# Localized integration of iron-based nanoparticle micromagnets on planar inductors for RF applications

Mélik Maksem, Adrien Bourgine, Kosseila Ait-Oukaci, Angélique Gillet, Thierry Leïchlé, David Bourrier, Guillaume Viau, Nicolas Ratel-Ramond, Simon Cayez, Adeline Pham, et al.

► To cite this version:

Mélik Maksem, Adrien Bourgine, Kosseila Ait-Oukaci, Angélique Gillet, Thierry Leïchlé, et al. Localized integration of iron-based nanoparticle micromagnets on planar inductors for RF applications. Journal of Magnetism and Magnetic Materials, 2025, 631, pp.173498. 10.1016/j.jmmm.2025.173498. hal-05249754

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Distributed under a Creative Commons Attribution 4.0 International License
Localized integration of iron-based nanoparticle
micromagnets on planar inductors for RF applications

Mélik E. Maksem¹,², Adrien Bourgine³, Kosseila Ait-Oukaci¹,², Angélique Gillet¹, Thierry Leïchlé²,
David Bourrier², Guillaume Viau¹, Nicolas Ratel-Ramond¹, Simon Cayez¹, Adeline Pham¹, Touati
Douar¹, Damien Saugnon², Alexandre Rumeau², Thierry Parra²*, Thomas Blon¹*, Lise-Marie
Lacroix¹,⁴*

1 Université de Toulouse, UMR 5215 INSA, CNRS, UT3, Laboratoire de Physique et Chimie des Nano-Objets, 135 avenue de Rangueil F-31077 Toulouse cedex 4, France

2 Laboratoire d'analyse et architecture des systèmes, CNRS, UT3, Toulouse cedex 4, France

3 Toulouse Tech Transfer, 118 route de Narbonne, 31432 Toulouse

4 Institut Universitaire de France (IUF), 103 boulevard Saint Michel, 75005 Paris, France

Corresponding author:

parra@laas.fr, tblon@insa-toulouse.fr, lmlacroi@insa-toulouse.fr, Tel: +33567048833, Fax:
+33561559697

**Abstract:**

High permeability magnetic cores are often used in electronic components to concentrate electromagnetic field lines in order to enhance their radiofrequency properties or to reduce the device size while maintaining their performances. For that purpose, efficient magnetic materials are required, with major magnetic properties, dielectric behavior and soft techniques of integration. Here we present a new bottom-up approach for integrating localized magnetic dielectric materials onto planar inductors. Magnetic nanoparticles are first synthesized by a liquid-phase chemical approach and then assembled into submillimeter magnets onto inductors and coplanar waveguides by a magnetophoresis-directed process, performed at atmospheric pressure and room temperature. This approach allows a conformal deposition while limiting material losses. Permittivity and permeability of Fe, FeC and FeCo particles based-materials are extracted up to 30 GHz. Optimizing the magnetic properties of the magnets through the size and chemical composition of the nanoparticles allow increasing of 40 to 60% the nominal inductance values of 2 and 13 nH up to 3 GHz. These results open new perspectives for the design of radio-frequency electronic micro-components.

**Keywords:** magnetic nanoparticles, magnetophoresis, magnetic-core, micromagnets, permeability, radio-frequency electro-magnetic characteristics.
# 1. Introduction

In the context of a society driven by wireless communications, which are now at the heart of key sectors such as medicine and security, it has become essential to limit excessive energy consumption [1]. Integrating soft magnetic materials into inductors allows the electromagnetic field lines to be concentrated locally, leading to limited losses and improved integration densities. Regarding inductors, it leads to higher inductance to volume ratios when coupled with a soft magnet [2]. A small reduction in size or weight can be of key importance for applications requiring the integration of a greater number of functional systems. Soft magnets are often composed of metallic iron-based materials since they combine real permeabilities ($\mu'$) and saturation magnetization ($M_s$) among the highest reported. They also exhibit low magnetic anisotropies, which can be finely tuned by adding Co and/or Ni [3]. To limit losses, such as eddy currents or domain wall dynamics, it is interesting to focus on a material constituted of nanoparticles (NP). Indeed, thanks to their size below the skin depth, the nanoparticles can exhibit a single-domain magnetic behavior [4,5] and the organic shell at their surface can act as an electrical insulating barrier[6,7].

