3 engages all four arms simultaneously (**Figure 4a3**, Movie S11, Supporting Information). For the Y-shaped structures, the number of activated arms varies with the configuration: one arm in modes M4 (**Figure 4b2**), two arms in mode M6 (**Figure 4b3**), and all three arms in mode M7 (**Figure 4b4**). Finally, the hexapod structure exhibits mode M8 when the magnetic field aligns with the long axis of two arms and the short axis of the other two (**Figure 4c2**). In mode M9, a hexapolar Halbach configuration is used to align the magnetic field along the long axis of all six arms (**Figure 4c3**, Movie S12, Supporting Information), enabling coordinated multi-arm actuation.

To understand why no bending is observed when the nanoparticle chains are oriented at an angle $\theta=60°$ or $90°$ relative to the arm's main axis, we developed a simple model (described in the Supplementary Information). This model estimates the magnetic torque exerted by a magnet placed at a distance equal to the magneto-responsive arm's length, with the arm fixed at one end. The applied magnetic field, approximately 100 mT, far exceeds the material's coercive field (~13 mT).[16] Under these conditions, the remanent magnetic moments of the nanoparticles —initially aligned along the printing field— can reorient collectively along the local field imposed by the external magnet and nearby particles. Thus, each nanoparticle experiences an attractive force due to the magnetic field, and the cumulative effect of these forces generates a macroscopic torque that tends to rotate the chains. The system thus behaves like an elongated ellipsoidal cluster of paramagnetic nanoparticles, with anisotropic magnetic susceptibility and an easy magnetization axis along the chain direction.[78] This mechanism explains why arms containing chains aligned parallel to their main axis respond strongly and consistently to the external magnetic field, bending toward the magnet regardless of the printing field direction. In contrast, **Figure 5** shows that the bending torque decreases by 60% when the angle $\theta$ increases from 0° to 45°. This reduction is even more pronounced at 60° and 90°, reaching 80% and 96%
respectively, resulting in a torque lower than that estimated for randomly distributed nanoparticles in the arm.

<figure><img src="image_4.png" /><figcaption>**Figure 4.** Multimodal magnetic actuation of composite LCEs embedding Fe₃O₄ nanoparticles and printed in isotropic phase. (a1), (b1), and (c1) show control samples printed without applying a magnetic field (B = 0 mT), resulting in isotropic dispersion of Fe₃O₄ nanoparticles. For the cross-shaped structure, a2) corresponds to actuation mode M1, where two arms are activated, while a3) shows mode M3, in which all four arms are simultaneously engaged. In Y-shaped structures, (b2) shows mode M4 with a single activated arm, (b3) corresponds to mode M6 with two activated arms, and (b4) displays mode M7 with full three-arm actuation. For the hexapod structure, (c2) illustrates mode M8, where actuation occurs in two arms aligned with the field, while (c3) shows mode M9, in which a hexapolar Halbach configuration enables coordinated activation of all six arms. (d) Molecular dynamics simulation showing how the bending torque magnitude varies with the angle between the nanoparticle chains and the printed arm's long axis, normalized with respect to the torque at zero angle, Movie S13. The dashed line corresponds to the value for randomly distributed nanoparticles, see **Figure S14**, Supporting Information.</figcaption></figure>
## 2.4 Multimodal and Multifunctional Thermo-Magneto-Responsive LCE Nanocomposite Actuations

In Sections 2.2–2.3, we demonstrated the device’s ability to magnetically align components requiring different field strengths (≈100 mT for LCEs and ≈10 mT for magnetic NPs). Accordingly, we fabricated objects that were exclusively thermo-active (monodomain nematic LCEs, Section 2.2) or magneto-active (polydomain nematic LCE and Fe₃O₄ NPs, Section 2.3). Here, we address the challenge of printing an object that integrates both thermal and magnetic activation mechanisms, thereby demonstrating true multifunctionality through the simultaneous coupling of both alignment processes. This was achieved using the formulation described in Section 2.2 (RM257 + EDDET + E7, in the monodomain nematic phase), into which Fe₃O₄ NPs were incorporated at 4 wt%. To decouple the thermal and magnetic effects, Fe₃O₄ nanoparticles were deliberately left non-functionalized, thereby preventing grafting onto the LCE mesogens and avoiding potential cross-interactions.

The strategy we adopted to introduce the multifunctionality is based on the following experimental observations. Fe₃O₄ nanoparticles remain homogeneously dispersed within the resin up to an applied magnetic field of approximately 10 mT. [47] At higher field strengths, the fillers migrate along the direction of the applied field, leading to a depletion of the printing zone. In contrast, the alignment of mesogens requires magnetic fields exceeding approximately 100 mT. As a result, it is not possible to simultaneously achieve both nanoparticle and mesogen alignment within a single printed layer. To overcome this limitation, we exploited controlled nanofillers migration to fabricate a bilayer element composed of two superposed layers that respond differently to stimulation through magnetic and thermal, **Figure 5a**. Specifically, the first layer is printed under a magnetic field of 10 mT for 2 minutes, enabling the formation of homogeneously distributed chains of magnetic fillers while the LCE mesogens remain unaligned, Steps I-II. Photocuring under these conditions fixes the material into a magnetic aligned configuration determined by the employed Halbach array (dipolar, quadrupolar, or hexapolar), Step III. The magnetic field is then increased to 100 mT for 10 minutes to align the mesogens while promoting the migration of nanoparticles out of the printing region, step IV. A second photocuring step stabilizes this configuration, producing a pattern determined by the chosen Halbach array, Step V. This approach enables the fabrication of multifunctional bilayer architectures, Step VI and **Figure 5b**.

**Multimodality** is achieved by printing same geometries for both layers—such as cross-shaped, Y-shaped, or hexapod architectures —while encoding distinct magnetic field patterns (dipolar, quadrupolar, or hexapolar) for each layer. This design approach adds an extra level of tunability,
endowing the printed constructs with programmable **multifunctionality** and **multimodality**, **Figures 5c–e**. These capabilities are illustrated through a series of distinct yet interconnected thermo-magnetic actuation modes (M1–M3, M4–M6, and M8–M9) obtained on the same element. For the cross-shaped structure, the magnetic mode M1 is programmed with a dipolar Halbach array, which selectively bends two opposite arms (**Figure 5c1**, Movie S14). The thermal mode M3, obtained using a quadrupolar array, instead causes all four arms to bend simultaneously (**Figure 5c2**, Movie S15). In the Y-shaped tripod, the magnetic mode M4 (dipolar array) activates only one arm (**Figure 5d1**, Movie S16), while the thermal mode M6 (quadrupolar array) produces bending in all arms (**Figure 5d2**, Movie S17). For the hexapod, the magnetic mode M8 (hexapolar array) activates all the arms (**Figure 5e1**, Movie S18), whereas the thermal mode M9 (dipolar configuration) generates a combined deformation, with two arms bending and four twisting (**Figure 5e2**, Movie S19).

<figure><img src="image_5.png" /></figure>

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Magnetic

Thermal

<figure><img src="image_7.png" /></figure>

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<figure><img src="image_10.png" /></figure>

<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /></figure>

<figure><img src="image_13.png" /></figure>

<figure><img src="image_14.png" /></figure>

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**Figure 5.** Multimodal thermo-magnetic actuation in composite LCEs embedding Fe₃O₄ nanoparticles. (a) Schematic of the fabrication sequence for a thermo-magnetic bifunctional material. (b) Cross-sectional optical image showing a bilayer structure composed of isotropic Fe₃O₄ nanoparticle chains within non-aligned LCE mesogens (dark color) and an aligned LCE layer (bright color). Distinct magnetic modes were encoded in three architectures: cross-shaped, Y-shaped, and hexapod. For the cross, (c1) shows magnetic mode M1 with two activated arms, while (c2) shows thermal mode M4 engaging all four arms. In the Y-structure, (d1) corresponds to magnetic mode M4 with one activated arm, and (d2) to thermal mode M6 activating all arms. For the hexapod, (e1) represents magnetic mode M9, where a hexapolar Halbach configuration drive coordinated activation of six arms, and (e2) thermal mode M8, inducing two bending and four twisting deformations.