In the literature, several studies report on the integration of magnetic materials at the surface of micro-inductors. Such an architecture, consisting of a magnetic material deposited only on one side of a planar inductor, can achieve theoretically a maximum of 100% increase of $L$ [8]. The thickness of the magnet plays a key role as it does influence the relative permeability of the magnet. Roshen [9] has illustrated the effect of finite magnetic film thickness on planar inductors using method of images to solve the equations governing this physical system. For a magnetic film with a relative permeability of 100, a thickness of 100 µm yields an inductance increase of approximately 60%, whereas a 1000 µm thick film can result in an inductance increase of up to 90%. Wang et al. [10] have reported a novel on-chip inductor incorporating a black hollow structure partially filled with a 205 nm thick film of CoFeB/ZnO/CoFeB. This design achieved a significant inductance enhancement of 41% to 71% over the 0.1–8 GHz frequency range, with no degradation in the quality factor up to 4 GHz. However, this approach relies on relatively complex fabrication process combining deep Si etching with sputtering deposition. As a result, recent research efforts have focused on alternative strategies for the integration of magnetic materials, among which assembled magnetic nanoparticles. Yun et al. [11] have reported
the size-dependent permeability of magnetite and maghemite nanocrystals and their integration, as
compacted material within a 3D millimeter toroidal inductance. This nanostructured material exhibits a
ferromagnetic resonance at low frequency (100 MHz). Koh *et al.* [12] deposited polydisperse FeNi₃
particles (50 - 150 nm), forming a 90 µm thick deposit resulting in a 50% inductance increase up to 3
GHz. Desvaux *et al.* reported a 40% improvement of planar inductors decorated with self-assemblies of
15 nm FeCo NPs passivated with a carbon shell [5]. By optimizing the deposition parameters and
inductor design, Venturin *et al.* improved the performance of the 20 µm thick material with 80% increase
of the inductance value up to 1-3 GHz, fairly close to the expected maximum [[6,7]. In our group, we
have previously reported a 27% improvement of commercial inductor-based filters by adding a
composite material consisting of 10 nm FeCo nanoparticles embedded in an epoxy resist [13].

These results are fairly encouraging but remains lacunar. Indeed, no systematic study on the effect of
the metallic nanoparticles used, in terms of mean NP diameter, size distribution and chemical
composition was reported so far to the best of our knowledge. Moreover, the integration of the magnetic
material onto the inductors is mostly handmade, using a pick and place method, or through a drop-
casting method without a precise thickness control, thus lacking reproducibility.

The study presented here relies on a bottom-up approach to define submillimeter magnets on coplanar
waveguide (CPW) and planar inductors using Fe, FeC and Fe<sub>100-x</sub>Co<sub>x</sub> nanoparticles chemically
synthesized. Fe and FeCo NPs were considered in order to focus on high real permeabilities values
whereas FeC ones were investigated because of their resistance against oxidation [14,15]. By adjusting
experimental conditions, the size and the chemical composition of the nanoparticles could be finely
tuned to adjust their magnetic properties. Localized magnets are directly assembled on chips using the
magnetophoresis method [16]. This fabrication process, which takes benefit of locally induced magnetic
field gradients, is performed at room temperature and atmospheric pressure and yield conformal magnets
with controlled thickness. The resulting radio-frequency (RF) electromagnetic properties, studied up to
30 GHz, reveal important benefits of carbidization or cobalt doping of the iron NPs building blocks.

## 2. Material and Methods
## 2.1. Synthesis of nanoparticles

The nanoparticles are synthesized following organometallic approaches under mild condition, using $H_2$ as reducing agent, as previously reported [13,17–23]. Further details can be found in supplementary information.

## 2.2. Characterization of the NPs.

Magnetic measurements were performed using a Quantum Design Physical Property Measurement System (PPMS) 9 T Evercool II magnetometer system in the Vibrating Sample Magnetometer (VSM) configuration. The capsules were filled in the glovebox with approximately 10 mg of dried powder of NPs and rapidly introduced into the VSM to avoid air-exposure. ±3 T hysteresis loops were recorded at 300 K for the different random oriented NPs. The magnetization values were normalized by the powder mass, thus considering both the NPs and their surrounding ligands. X-Ray diffraction (XRD) were recorded using a Malvern Panalytical Empyrean diffractometer equipped with a Co anticathode X-ray source (Co Kα = 1.790 Å), Bragg-Brentano HD mirror and a PIXCell3D detector. The sample were prepared in the glovebox, and encapsulated between two thin layers of Kapton film for avoiding any oxidation.

The microscopy images were obtained from a transmission electron microscopy (TEM) JEOL 1011 microscope operating at 100 kV and from a scanning electron microscope (SEM) JEOL JSM-7800F microscope. Small-angle X-ray scattering (SAXS) measurements were carried out on the SWING beamline at the SOLEIL synchrotron (Paris, France). A beam energy of 12 keV, a *q* range of 0.015 – 1.15 Å⁻¹, acquisition times of 10 ms are used, with a spot size of 75 × 75 µm².

## 2.2. Electrical characterization chip

In order to evaluate the RF properties of the nanoparticles, test chips were fabricated following conventional microfabrication processes further detailed in the supplementary information. CPW lines and CPW access of inductors have been designed for avoiding any electrical discontinuities during test under Ground-Signal-Ground-probes (G-S-G) with a pitch of 150 µm. Different inductors surrounded with a ground-ring have been designed thanks to simulations and implemented by varying the strip width ($W_s$), the inter-spiral gap ($S_s$) and the number of turns in order to present inductance values, Q-factors
and working frequencies covering a wide range of potential applications (Table S1). In this study, only inductors 1 and 6 will be shown as they represent two extremes: inductor 1 has a low inductance value and a high self-resonance frequency $f_r$, while inductor 6 exhibits a large inductance but in a restricted frequency range. Ni blocks electroplated on both side of each component allow for the magnetophoresis-driven assembly (Figure S1). These blocks serve as flux concentrator under an in-plane external magnetic field, generating magnetic field gradients at their vicinity, as previously reported [16,24].

## 2.3. Directed assembly assisted by magnetophoresis

The magnetophoresis process allows assembling particles in solution directed by a combination of an external magnetic field and local magnetic gradients as previously reported [16,24] and further detailed in the supplementary information (Figure S2). The directed assembly was performed either in air, applying an external magnetic field of 0.5 T, or under a controlled argon atmosphere in a glovebox, with an external field of 0.4 T.

## 2.4. Microwave characterization

The RF test structures were characterized up to 30 GHz before and after the micromagnet deposition using the S-parameters of transmission ($S_{21}$) and of reflection ($S_{11}$). Measurements were carried out using a vector network analyser (Keysight, N5247B PNA-X) connected to the device through G-S-G probes (Form Factor, PA200 probe station). A SOLT calibration was performed that locates measurements at the probe planes. CPW transmission lines without material were first measured to get the data required to the de-embedding. This calculation process allows to move the reference planes of $S_{21}$ and $S_{11}$ measurements from probes to the magnet sides by removing the influence of the access, i.e., parts of the line without magnetic material [25]. Once the de-embedding is performed and the S-parameters defined to the magnet sides, the effective dielectric permittivity ($\epsilon_{eff}$) and magnetic permeability ($\mu_{eff}$) were extracted using the following expressions [25,26]:

$$ \Gamma = \chi \pm \sqrt{\chi^2 - 1} \qquad (1) $$
$$ \chi = \frac{S_{11}^2 - S_{21}^2 + 1}{2S_{11}} \qquad (2) $$

$$ P = \frac{S_{11} + S_{21} - \Gamma}{1 - (S_{11} + S_{21})\Gamma} = |P|e^{j\varphi} \qquad (3) $$