## 2.5 Charge Transport in Vertically Aligned Fe₃O₄ Nanoparticle Networks

To ensure compatibility with VAT-based photopolymerization, the Halbach cylinders are designed to generate magnetic fields parallel to the build platform, i.e., in the x-y plane. However, as mentioned in the introduction, our device also enables precise control of the magnetic field along the vertical (z) axis. This three-dimensional field-tuning capability is achieved by integrating a coaxial coil within the central region of the nested Halbach cylinder (see Supplementary Information). The coil generates a magnetic field along the z-direction, described by $B_z=\mu_0NI$, where $\mu_0$ is the vacuum permeability, N is the number of turns per unit length, and I is the current through the coil. This configuration allows the generation of vertical magnetic fields up to 10 mT (**Figure S5**, Supporting Information), thereby expanding the range of programmable field orientations during printing and offering greater flexibility for magnetic alignment of nanoparticles within the resin. To demonstrate its capabilities, the device was used to fabricate vertically conductive pathways within the printed structures. To facilitate electrical measurements and microscopy preparation, a stiffer photocurable resin—bisphenol A ethoxylate diacrylate (BEDA)- was employed. Magnetic nanocomposites with integrated electrical functionality were then printed from a formulation comprising BEDA, Fe₃O₄ nanoparticles, and BAPO as photoinitiator. Single layers with thicknesses ranging from 25 to 500 µm and Fe₃O₄ concentrations between 0.25 and 4.0 wt% were printed using material test parameters (**Figure S12**, Supporting Information). To induce vertical alignment of the nanoparticles, a 10 mT magnetic field was applied to the liquid resin for 30 s prior to printing. After fabrication, a 100 nm gold layer was deposited on both surfaces of each sample to enable resistivity and current-voltage (I-V) measurements (**Figure S16** and **Figure S17**, Supporting Information).
<figure><img src="image_19.png" /><figcaption>**Figure 6.** Resistivity measurements as a function of sample thickness reveal two regimes: (a) Regime I (≤ 200 µm) shows an exponential decrease in resistivity with increasing thickness and Fe₃O₄ content, reflecting improved charge transport; (b) Regime II (> 200 µm) exhibits an exponential increase in resistivity up to 10⁵ Ω·m, indicating a transition to insulating behavior. Samples used as resistive component of an electric circuit: (c) In Regime I, the LED lights up under an applied voltage of 5 volts, (d) whereas in Regime II, the sample's resistivity is too high to allow LED activation.</figcaption></figure>

Resistivity measurements, presented in **Figure 6**, reveal two distinct regimes. The first, Regime I, is observed for sample thicknesses up to ~ 200 µm and is characterized by an exponential decrease in resistivity with increasing thickness, as shown in **Figure 6a, 6c**. Concurrently, resistivity is also found to decrease with increasing Fe₃O₄ nanoparticle content in the resin. In Regime II (**Figure 6b, 6d**), corresponding to sample thicknesses above ~200 µm, the trend reverses: resistivity increases exponentially with thickness, rapidly reaching values on the order of 10⁵ Ω·m. This sharp rise indicates a transition to insulating behavior, likely to reduce percolation of conductive paths over larger distances.

To describe the resistive behavior of the printed layers, we developed a statistical model assuming chain lengths of vertically aligned magnetic nanoparticles follow a Gaussian distribution with mean length $L_m$ and standard deviation $\sigma$, (**Figure S13**, Supporting Information). We assume that only chains longer than the film thickness $d$ can span the entire layer and contribute to electrical conduction. Each conductive chain behaves as a resistor with resistance $R_0$, and the chains are uniformly distributed with a surface density $\eta$ (directly related to the initial nanoparticle concentration). Under these assumptions, the film's resistivity can be expressed as (**Figure S10**, Supporting Information):

$$ \rho(d) = \frac{2R_0}{\eta d} \frac{1}{Erfc(\frac{d-L_m}{\sqrt{2}\sigma})} \quad (1) $$
where Erfc is the complementary error function.

From the analysis of Eq. 1, two experimentally observed regimes can be identified: For $L_m>d$ most of the chains are long enough to bridge the film. In this case, the argument of the error function becomes a constant, i.e., Erfc≈constant, and the resistivity simplifies to:

$$ \rho(d) \propto \frac{1}{\eta d} \qquad (2) $$

Thus, in regime I, resistivity exhibits a clear inverse relationship with film thickness: $ρ(d) \propto 1/d$. However, the surface concentration η also plays a critical role. At small thicknesses, lower concentrations of contacted chains lead to higher resistivity due to fewer conductive chains per unit area. As the film thickness increases, these differences gradually diminish, as the geometric factor (i.e., the $1/d$ scaling) becomes dominant, causing resistivity values to converge. For $L_m<d$, only a small fraction of chains is long enough to span the film thickness. As $d$ increases, the argument of Erfc grows rapidly, leading to a sharp rise in resistivity, primarily driven by the exponential decrease in the number of bridging chains. In this regime, $ρ(d)$ exhibits strongly nonlinear behavior.

Next, we further evaluate how nanoparticle dispersion and concentration influence the electrical behavior of the composites by analyzing their current-voltage (I-V) characteristics over a -5 V to +5 V range. The resulting I-V curves (Figure S17, Supporting Information) exhibit linear conduction at low voltages, indicative of Ohmic behavior, and suggesting that charge transport is dominated by direct conduction pathways formed by well-connected nanoparticle chains.

Finally, we evaluate whether electrical conductivity could be preserved when multiple layers were printed sequentially (Figure S18, Supporting Information). The goal was to assess the feasibility of vertical integration and interlayer electrical connectivity within the stacked structure. However, the results were negative, as no measurable conductivity was observed between layers. This is likely due to the low probability that nanoparticle chains from adjacent layers align perfectly to form continuous conductive paths across the interfaces. In SI we estimated the probability of interlayer connectivity as a function of fillers concentration. It provides a useful estimate for the probability of electrical contact and highlights a key parameter for optimization. In particular, it suggests that adjusting the concentration of embedded nanostructures — provided that good printability is maintained— could enable reliable electrical contact in multilayer printed architectures. If successful, the approach will offer a robust platform for directional charge transport and integration into three-dimensional device architectures.
### 3. Conclusions

In this work, we present a scalable and versatile approach to encode magnetic anisotropy directly during DLP 3D printing, enabling the creation of 4D-printed composites with tailored, multifunctional properties. To overcome the geometric and optical constraints typically associated with anisotropy induction in photopolymerization-based printing, we developed a hybrid magnetic setup that combines nested Halbach arrays with a central coil. This configuration offers precise, real-time control of fully tunable 3D magnetic fields—including their spatial direction, gradient, and intensity—while preserving transparency of the printing vat. This enables controlled spatial alignment of anisotropic fillers during crosslinking, unlocking new possibilities for spatially programming functional responses.

Besides, this platform enables the fabrication of multifunctional architectures exhibiting complex, direction-dependent actuation modes arising from the synergistic coupling of aligned mesogens and magnetically ordered nanoparticle chains. Such dual-responsive structures can undergo either independent magnetic or thermal actuation, or a combined multimodal response within a single printed element, while programmable field configurations—dipolar, quadrupolar, or hexapolar—allow selective activation of deformation pathways in Y-junction, cross, and hexapod geometries. Finally, we also achieve vertical alignment of $Fe_3O_4$ nanoparticle chains, producing embedded, electrically conductive nanostructures within printed components. This dual mechanical–electronic functionality paves the way for advanced applications in soft robotics, reconfigurable electronics, and multifunctional sensing. Altogether, this platform establishes a new direction in magnetically assisted 3D printing, where fine-tuned magnetic control, multimaterial responsiveness, and integrated microstructural design converge in a single fabrication step —laying the foundation for next-generation intelligent soft systems.

### Experimental Section/Methods

**Materials:** 1,4-Bis[4-(3-acryloyloxypropyloxy)benzoyloxy]-2-methylbenzene (≥95%, RM257) was purchased from Smolecule (San Antonio, USA). 2,2-(Ethylenedioxy)diethanethiol (≥95%, EDDET), Toluene (≥99,5%), 2,6-di-tert-butyl-4-methylphenol (≥99%, BHT), phenylbis(2,4,6-trimethylbenzoyl)phosphine oxide (≥97%, BAPO), Iron(II,III) oxide (50-100 nm, 97% purity, magnetite) and Bisphenol A ethoxylate diacrylate (BEDA) were purchased from Sigma-Aldrich (France). 4-Cyano-4'-pentylbiphenyl
(≥98%, E7) was purchased from TCI (via https://zentek.it/). All chemicals were used as-received without further purification.

**Precursor Formulations:**

a) preparation of the isotropic formulation. In an amber flask, RM257, BHT (0.5 wt%), and BAPO (2 wt%) were introduced, followed by the addition of toluene at a weight ratio of 1:1 (with respect to RM257). Toluene was used to stabilize the isotropic phase at room temperature. BHT was included as a free-radical inhibitor to enhance the storage stability of the resin. BAPO acted as a photoinitiator for subsequent UV-induced polymerization. The mixture was heated to 80 °C for 5 minutes to reach the isotropic state. After cooling to room temperature, EDDET was added at an acrylate-to-thiol molar ratio of 1.2:1, and the resulting isotropic mixture was homogenized using vortex mixing. Finally, magnetite (4 wt%) was incorporated and dispersed using an ultrasonic bath.

b) preparation of the nematic formulation. RM257 and the nematic liquid crystal E7 were combined in an amber flask at a weight ratio of 1:1.5. BAPO (2 wt%) was then added. The mixture was heated to 90 °C for 5 minutes and subsequently cooled to room temperature, at which point the mixture remained in the nematic phase due to the stabilizing effect of E7. EDDET was added dropwise (acrylate-to-thiol molar ratio of 1:1), and the formulation was homogenized by vortex mixing.

c) preparation of the magneto-electrical formulation for charge transfer experiments. Bisphenol A ethoxylate diacrylate (BEDA) was combined with a photoinitiator solution prepared by dissolving BAPO (2 wt%) in acetone (10 wt%) at 40 °C under gentle stirring. The resulting mixture was homogenized using a mechanical stirrer at 500 rpm. Magnetite nanoparticles were then incorporated into the resin at various weight concentrations ranging from 0.5 wt% to 4 wt% and vortexed prior to use to ensure uniform dispersion of the magnetic filler.

**Material Test Calibration Procedure:** Preliminary exposure tests were performed to calibrate the light curing parameters for each formulated resin (see SI S.5). Using the Spot Timer function of the Asiga 3D printer, a circular spot of 1.5 mm diameter was projected onto a resin layer in the resin tank. Exposure times ranged systematically from 0.1 s to 15 s, depending on the resin's reactivity. After each exposure, the cured sample was removed and its thickness measured. Plotting the cured thickness against exposure time showed a logarithmic trend, from which an empirical equation was established. This equation was used to determine the exposure times needed to obtain the desired layer thicknesses during printing.
**DLP Printing:** All geometries were designed using Fusion360 and exported as STL files. Three-dimensional structures were fabricated using a DLP printer (ASIGA Max X27) equipped with a 385 nm UV light source operating at an intensity of 59 mW/cm². The printing parameters were optimized for each formulation using the material test calibration procedure,[⁷⁹] as shown in SI S.5. The layer thickness was fixed at 50 µm for all prints. The objects were printed with an illumination time of 4.6 s for the first two layers and 1.0 s for the subsequent layers when using the isotropic formulation. For the nematic formulation, the exposure time was reduced to 0.6 s for the initial two layers and 0.1 s for the following ones. For the isotropic LCE formulation, magnetic nanoparticles were aligned by applying a magnetic field of 10 mT for 2 minutes before polymerization. For the nematic LCE formulation, mesogen alignment was achieved by exposing the resin to a 100 mT magnetic field for 15 minutes. Following the alignment phase, the printing process was initiated without disturbing the resin. After printing, the samples were rinsed in ethanol to remove uncured resin. Control samples were fabricated in the absence of any magnetic field, under otherwise identical printing conditions, to serve as unaligned references.

**Magnetic Device:** Details on the device used to introduce magnetic anisotropies into the photocurable formulations are reported in the SI S.1.

**UV Postprocessing:** After printing, the samples were subjected to UV post-curing using the Asiga Flash curing chamber for 10 minutes to ensure complete polymerization and enhance the mechanical properties of the material.

**Differential Scanning Calorimetry Measurements (DSC)** were performed using a PerkinElmer DSC 7 system (Shelton, USA) to investigate the thermal transitions of various resin formulations. Approximately 7 mg of each sample was placed in 30 ul aluminum DSC pans from the same manufacturer and sealed. The thermal protocol consisted of an initial isothermal hold at 20 °C for 1 minute, followed by heating to 100 °C at a rate of 20 °C/min. After a 1-minute isotherm at 100 °C, the samples were cooled back to 20 °C at the same rate. The melting temperature ($T_m$) and the nematic-isotropic transition temperature ($T_{ni}$) were determined from the first heating cycle. $T_m$ was identified as the minimum of the first endothermic peak, corresponding to the phase transition of the mesogens from the crystalline to the nematic state. $T_{ni}$ was determined as the minimum of the second endothermic peak, associated with the phase transition of the mesogens from the nematic to the isotropic state.
**Optical microscopy** images were acquired using a LEICA DM microscope (Nanterre, France) equipped with a CCD K3C camera and a cross-polarizer to enhance contrast in anisotropic structures. The system was configured with ocular lenses and objective lenses providing magnifications of 10× and 50×. This setup enabled the visualization of microstructural features and alignment patterns within the material using a LAS X software.

**Wide-angle X-ray scattering (WAXS).** The SAXS–WAXS experiments were performed at the Laboratoire Interdisciplinaire sur l’Organisation Nanométrique et Supramoléculaire (LIONS), CEA–CNRS, Université Paris-Saclay, NIMBE, France. The measurements were carried out using a commercial Xeuss 3.0 instrument (XENOCS). The beam diameter at the sample position was 0.7 mm, delivering approximately 5 × 10⁷ photons s⁻¹. For the WAXS configuration, the sample was placed at a distance of 0.041 m (normal incidence point) from the detector, providing a q-range from 0.1 Å⁻¹ to 3.9 Å⁻¹. The acquisition time was 300 s. The order parameter (S) was calculated using the following equation [56]

$$S = \frac{\int_{0}^{\frac{\pi}{2}} I(\theta) \frac{3\cos^2\theta - 1}{2} \sin\theta d\theta}{-\frac{1}{2} \int_{0}^{\frac{\pi}{2}} I(\theta) \sin\theta d\theta} \quad (3)$$

where θ is the angle between the director and mesogenic units and I(θ) is the azimuthal intensity distribution. The calculation was carried out for θ between 0 and 90°.