$$ \gamma = \frac{1}{L} \cdot \ln\left(\frac{1}{|P|}\right) + j\frac{-\varphi}{L} \qquad (4) $$

$$ \gamma_0 = j\frac{\omega}{c} \qquad (5) $$

$$ \varepsilon_{eff} = \left(\frac{\gamma}{\gamma_0}\right) \cdot \left(\frac{1-\Gamma}{1+\Gamma}\right) = \varepsilon'_{eff} - j\varepsilon''_{eff} \qquad (6) $$

$$ \mu_{eff} = \left(\frac{\gamma}{\gamma_0}\right) \cdot \left(\frac{1+\Gamma}{1-\Gamma}\right) = \mu'_{eff} - j\mu''_{eff} \qquad (7) $$

With Γ the reflection coefficient (in equation (1), the plus or minus sign is chosen to yield |Γ|<1), χ the transmission coefficient, P the propagation factor, φ its phase, γ the propagation constant in presence of material, and γ₀ the propagation constant of free space.

In this study, the effective permittivity (ε<sub>eff</sub>) and permeability (μ<sub>eff</sub>) have been extracted and compared directly. The effective electromagnetic characteristics consider an homogeneous single dielectric for the transmission line, which is formed here from the magnet and the silicon substrate . Even they do not give the actual characteristics of the magnetic material, effective constants are still useful for material comparison since they are directly extracted from measurements under the only quasi-TEM propagation approximation.

Note that the relative values of the micromagnet ε<sub>r</sub> and μ<sub>r</sub> could be approximated using the conformal mapping method applied to the coplanar line [27], considering the silicon substrate (ε<sub>substrate</sub>= 11.9 and μ<sub>substrate</sub>= 1.0):

$$ \varepsilon_r = 2\varepsilon_{eff} - \varepsilon_{substrate} \qquad (8) $$

$$ \mu_r = \frac{\mu_{eff}}{2-\mu_{eff}} \qquad (9) $$

From these relationships and considering that ε<sub>r</sub> > 1 and 1 ≤ μ<sub>r</sub> ≤ ∞, it can be deduced that ε<sub>eff</sub> > 6.45, and that in most cases (when the relative characteristics of the material are not too large to remain within the approximation) the effective permeability μ<sub>eff</sub> will present a value between 1 and 2 [25,26].
The performances of the micro-magnets were also directly evaluated from the inductor characterization.

The quality factor (Q) characterizes the efficiency of an inductor by comparing the energy it stores to the energy it dissipates per cycle. Specifically, Q is the ratio of the reactive (stored) power to the average power loss. A high Q is desirable in applications such as resonant circuits and filters, where it enhances frequency selectivity and reduces energy loss. The quality factors and the inductance values L were extracted from the Y admittance parameters calculated from the S-parameters:

$$Q = - \frac{\mathrm{Im}(Y_{11})}{\mathrm{Re}(Y_{11})} \qquad (10)$$

$$L = \frac{\mathrm{Im}(Y_{11}^{-1})}{\omega} \qquad (11)$$

where $Y_{11}$ corresponds to the input admittance.