## Finite Element Simulation of Thermo-Responsive Liquid Crystal Elastomer

To numerically simulate these deformations, the LCE is modelled as an incompressible thermoelastic solid with temperature-dependent thermal expansion behavior. Upon heating, the LCE contracts along its nematic direction, which refers to the magnetically aligned direction set during the DLP printing, and expands slightly in the two other orthogonal directions. This anisotropic deformation is represented by assigning a negative coefficient of thermal expansion (CTE) along the nematic direction and a transversely isotropic expansion (non-uniform) in the perpendicular directions. The contractile thermal strain along the nematic direction is denoted as e_T, while the expansion in the transverse directions is approximated as -e_T/2. The thermal strain depends only on the current temperature T and a reference temperature of the material T ref, at which the strain is zero. This LCE model serves as the active material in all case studies presented in this paper. For the Finite element (FE) simulations, both types of layers are meshed using C3D8R elements in the commercial software Abaqus (Version 2023, Dassault Systèmes, Vélizy-Villacoublay, France). A linear elastic material is employed instead of a hyperelastic one due to the limitation of Abaqus in handling anisotropic thermal expansion in hyperelastic formulations. The material behavior is adapted from Peng et al. and from Athinarayanarao et
al. [80,81] and calibrated with experimental tests. Specifically, the anisotropic thermal expansion coefficients were derived experimentally from uniaxial thermomechanical tests on magnetically aligned LCE samples. The longitudinal thermal strain (along the nematic direction) was directly measured as a function of temperature. The corresponding transverse expansion was assumed to satisfy volume conservation, resulting in a strain ratio of approximately -1/2 in the perpendicular directions. These experimentally derived values were used to define the direction-dependent coefficients of thermal expansion in the FE model. In the numerical simulations, we assumed a uniform mesogen alignment, consistent with the magnetostatic simulations shown in Fig. S1. The observed bending of the bilayer structures arises from the mismatch in the coefficients of thermal expansion between the two layers, a property that is governed by their respective crosslink densities. Figure S19 shows the FE predictions corresponding to the printed cases illustrated in Figure 3.

For **electrical characterization**, the 3D-printed samples were first contacted by sputter-depositing a 100 nm gold layer on both surfaces using a Quorum Q150T S sputter coater system. Resistivity and current-voltage (I-V) characteristics were measured using a Keithley 4200A-SCS Source Measure Unit in a two-point probe configuration. Tungsten microneedles were used to contact the top and bottom surfaces of the printed samples (5 × 5 mm). Measurements were performed using a linear voltage sweep in the range of ±5 V, with a scan step of 0.1 V and a current compliance limit set at 70 mA. The reported I-V curves represent the average of three measurement cycles.

**Morphological Characterization.** Samples were prepared in cross-section at room temperature using a Leica UC7 ultramicrotome. Imaging was performed using field emission scanning electron microscopy (FESEM) with a Hitachi S-4800, equipped with an EDX system for compositional analysis. All images were acquired in high-vacuum mode at an accelerating voltage of 10 keV.

**Acknowledgements**

The authors gratefully acknowledge Sami Laroui (LMS, École Polytechnique) for his assistance with conductive measurements, Florian Aubrit (LSI, École Polytechnique) for providing the FESEM images, and Laurance Bodelot (LMS, École Polytechnique) for support with mechanical testing. EA, GCR and DL also thank Olivier Tache and Emeline Cournede (CEA-Saclay, NIMBE-LIONS) for their support with WAXS measurements at SWAXS platform.

**Data Availability Statement**

((include as appropriate, including link to repository))
Received: ((will be filled in by the editorial staff))

Revised: ((will be filled in by the editorial staff))

Published online: ((will be filled in by the editorial staff))

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**Supporting Information**

Supporting Information is available from the Wiley Online Library or from the author.

**Encoding Magnetic Anisotropies in Digital Light Processing 3D Printing**

Eléonore Aïdonidis, Andrea Cosola, Pierre Bourdon, Hichem Dammak, Marco Sangermano, Frédéric Demoly, Marco Faustini, Amélie Pérot, Didier Lairez, Rakine Mouhoubi, Sébastien Blanquer, and Giancarlo Rizza*

E. Aïdonidis, A. Cosola, P. Bourdon, Didier Lairez, G. Rizza, Laboratoire des Solides Irradies (LSI)
CEA/DRF/IRAMIS
Ecole Polytechnique
Institut Polytechnique de Paris
Palaiseau 91128, France

E-mail: giancarlo.rizza@polytechnique.edu

A. Cosola, M. Sangermano
Department of Applied Science and Technology
Politecnico di Torino
Corso Duca degli Abruzzi 24,
Torino 10129, Italy

H. Dammak
Laboratoire Structures Propriétés et Modélisation des Solides (SPMS),
Université Paris-Saclay, CentraleSupéle, CNRS
Gif-sur-Yvette F 91190, France

F. Demoly
Université Marie et Louis Pasteur, UTBM, CNRS, ICB UMR 6303, 90010 Belfort, France

F. Demoly
Université Bourgogne Europe, CNRS, Laboratoire Interdisciplinaire Carnot de Bourgogne ICB
UMR 6303, 21000 Dijon, France

M. Faustini, A Pérot
Sorbonne Université, CNRS, UMR 7574
Chimie de la Matière Condensée de Paris
Paris F-75005, France

M. Faustini, F. Demoly
Institut Universitaire de France
Paris 75231, France

Rakine Mouhoubi, Sébastien Blanquer
Charles Gerhardt of Montpellier Institute
CNRS Occitanie Est
Pôle Chimie Balard Recherche UMR 5253
34293 MONTPELLIER cedex 5, FRANCE
Table of contents

<table><tr><td>S.1 Magnetic device</td><td>2</td></tr><tr><td>S.1a Design Approach for Embedding Magnetic Anisotropies in DLP 3D Printing.</td><td>2</td></tr><tr><td>S.1b Numerical Simulation of Magnetic Fields Generated by Halbach Arrays</td><td>2</td></tr><tr><td>S.1c Controlling field intensity using Halbach arrays</td><td>4</td></tr><tr><td>S.1d Controlling field direction in x-y plane using Halbach arrays</td><td>5</td></tr><tr><td>S.1e Controlling field intensity and direction in Z-direction with coil</td><td>5</td></tr><tr><td>S.1f CAD model of a Halbach array installed on a DLP printer</td><td>6</td></tr><tr><td>S.2 Stability of the formulation</td><td>6</td></tr><tr><td>S.3 Differential Scanning Calorimetry (DSC)</td><td>7</td></tr><tr><td>S.4 Polarized Optical Microscopy (POM)</td><td>7</td></tr><tr><td>S.5 Material test</td><td>8</td></tr><tr><td>S.6 Optical image of horizontally aligned chains of Fe3O4 NPs</td><td>9</td></tr><tr><td>S.7 Model and numerical simulations for magnetic actuation</td><td>9</td></tr><tr><td>S.8 Optical image of sputtered gold layer for resistivity measurements</td><td>10</td></tr><tr><td>S.9 FESEM images of vertically aligned and contacted chains of Fe3O4 NPs</td><td>10</td></tr><tr><td>S.10 Model for the Resistivity of Vertically Aligned Magnetic Chains</td><td>11</td></tr><tr><td>S.11 Current-voltage (I-V) characteristic</td><td>12</td></tr><tr><td>S.12 Probability that there exists at least one point of partial overlap across all n layers</td><td>13</td></tr><tr><td>S.13 Finite Element Simulation of Thermo-Responsive Liquid Crystal Elastomer</td><td>15</td></tr><tr><td>S.14 Wide-Angle-X-rays-Scattering (WAXS)</td><td>16</td></tr><tr><td>S.15. Angular amplitude of shape morphing</td><td>16</td></tr></table>
## 1.a - Design Approach for Embedding Magnetic Anisotropies in DLP 3D Printing.

This section provides a brief introduction to the key elements underlying the device, which will later be used to encode magnetic anisotropies during the printing process. When a magnetic dipole **m** is placed in an external magnetic field **B**, it experiences forces and torques that drive it toward a configuration of minimum magnetic potential energy, $U = -\mathbf{m} \cdot \mathbf{B}$.[1] This results in both translational and rotational motions. To encode magnetic anisotropies within a photocurable resin, it is essential to harness these effects to guide magneto-responsive elements into specific spatial arrangements. The magnetic torque ($\tau = \mathbf{m} \times \mathbf{B}$) promotes the alignment of dipoles along the direction of the field, while the magnetic force, which depends on field gradients ($\mathbf{f}=(\mathbf{m} \cdot \nabla)\mathbf{B}$), pulls the system toward regions of higher magnetic field intensity. A Halbach array is a specific arrangement of permanent magnets that enhances the magnetic field on one side while nearly canceling it on the opposite side. In the ideal case, a Halbach array is modeled as an infinitely long tube with a continuously rotating magnetization.[2] However, since this is not feasible in practice, real Halbach arrays are designed using discretization methods. This involves dividing the Halbach cylinder into *P* magnets of identical shape and magnetization, but with different magnetization orientations, where the direction of a magnetic dipole, $\phi$, is an integer multiple of its angular position, $\theta$, such that $\phi=(k+1)\theta$. The polarity of the magnetic field generated by a Halbach array is characterized by the parameter *k*. A dipolar configuration (*k* = +1) produces a uniform field, while increasing *k* to +2 or +3 results in quadrupolar and hexapolar configurations, respectively, which generate progressively graded and spatially varying magnetic fields. To maintain the compatibility with digital light processing 3D printing —where light passes through a transparent vat— Halbach array can only generate magnetic fields parallel to the build platform. For this reason, in our device the field in the *z* direction is obtained by introducing a coil in the inner portion of the nested Halbach array. The resulting magnetic field in *z*-direction is $B_z=\mu_0NI$, where $\mu_0$ is the vacuum permeability, *N* the number of turns per unit length, and *I* the current in the coil. By combining the in-plane field $B_{x-y}$ from the Halbach array with the out-of-plane field $B_z$ from the coil, a fully adjustable 3D magnetic field—controllable in intensity, direction, and gradient—can be achieved. Finally, the device was integrated into a commercial DLP 3D printer (Asiga Max X27, Sydney, Australia) and is remotely controlled via a microcontroller and a Python-based application.

## 1.b - Numerical Simulation of Magnetic Fields Generated by Halbach Array

Numerical simulations were used to study the generated magnetic fields. The study was conducted using the **NumPy**, **SciPy**, and **Matplotlib** libraries. These tools enable the exploration of not only the fields generated by a single cylinder, but also the interactions between two nested cylindrical arrays, which can produce even more intense and complex fields. Several parameters are essential for the simulations: i) the number of dipoles *N* forming the Halbach ring, the side length of each magnet (*Size-magnet*), the dipole polarity *k* (*k*=1 for a dipolar configuration, *k*=2 for a quadrupolar configuration, and *k*=3 for a hexapolar configuration), the cylinder radius *R*, and the magnetic moment intensity of the dipoles (*amplitude*<sub>*m*</sub>) (A·m²).

These parameters must be defined for each of the two cylinders when simulating nested cylinders, along with the desired rotation between the two cylinders. The dipoles are first uniformly distributed in the plane using Cartesian coordinates. The coordinates of the *N* dipoles are determined as follows:

$$ \mathbf{r}_i = [R \cdot \cos(\theta[i]), R \cdot \sin(\theta[i]), 0] \qquad (\text{Equation S1}) $$

with
$$ \theta = np. linspace(0, 2\pi, N + 1) \qquad (\text{Equation S2}) $$

The direction of the magnetic moment of each dipole, **m**<sub>i</sub>, is calculated based on the angle φ, which is proportional to *k*:

$$ \mathbf{m}_i = [\cos(\Phi[i]), \sin(\Phi[i]), 0] \qquad (\text{Equation S3}) $$

with

$$ \Phi=(k+1)\theta \qquad (\text{Equation S4}) $$

The magnetic field **B**=(**B**<sub>x</sub>, **B**<sub>y</sub>, **B**<sub>z</sub>) generated by a Halbach array made up of N permanent dipoles is computed as the vector sum of the magnetic fields generated by each individual dipole. [3] Each dipole, defined by its magnetic moment **m**<sub>i</sub> and position **r**<sub>i</sub> (as above), generates a magnetic field at an observation point **r**<sub>j</sub>, calculated using the following equation:

$$ \mathbf{B}(\mathbf{m}_i, \mathbf{u}_{ij}) = \frac{\mu_0}{4\pi} \left( \frac{3(\mathbf{m}_i \cdot \mathbf{u}_{ij})\mathbf{u}_{ij} - \mathbf{m}_i}{r_{ij}^3} \right) \qquad (\text{Equation S5}) $$

$r_{ji}$ is the distance between dipoles and $\mathbf{u}_{ji} = \frac{\mathbf{r}_i - \mathbf{r}_j}{r_{ji}}$ is the unit vector. For simulations involving nested cylindrical arrays, the total magnetic field is calculated as the vector sum of the fields produced by each Halbach array.

To perform the calculation, a 2D grid of observation points $\mathbf{r}_i$ in Cartesian coordinates is created using np.linspace and np.meshgrid functions for the x and y dimensions. The magnetic field components (B<sub>x</sub>, B<sub>y</sub>, B<sub>z</sub>) are computed at each point $\mathbf{r}_j$ on the grid. The magnitude of the magnetic field is then determined using the formula: $B_{\text{magnitude}} = \sqrt{B_x^2 + B_y^2 + B_z^2}$. This value is normalized by the field intensity at the surface of one of the magnets, B<sub>0</sub>. The x and y distances are also normalized by the cylinder radius R to facilitate the interpretation of the results.

<figure><img src="image_20.png" /><figcaption>**Figure S1.** Simulations obtained for three Halbach array configurations with a radius **R** = 55.7 mm, containing **N** = 12 magnets with a side length of 1.76 cm and a magnetic moment intensity of **amplitude**<sub>m</sub> = 11.35 A·m<sup>2</sup>. Black arrows indicate the direction of the dipole moments. The axes represent distances normalized by **R**. The magnitude of the magnetic field generated by the cylinder, normalized by **B**<sub>0</sub>, is shown by the color scale. Black lines represent the magnetic field lines. (a) Dipolar configuration: uniform field at the center (0.24 **B**<sub>0</sub>), reaching 0.33 **B**<sub>0</sub> at the edges. (b) Quadrupolar configuration: zero field at the center, reaching 0.42 **B**<sub>0</sub> at the edges. (c) Hexapolar configuration: zero field at the center, reaching 0.30 **B**<sub>0</sub> at the edges.</figcaption></figure>
The three Halbach cylinder configurations introduced in **Figure S1** were simulated in order to assess the validity of the Python program used to reproduce theoretical magnetic field distributions. The simulations were performed for a cylinder with a radius $R = 55.7$ mm, composed of $N = 12$ magnets with a side length of 1.76 cm and a magnetic moment intensity of amplitude $m = 11.35$ A·m². Only the polarity parameter $k$ was varied: $k = 1$ for the dipolar configuration, $k = 2$ for the quadrupolar configuration, and $k = 3$ for the hexapolar configuration. While a single Halbach array can only generate a specific magnetic configuration, [4] multiple concentric structures, **also known as nested Halbach arrays**, allows the creation of additional tunable magnetic field **patterns**. For example, the relative mechanical rotation of the inner and outer cylindrical arrays in dipolar configuration allows for adjustable field intensity (S.1c) and orientation (S.1d) without the need for additional power sources. Simulations were also performed for nested dipolar cylinders. In each simulation, the rotation of the outer cylinder relative to the inner cylinder was specified, and the positions of the outer cylinder's dipoles were adjusted accordingly. The result for two nested dipolar cylinders with a relative rotation of $\pi/4$ is illustrated in **Figure S2**.