### 3. Results and discussion

#### 3.1. Synthesis of the nanoparticles

Nanoparticles of different sizes and composition have been synthesized using an organometallic approach (supplementary information). While 14 to 17 nm NPs exhibiting a cubic-like shape were obtained for Fe and Fe<sub>100-x</sub>Co<sub>x</sub> NPs, fairly spherical NPs were obtained after carbidization leading to 14 nm FeC NPs, as revealed by electron microscopy (Figure 1a-d and S3-S4). X-Ray Diffraction patterns show that the Fe and FeCo NPs were highly crystalline exhibiting the expected bcc structure (Figure 1e). The full carbidization of the initial Fe<sup>0</sup> NPs was confirmed, leading to the pseudo-hexagonal Fe<sub>2.2</sub>C structure (Figure 1e) [21,22]. The magnetic properties of the NPs in a powder state were measured at 300 K (Figure 1f). The saturation magnetization, determined for μ<sub>0</sub>H = 3T, increases from 105 Am<sup>2</sup>.kg<sup>-1</sup>NPs for FeC NPs to 205 Am<sup>2</sup>.kg<sup>-1</sup>NPs for Fe<sub>77</sub>Co<sub>23</sub> NPs (Figure 1f). As expected, these saturation magnetizations are a bit lower than the bulk values, due to the presence of organic ligands at the NP surface. During the carbidization process, the material hardens, the magnetic saturation decreases and the coercive field increases. For evaluating the size and composition effect on RF properties, 8 nm Fe NPs, 10 nm Fe<sub>70</sub>Co<sub>30</sub> NPs, and 19 nm Fe NPs have also been synthesized (Figure S4-S5).
<figure><img src="image_2.png" /><figcaption>Figure 1. (a-d) TEM images, e) XRD diffractograms and f) magnetic hysteresis loops recorded at 300 K on randomly oriented powders of a) 15 nm Fe (red line in e and f), b) 14 nm FeC (blue), c) 17 nm Fe<sub>89</sub>Co<sub>11</sub> (marron) and d) 17 nm Fe<sub>77</sub>Co<sub>23</sub> NPs (orange). Inset: enlarged view of the switching behavior of the NP powder.</figcaption></figure>
## 3.2. Elaboration of the integrated micromagnets – Fe, FeC and FeCo NPs

Integrated Fe-based micromagnets were prepared using the magnetophoresis approach either under air (0.5 T), or in the glove box under an Ar atmosphere (0.4 T) to prevent the NP oxidation. The optical image of the chips after air deposition evidences the selectivity of the magnetophoresis (Figures 2a-2c): the majority of the magnetic nanoparticles are located between the nickel blocks. Fairly similar results were obtained under inert atmosphere, the micromagnets could then be further protected using an epoxy layer (Figure 2b). For 10 nm Fe<sub>70</sub>Co<sub>30</sub> micromagnets, SEM images reveal a fairly dense assembly of NPs with only few cavities (inset Figure 2c). The nanostructured magnet was characterized using Small Angle X-Ray Scattering (SAXS), a technique which allow probing the entire volume and not only the surface as the SEM does. The 2D SAXS pattern (inset Figure 2d) reveals an assembly with a slight anisotropy perpendicularly to the external magnetic field applied during the magnetophoresis process (red arrow in Figure 2d). This agrees with an alignment of the NPs along the magnetic field. Indeed, a NP alignment leads to a perpendicular diffusion pattern in the reciprocal space. The I(q) curve obtained by the radial integration of the whole pattern exhibit a correlation peak corresponding to a mean center-to-center distance of 13-14 nm (Figure 2d). Such a value is in good agreement with the 10 nm NP size determined by TEM and the typical 2-3 nm organic shell surrounding the NPs [28–30]. The nanostructured magnet is thus fairly dense over its entire volume.
<figure><img src="image_3.png" /></figure>

<figure><img src="image_4.png" /></figure>

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

<figure><img src="image_6.png" /></figure>
Figure 2 Optical image of a chip with NP-based micromagnets between Ni blocks after magnetophoresis performed a) at air and b) in glovebox and further protected by an epoxy layer. c) SEM images of the micromagnets deposited onto CPW lines prepared from 10 nm $Fe_{70}Co_{30}$ NPs. Inset: enlarged view revealing the constituting NPs. d) The corresponding SAXS radial integration. Red arrow: direction of the external magnetic field used during the magnetophoresis-driven assembly. Inset: 2D SAXS pattern recorded in transmission mode.