<figure><img src="image_21.png" /><figcaption>**Figure S2.** Simulations obtained for two nested dipolar cylinders. The images are captured at each relative rotation of the outer cylinder with respect to the inner cylinder by $\pi/4$. They are read from **left to right** and **top to bottom**. The magnitude of the magnetic field generated by the nested cylinders, normalized by that of the field generated by the inner cylinder, is shown by the color scale.</figcaption></figure>

1.c - Controlling Field Intensity Using Halbach Arrays

<figure><img src="image_22.png" /></figure>
**Figure S3.** In a nested Halbach array configuration—where both the inner and outer cylindrical arrays are designed to generate magnetic fields of equal intensity B₀—the overall magnetic field intensity can be tuned by rotating the two cylindrical arrays relative to each other by an angle θ, in opposite directions (clockwise and counterclockwise, respectively), as illustrated in Figure S2. When the outer and inner cylinders are aligned, the generated magnetic field is twice as strong as that produced by the inner cylinder alone. When the outer cylinder is rotated by π relative to the inner cylinder, the total magnetic field at the center is nearly zero, as theoretically expected. [5] This behavior is particularly interesting, as it shows that a simple rotation of the outer cylinder is sufficient to cancel the generated magnetic field. As shown in Figure S3d, this relative rotation modulates the field intensity without altering its direction.

1.d - Controlling Field Direction in x-y Plane Using Halbach Array

<figure><img src="image_23.png" /></figure>

**Figure S4.** (a-d) Once the field intensity is set as described in section S.1c, the direction of the magnetic field can be tuned by rotating the two cylindrical arrays relative by the same angle β.

1.e - Controlling Field Intensity and Direction in z-Direction with Coil

<figure><img src="image_24.png" /></figure>

**Figure S5.** (a) A solenoid was integrated into the Halbach device to generate a tunable magnetic field along the z-direction. Acting as an electromagnet, the solenoid produces a uniform field when current flows through its coil. The field at its center is given by B<sub>int</sub>=μNI/h, where μ is the magnetic permeability, N the number of turns, I the current, and h the solenoid height. (b) Once the geometry is fixed, the magnetic field can be tuned by adjusting the input voltage. The figure illustrates the relationship between the applied current and the resulting magnetic field generated along the z-direction. The plot also includes, in red, the corresponding temperature increase caused by the Joule heating, highlighting how thermal effects evolve with increasing current. The temperature was measured 10 min after the activation of the coil using a FLIR E5
thermal camera. This dual representation provides insight into both the magnetic performance and thermal behavior of the system under electrical excitation. As shown in **Figure S14**, this activation of the coil allows the vertical alignment of the Fe₃O₄ nanoparticles.

1.f - CAD Model of a Halbach Cylindrical Array Integrated into a DLP printer

<figure><img src="image_25.png" /></figure>

**Figure S6.** CAD representation of the 3D printer used, illustrating the integrated Halbach device and its components in an exploded view. The model was created using Fusion 360® software.

2 - Stability of the Formulation

<figure><img src="image_26.png" /></figure>

**Figure S7.** Stability over time of the formulation containing the maximum content of Fe₃O₄ nanoparticles (4 wt%). The formulations are stable for 2h, while sedimentation of Fe₃O₄ nanoparticles starts after about 3h and it is clearly evident after 24h.
### 3 - Differential Scanning Calorimetry (DSC)

<figure><img src="image_27.png" /></figure>

**Figure S8.** For the formulation RM257+EDDET+Toluene+BAPO: (a) DSC scans indicate that increasing the concentration of toluene progressively reduces the extent of the nematic phase, and (b) starting from a concentration above 50 wt%, the nematic phase is no longer present in the formulation.

<figure><img src="image_28.png" /></figure>

**Figure S9.** DSC analysis of pure (a) RM257 and (b) RM257:E7 mixture (1:1.5). For RM257, two transition temperatures are observed: melting (T<sub>m</sub>) and nematic-isotropic (T<sub>ni</sub>) transitions. For the mixture, a single T<sub>ni</sub> transition occurs, indicating a stable nematic phase at room temperature.

### 4 - Polarized Optical Microscopy (POM)

<figure><img src="image_29.png" /></figure>

**Figure S10.** Polarized optical microscopy images of a liquid crystal elastomer (LCE) observed under cross-polarized light. (a) In the nematic phase, the sample exhibits characteristic birefringent textures due to the orientational order of the mesogens. (b) In the isotropic phase,
the texture disappears, and the sample appears dark, indicating the loss of long-range orientational order.

**5 - Material Test for 3D printing**

<figure><img src="image_30.png" /></figure>

**Figure S11.** Material test using the Asiga Max X27 printer. Comparison between the pure LCE formulation — RM257 + EDDET + E7 + BAPO (blue) — and the LCE formulation containing 4 wt% Fe₃O₄ nanoparticles — RM257 + EDDET + toluene + Fe₃O₄ NPs + BAPO (orange).

<figure><img src="image_31.png" /></figure>

**Figure S12.** Material test using the Asiga Max X27 printer. BEDA+BAPO formulation for increasing concentration up to 4 wt% of Fe₃O₄ nanoparticles.
## 6 - Optical Image of Horizontally Aligned Chains of Fe₃O₄ NPs

<figure><img src="image_32.png" /><figcaption>**Figure S13.** Optical images of Fe₃O₄ NPs. (a) as dispersed (2 wt%) and after the application of dipolar field at 10 mT for 10 minutes, (b) 2 wt%, and (c) 4 wt%.</figcaption></figure>

## 7 - Model and Numerical Simulations for Magnetic Actuation

The aim is the modelling of the nanoparticle chains filling the LCE arm and the computation of the induced magnetic torque in response to an external magnetic field applied by a magnet. Based on the magnetic measurements performed on a densely packed dry powder composed of these magnetite nanoparticles, [6] each nanoparticle, with an average diameter d = 100 nm, is assumed to behave as a perfectly isotropic spherical ferrimagnet, with an estimated external susceptibility of $\chi = 3$ and a remanent magnetization of approximately $M \approx 50,000 \text{ A} \cdot \text{m}^{-1}$. Using the point dipole approximation, the moment of a NP, $i$, writes:

$$ \mu_i = \frac{\pi}{6} d^3 \left( \chi \frac{B_i}{\mu_0} + \mathbf{M}_i \right) \qquad (\text{Equation S6}) $$

where $\mu_0$ is the vacuum permeability. $B_i$ is the magnetic field at the NP position, $\mathbf{r}_i$, which is the sum of the external magnetic one, $B_e(\mathbf{r}_i)$ applied by the magnet, and the fields $B(\mu_j, \mathbf{r}_{ji})$, applied by the neighboring NPs:

$$ \mathbf{B}(\mu_j, \mathbf{r}_{ji}) = \frac{\mu_0 \frac{3(\mu_j \cdot \mathbf{u}_{ji})\mathbf{u}_{ji} - \mu_j}{4\pi \mathbf{r}_{ji}^3}} \qquad (\text{Equation S7}) $$

$$ \mathbf{B}_i = \mathbf{B}_e(\mathbf{r}_i) + \sum_{j \neq i} \mathbf{B}(\mu_j, \mathbf{r}_{ji}) \qquad (\text{Equation S8}) $$

$\mathbf{r}_{ji}$ is the distance between dipoles and $\mathbf{u}_{ji} = \frac{\mathbf{r}_i - \mathbf{r}_j}{r_{ji}}$ is the unit vector. For a given distribution of nanoparticles, a self-consistent iterative scheme is used to ensure the convergence of the dipole moments $\mu_i$ through the three-coupled equations. In this scheme, the remanent magnetization $\mathbf{M}_i$ of each nanoparticle is oriented along the field $\mathbf{B}_i$.

The arm is defined as a rectangular parallelepiped with dimensions $L_1, L_2$, and $L_3$ along the x-, y-, and z-axes, respectively. The magnet is represented by a series of twenty point magnetic dipoles, $\mathbf{m}_k$, uniformly distributed in the xy-plane and aligned along the x-direction, over an interval of width $2L_1$, and located at a distance $D = L_1$ from the main axis of the arm (Figure S14a,b).

Since the nanoparticle content is low (4 wt%), we considered long chains of nanoparticles, as reported in Lantean et al.[7] These chains can also assemble in a parallel fashion, forming a hexagonal lattice in a plane parallel to the main chain axis.[8] To model a printed arm, we constructed a network of nodes using a face-centered tetragonal lattice with parameters $a =$
1.16 d, b = c = √3 a. This unit cell contains four nodes located at positions: (0; 0; 0), (0; 1/2; 1/2), (1/2; 0; 1/2) et (1/2; 1/2; 0).

Figure S14c shows a model of the arm represented by a supercell obtained by a 34 × 1 × 3 replication of the tetragonal unit cell, where 136 nanoparticles are positioned on the lattice nodes along the a (|| x ) axis. When the chains form an angle θ with respect to the arm’s x -axis, the supercell of Figure S14c is rotated by θ around the y -axis. Periodic boundary conditions are applied to preserve the nanoparticle density in the arm while maintaining its dimensions at 19.63 b × b × 3 b (Figure S14d).

Using the well-known expression for the interaction force between two magnetic dipoles:

$$
\mathbf{F}(\mathbf{\mu}_j, \mathbf{\mu}_i) = \frac{3\mu_0}{4\pi r_{ji}^4} \left[ (\mathbf{\mu}_j \cdot \mathbf{u}_{ji})\mathbf{\mu}_i + (\mathbf{\mu}_i \cdot \mathbf{u}_{ji})\mathbf{\mu}_j + (\mathbf{\mu}_j \cdot \mathbf{\mu}_i - 5(\mathbf{\mu}_j \cdot \mathbf{u}_{ji})(\mathbf{\mu}_i \cdot \mathbf{u}_{ji}))\mathbf{u}_{ji} \right] \quad (\text{S.E9})
$$

the total force F i acting on the i-th nanoparticle is the sum of the forces exerted by the twenty
magnetic dipoles m k modeling the magnet and by the neighboring dipoles µ j :

$$
\mathbf{F}_i = \sum_{k=1}^{20} \mathbf{F}(\mathbf{m}_k, \mathbf{\mu}_i) + \sum_{j \neq i} \mathbf{F}(\mathbf{\mu}_j, \mathbf{\mu}_i) \quad (\text{Equation S10})
$$

All magnetic moments **m**_k are oriented along the y-direction and have a fixed magnitude of 3 × 10⁻¹² A·m², which allows generating a total magnetic field close to 100 mT at the free end of the arm. For comparison, the remanent magnetic moment of a single nanoparticle is equal to 2.6 × 10⁻¹⁷ A·m².

Finally, the bending torque around the z-axis, computed with respect to the fixed end of the arm,
is given by:

$$
\tau_z = \mathbf{u}_z \cdot \sum_i \mathbf{r}_i \times \mathbf{F}_i \qquad (\text{Equation S11})
$$

<figure><img src="image_33.png" /><figcaption>**Figure S14.** (a) and (b) Schematic views of the printed arm defined as a parallelepiped with size ratios 19.63 × 1 × 3 along the *x*, *y* and *z* axes, respectively. The twenty thick arrows indicate magnets arranged in the *xy* plane and evenly distributed along the *x*-axis over a length twice that of the arm. (c) Distribution of nanoparticles (large grey circles) within the arm, forming a long chain aligned with *x*-axis. (d) Arrangement of nanoparticles along multiple chains oriented at an angle θ with respect to *x*-axis. The small circles represent unoccupied sites of the tetragonal lattice within the arm. The nanoparticle density remains nearly constant and thus θ independant.</figcaption></figure>
## 8 - Optical Image of Sputtered Gold Layer for Resistivity Measurements

<figure><img src="image_34.png" /></figure>

**Figure S15.** For resistivity measurements, 100 nm gold layers were sputtered onto 0.5 × 0.5 cm² areas on both sides of 1 × 1 cm² printed samples with varying thicknesses (d = 25–400 µm), using a Quorum Q150T S (Laughton, England) sputter coater system.

## 9 - FESEM Images of Vertically Aligned and Contacted Chains of Fe₃O₄ nanoparticles

<figure><img src="image_35.png" /></figure>

**Figure S16.** (a) High-resolution SEM image of a single chain of Fe₃O₄ nanoparticles, aligned along the direction of the applied magnetic field. (b) Low-magnification view of a cross-section of the sample, showing multiple vertically aligned chains embedded in the matrix (underneath the surface of the sample). The chains extend up to the top surface of the sample, where a gold (Au) layer was deposited to ensure conductivity. (c) EDX map of the Fe Kα signal (red): highlights the presence of iron along the chains, confirming their Fe₃O₄-based composition. (d) EDX map of the Au Lα signal (magenta): shows the distribution of gold, mainly localized near the top surface of the sample, consistent with a deposited Au coating. (e–f) EDX maps of the C Kα (blue) and O Kα (white) signals show a uniform distribution of carbon in the matrix and oxygen along the chains and matrix, indicating a carbon-based polymeric matrix and the oxidized nature of both the Fe₃O₄ nanoparticles and the surrounding material.
## 10 - Model for the Resistivity of Vertically Aligned Magnetic Chains

We assume that an ensemble of chains of length L follows a Gaussian distribution characterized by a mean length Lm and a standard deviation σ. The Gaussian probability of having a chain of length L is given by the distribution function:

$$P(L) = \frac{1}{\sqrt{2\pi}\sigma} \exp\left(-\frac{(L-Lm)^2}{2\sigma^2}\right) \qquad (\text{Equation S12})$$

The total number of chains is N₀, and they are located within a film of thickness d. The number of chains that can be contacted are those longer than the thickness of the film, L > d:

$$N(d) = N_0 \int_{d}^{\infty} P(L)dL \qquad (\text{Equation S13})$$

To calculate this function, we consider the cumulative distribution function (CDF), which gives the probability that a variable x is less than or equal to a given value, e.g., the layer thickness d. Φ(x)=P(x < d):

$$\Phi(x) = \int_{-\infty}^{d} \frac{1}{\sqrt{2\pi}} \exp\left(\frac{x^2}{2}\right) dx \qquad (\text{Equation S14})$$

The normalized variable x can be expressed as:

$$x = \frac{d-Lm}{\sigma} \qquad (\text{Equation S15})$$

So the number of chains that can be contacted will be (after some calculations):

$$N(d) = N_0[1 - \Phi(x)] = \frac{N_0}{2} \text{Erfc}\left(\frac{x}{\sqrt{2}}\right) = \frac{N_0}{2} \text{Erfc}\left(\frac{d-Lm}{\sqrt{2}\sigma}\right) \qquad (\text{Equation S16})$$

If the surface density of chain is η, then the number of conductive chains over an area A will be N₀=ηxA and N(d) can be written as

$$N(d) = \frac{\eta A}{2} \text{Erfc}\left(\frac{d-Lm}{\sqrt{2}\sigma}\right) \qquad (\text{Equation S17})$$

We can now move on to the calculation of the resistivity.