### 3.3. Optimization of the integrated micromagnets – effect of the NP composition

Micromagnets, constituted of single domain Fe, FeC and $Fe_{100-x}Co_x$ NPs of around 15nm [31,32], have been integrated onto CPW transmission lines and inductors. In this section, Fe NPs have been deposited under air, which can result in oxidized NPs, while FeC and $Fe_{100-x}Co_x$ ones have been deposited in the glovebox under Ar atmosphere. The $Fe_{100-x}Co_x$ ones have been further protected from air exposure thanks to an epoxy capping, contrarily to FeC, as this material is supposed to be less prone to oxidation according to previous results [14]. The real and imaginary parts of the effective permittivities and permeabilities are displayed on Figure 3a and Figure 3b, respectively. First, the magnet prepared from Fe NPs in air exhibit a dielectric behavior with fairly low losses, as revealed by the dissipation angle $\tan \delta = \varepsilon''/\varepsilon' < 1$ over nearly the entire frequency range. The NPs are thus electrically insulated from each other thanks to the organic layer at their surface, and/or the oxide shell that may form under air. For $f < 4$ GHz, $\mu'_{eff}$ is around 1.4 with very low magnetic losses over the whole frequency range, i.e., $\mu''_{eff} < 0.3$ up to 30 GHz. A broad maximum is observed around 10 GHz, which can be attributed to the ferromagnetic resonance (FMR) of the micromagnet. Deposited on inductors, Fe NPs led to a moderate increase of about 10% on both $L_1$ and $L_6$ (Figure 3c-d) due to their modest $\mu'_{eff}$, and this until almost the self-resonance frequencies of the inductors (12 GHz and 3 GHz, respectively). This confirms that the FMR of the magnet is at high frequency and thus not affecting the inductor behavior.

In comparison to pure Fe NPs, iron carbide NPs exhibit the same dielectric behavior with fairly low losses, and a high permeability values up to 4 GHz: $\mu'_{eff}$ is about 1.8 for $f < 1.7$ GHz. This material provides a stable ~20% increase in inductance for every inductor (Figure 3c-d). In comparison, 17 nm $Fe_{89}Co_{11}$ NP-based magnet protected with epoxy exhibit a higher dielectric behavior ($\varepsilon'$), while $\mu'_{eff}$ ~ 1.6 until 2.0 GHz (Figure 3b). These nanoparticles lead to a moderate improvement of the inductance
value, fairly similar to the one measured with Fe nanoparticles exposed to air. Tuning the proportion of cobalt within the FeCo NPs allows improving these performances. 17 nm Fe<sub>77</sub>Co<sub>23</sub> NPs protected by the epoxy layer indeed exhibit the best magnetic performance, with a maximum real permeability (μ'<sub>eff</sub>) above 2.0 at approximately 1.0 GHz.

<figure><img src="image_7.png" /><figcaption>Figure 3. a) Effective permittivities and b) magnetic permeabilities (solid lines: real part; dashed lines: imaginary part) of CPW; evolution of the inductance value as a function of frequency for inductors c) #1 and d) #6 decorated with Fe (red), Fe<sub>89</sub>Co<sub>11</sub> (marron), Fe<sub>77</sub>Co<sub>23</sub> (orange) and FeC (blue) NP-based micromagnets. The intrinsic inductor behavior was indicated as reference (black).</figcaption></figure>

As a result of high μ'eff values up to the FMR, inductors with Fe<sub>77</sub>Co<sub>23</sub> NP-based magnet induce an increase of the inductance ranging from 40% to 60% up to 4 GHz (Figure 3c-d), while the Q factor remains fairly unchanged up to almost 1 GHz (Figure 4). Such results compete with the best reports in the literature based on nanoparticle deposits [7,12,33–35]. Q<sub>max</sub> of 9 and 8 are measured for Fe<sub>77</sub>Co<sub>23</sub> magnet on inductor #1 and #6, respectively, (Figure 4). Variations of the Q-factor versus frequency are consistent with the results of the magnet characterization determined on the CPW structures. At low frequencies, the Q-factor is limited only by resistive losses in the metal strip, and Q values are fairly the
same for inductors with or without magnet. As the frequency increases, the losses in the dielectric increase eventually becoming predominant and resulting in the Q-factor decrease. This is more pronounced in presence of the deposited magnet, mainly due to the inherent magnetic losses, in agreement with the increasing imaginary part of the effective permeability ($\mu''_{eff}$) in Figure 3b.

<figure><img src="image_8.png" /><figcaption>Figure 4. Comparisons of the quality factor of (a) inductor #1 and (b) inductor #6 with Fe₇₇Co₂₃ NPs and without materials.</figcaption></figure>

These results demonstrated the beneficial effect of Fe–Co alloying on high-frequency magnetic properties for nanoparticles with sizes around 15 nm. The benefit of iron-cobalt alloyed NPs has been confirmed for smaller sizes. Specifically, a comparison between magnets composed of 8 nm Fe nanoparticles and 10 nm Fe₇₀Co₃₀ nanoparticles, both encapsulated in epoxy, reveals superior
performance for the later one. The Fe₇₀Co₃₀ NP-based magnet exhibits a maximum $\mu'_{eff}$ exceeding 2.0 near 1.0 GHz, compared to approximately 1.6 at 1.0 GHz for Fe. Additionally, the inductance of the Fe₇₀Co₃₀ magnet is enhanced by roughly 40-60% (see figure S6).

### 3.3. Optimization of the integrated micromagnets – effect of the NP size

The influence of the NP size on the relative permeability has been previously reported on maghemite iron oxide NPs. Yun *et al.* [11] has reported an important size effect on the permeability when increasing the maghemite NPs from 8.6 to 17.0 nm. The relative permeability $\mu'_r$ increases from 1 to ~9, at 2 MHz, corresponding to a $\mu'_{eff}$ increasing from 1 to ~1.8.

In our case, we studied the properties of the micromagnet prepared with Fe NPs of 8 and 19 nm (Figure 5a-b), deposited under Ar and protected with epoxy to prevent any oxidation effect. For larger size, the material slightly hardens, the coercive field indeed increases from 6.9 to 23 mT (Figure 5c). The maximum $\mu'_{eff} \sim 1.6$ does not change much with size. However, one can notice that the permeability is slightly shifted towards higher frequencies for the 19 nm, indicating a higher ferromagnetic resonance frequency (Figure 5e). Regarding the micromagnets deposited onto the inductors, a 20-30% increase of inductance is reported for the 19 nm NPs, whereas an increase of 15-20% is only observed for the 8 nm NPs (Figure 5f). These results show that the Fe NP size has indeed an impact but it is fairly moderate for inductor core applications. Note that the RF properties of unprotected Fe 15 nm NPs present both lower $\mu'_{eff}$ and inductance values than the protected 8 and 19 nm ones (Figure 5d-f).
<figure><img src="image_9.png" /><figcaption>Figure 5. a) TEM images of 8 nm Fe, and b) 19 nm Fe nanoparticles and c) the corresponding magnetic hysteresis loops recorded at 300 K. d) Effective dielectric permittivities and e) magnetic permeabilities (solid lines : real part; dashed lines : imaginary part) of CPW. f) Evolution of the inductance value as a function of frequency for inductors #6 decorated with 8 nm Fe (red) or 19 nm Fe (green) NP-based micromagnets deposited under Ar and protected by an epoxy layer. For the sake of comparison, the 15 nm Fe NP based magnet deposited under air is recalled (blue) as long as the intrinsic inductor behavior, i.e. without any deposited magnet, as reference (black).</figcaption></figure>

4. Discussion

The major characteristics of the materials presented in this work are summarised in Table 1. The comparison of RF properties among Fe, Fe<sub>100-x</sub>Co<sub>x</sub>, and FeC-based micromagnets highlights the critical role of oxidation, the best performances being observed for the micromagnets prepared under Ar and further protected by an epoxy layer. Oxidation of the constituting NPs leads to a significant degradation
of their magnetic properties due to the non-magnetic or weakly magnetic oxide formed at the NP surface. Carbidization provides oxidation resistance without the need for epoxy protection, however, it comes along with a reduction in magnetic performance. The epoxy encapsulation is an efficient barrier to oxidation, even though the deposition process used is currently facing limitations in terms of uniformity and thickness control. These issues could be easily addressed through microfabrication-compatible masking techniques.