The N(d) chains touching both surfaces of the layer can be considered as resistances in parallel each having the same value of resistance, R₀(d). This value is function of the layer thickness and chains concentration. Thus, the equivalent resistance is given by:

$$\frac{1}{R_{eq}} = \sum_{i} \frac{1}{R_{i}} = \frac{N(d)}{R_{0}} \Rightarrow R_{eq} = \frac{R_{0}}{N(d)} = \frac{2 R_{0}}{\eta A \text{Erfc}\left(\frac{d-Lm}{\sqrt{2}\sigma}\right)} \qquad (\text{Equation S18})$$

The resistivity of the material with area A and thickness d can be expressed as:

$$\rho(d) = R_{eq}(d) \frac{A}{d} = \frac{R_0}{N(d)} \frac{A}{d} = \frac{2 R_0}{\eta A \text{Erfc}\left(\frac{d-Lm}{\sqrt{2}\sigma}\right)} \frac{A}{d} = 2 \frac{R_0}{\eta d} \frac{1}{\text{Erfc}\left(\frac{d-Lm}{\sqrt{2}\sigma}\right)} \qquad (\text{Equation S19})$$

where R₀ is the measured resistance for each layer thickness and chains concentration, η is the chains density, Lm is the average chains length, and σ is the standard deviation, as experimental parameters.
## 11 - Current-Voltage (I-V) Characteristic

<figure><img src="image_36.png" /><figcaption>**Figure S17.** I-V curves of the DLP printed nanocomposites as a function of the concentration of Fe3O4 nanoparticles</figcaption></figure>

## 12 - Probability That There Exists At least One Point of Partial Overlap Across All Layers

With the aim of determining the probability that, in the case of printing two or more layers (n=1 to 5) each containing vertically aligned chains, there is percolation between the layers, we calculated the probability that conductive channels form which electrically connect the two external surfaces of the printed sample. The resulting probability distribution is as follows.

$$P(\eta) = 1 - e^{-\frac{(1 - e^{-\eta\pi a^2})^n}{\pi a^2}} \quad (\text{Equation S20})$$

where η is the density of vertically aligned and contacted chains, and a is the diameter of each chain considered as a cylinder of base A=πa²/4.

We then estimated the density of chains that have sufficient length to be contacted. To do this, we defined a nominal film thickness on the order of 100 µm, since this corresponds to a thickness for which we observe measurable current for all studied concentrations (0.25–4.0 wt%).

To determine the average chain length, we followed this procedure: we placed a drop of resin containing nanoparticles dispersed at the desired concentration on a microscope slide. We then activated a coil to generate a vertical magnetic field (Bz = 10 mT). This field induces the formation of vertical chains, whose lengths were estimated by switching off the field (Bz = 0 mT) and allowing the chains to fall into the horizontal plane due to gravity. At this point, their lengths can be optically measured. The resulting length distribution allows us to estimate the density of chains longer than 100 µm, i.e. 0.9x10³ cm⁻², for the maximum nanoparticle concentration used in this work (here 4 wt%). This value is used to estimate the probability of electrical contact, which also ensures good printability. This value explains why, in our case, electrical contact cannot be achieved when printing two or more layers, while also highlighting a path to optimize the concentration of embedded nanostructures to ensure compatibility with the printing parameters.
<figure><img src="image_37.png" /></figure>

<figure><img src="image_38.png" /><figcaption>**Figure S18.** (a) Probability of having at least one point of partial overlap across all *n* stacked layers as a function of the chains density. Our experimental value is also reported (dashed vertical line). Measurement of average chain length by (b) first inducing vertical alignment (Bz = 10 mT), then (c) measuring collapsed chains optically after field removal.</figcaption></figure>

13 - Finite Element Simulation of Thermo-Responsive Liquid Crystal Elastomer

In magnetically assisted DLP 3D printing, our liquid crystal elastomer (LCE) is printed using two types of layers: (i) over-crosslinked layers, which ensure strong adhesion to the DLP substrate, and (ii) normally crosslinked layers, which form the main body of the printed structure. The over-crosslinking is achieved by adjusting the polymerization time and UV intensity, which leads to a higher crosslinking density and then an increased contractile force upon activation. By combining these two types of layers, we can achieve programmable shape changes such as bending or twisting, as illustrated in Figure 3. To numerically simulate these deformations, the LCE is modelled as an incompressible thermoelastic solid with temperature-dependent thermal expansion behavior. Upon heating, the LCE contracts along its nematic direction, which refers to the magnetically aligned direction set during the DLP printing, and expands slightly in the two other orthogonal directions. This anisotropic deformation is represented by assigning a negative coefficient of thermal expansion (CTE) along the nematic direction and a transversely isotropic expansion (non-uniform) in the perpendicular directions. The contractile thermal strain along the nematic direction is denoted as *e*<sub>T</sub>, while the expansion in the transverse directions is approximated as −*e*<sub>T</sub>/2. The thermal strain depends only on the current temperature *T* and a reference temperature of the material *T*<sub>ref</sub>, at which the strain is zero. This LCE model serves as the active material in all case studies presented in this paper. For the Finite element (FE) simulations, both types of layers are meshed using C3D8R elements in the commercial software Abaqus (Version 2023, Dassault Systèmes, Vélizy-Villacoublay, France). A linear elastic material is employed instead of a hyperelastic one due to the limitation
of Abaqus in handling anisotropic thermal expansion in hyperelastic formulations. The material behavior is adapted from Peng et al. and from Athinarayanarao et al. [9,10] and calibrated with experimental measurements. Specifically, the anisotropic thermal expansion coefficients were derived experimentally from uniaxial thermomechanical tests on magnetically aligned LCE samples. The longitudinal thermal strain (along the nematic direction) was directly measured as a function of temperature. The corresponding transverse expansion was assumed to satisfy volume conservation, resulting in a strain ratio of approximately -1/2 in the perpendicular directions. These experimentally derived values were used to define the direction-dependent coefficients of thermal expansion in the FE model. In the numerical simulations, we assumed a uniform mesogen alignment, consistent with the magnetostatic simulations shown in Fig. S1. The observed bending of the bilayer structures arises from the mismatch in the coefficients of thermal expansion between the two layers, a property that is governed by their respective crosslink densities. Figure S19 shows the FE predictions corresponding to the printed cases illustrated in Figure 3.

<figure><img src="image_39.png" /><figcaption>**Figure S19.** Finite element simulation of thermo-active LCE with magnetically aligned mesogens DLP 3D printing. Each FE prediction represents the “as actuated” structures corresponding to the printed structures shown in Figure 3.</figcaption></figure>
## 14. Wide-Angle-X-rays-Scattering (WAXS)

<figure><img src="image_40.png" /><figcaption>**Figure S20.** Optical images of printed active elements: (a1, b1, c1, d1) thermo-active elements and (d1) magneto-active element. WAXS images for different orientations are shown in (b2–b3, c2–c4, d2). (e) Measured angular intensity of the WAXS profiles. (f) Corresponding estimated values of the order parameters calculated using equation (3) in Materials and Methods.</figcaption></figure>

## 15. Angular amplitude of shape morphing

<figure><img src="image_41.png" /><figcaption>**Figure S21.** Angular amplitude of shape morphing for the different actuation modes (M1-M9)</figcaption></figure>
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Encoding Magnetic Anisotropies in Digital Light Processing 3D Printing

We present a hybrid magnetic device—combining a coaxial coil within a nested Halbach array—integrated into a DLP 3D printer to enable spatially resolved magnetic field control. This system enables complex, multimodal responses by programming liquid crystal elastomer resins for magnetic and thermal actuation, and by inducing electrically conductive, vertically aligned nanostructures within printed components.

<figure><img src="image_42.png" /><figcaption>ToC figure (50x55 mm)</figcaption></figure>