The choice of nanoparticle composition significantly affects the RF behavior, Fe<sub>100-x</sub>Co<sub>x</sub> alloyed NPs demonstrating superior permeability in the GHz frequency range compared to pure Fe or FeC compounds, due to their intrinsic magnetic properties, among which their smaller coercivities and higher saturation magnetization, which both increase with Co content (Table 1). Finally, nanoparticle size also plays a role in determining dynamic magnetic properties, especially in the GHz range. Larger Fe NPs exhibited a permeability slightly shifted towards higher frequencies. Thus, a clear roadmap for the fabrication of high-performance micromagnets is established, based on FeCo nanoparticles with sizes approaching the single-multi-domain transition, protected with a thin epoxy layer.

<table><caption>Table 1. Summary of the main characteristics of the NP-based micromagnet samples.</caption><thead><tr><th>Sample</th><th>Magnetophoresis</th><th>Size (nm)</th><th>Measured saturation magnetization (Am<sup>2</sup>.kg<sup>-1</sup>NP)</th><th>Bulk saturation magnetization (Am<sup>2</sup>.kg<sup>-1</sup>metal)</th><th>Coercive field µ<sub>0</sub>H<sub>c</sub> (mT)</th><th>Permeability µ'<sub>eff</sub> at 1 GHz</th></tr></thead><tbody><tr><td>Fe</td><td>air atmosphere</td><td>15±4</td><td>187</td><td>220</td><td>38</td><td>1.4</td></tr><tr><td>FeC</td><td>argon atmosphere</td><td>14±1</td><td>105</td><td>170</td><td>33</td><td>1.8</td></tr><tr><td>Fe<sub>89</sub>Co<sub>11</sub></td><td>argon atmosphere</td><td>17±3</td><td>190</td><td>225</td><td>10</td><td>1.6</td></tr><tr><td>Fe<sub>77</sub>Co<sub>23</sub></td><td>argon atmosphere</td><td>17±2</td><td>205</td><td>230</td><td>9</td><td>2.1</td></tr><tr><td>Fe</td><td>argon atmosphere</td><td>8±1</td><td>130</td><td>220</td><td>7</td><td>1.6</td></tr><tr><td>Fe<sub>70</sub>Co<sub>30</sub></td><td>argon atmosphere</td><td>10±2</td><td>210</td><td>245</td><td>13</td><td>2.1</td></tr><tr><td>Fe</td><td>argon atmosphere</td><td>19±3</td><td>174</td><td>220</td><td>23</td><td>1.6</td></tr></tbody></table>
**5. Conclusion**

We report here a detailed study on the RF properties of Fe, Fe<sub>100-x</sub>Co<sub>x</sub> and FeC-based micromagnets directly integrated onto CPW and inductors using the magnetophoresis-driven assembly process. The size of the constituting nanoparticles as long as their chemical composition plays a major role on the final magnet properties. Interestingly, the best performances are obtained for Fe<sub>100-x</sub>Co<sub>x</sub> NP-based magnets providing that they are protected from oxidation. By combining a deposition process performed under a controlled atmosphere with an efficient epoxy protective layer, the increase of the inductance values could reach up to 60%. Such an increase is among the highest reported in the literature for planar inductors covered by magnetic materials on one face [36]. To our knowledge, the record of 70% in planar inductor was obtained with a magnetic film deposited by sputtering process but was limited to narrow range around 7 GHz, below 5 GHz the increase is limited to 40% [10]. The approach proposed here allows limiting the quantity of material used by localising the deposit while being easily compatible with microelectronics processes.

**6. Acknowledgements**

This study is financed by INSA Toulouse, Toulouse Tech Transfer, the Occitanie region (France) and the EUR NanoX university research school (n° ANR-17-EURE-0009). SAXS experiments were performed on beamline SWING at the French synchrotron Soleil proposal (proposal number: 20220441). Thomas Bizien and Javier Perez are warmly thanked for their assistance provided for the use of the beam line. This study was supported by the Raimond Castaing microcharacterisation centre and the LAAS-CNRS technology centre member of the RENATECH network.

**Supplementary Information:**

Supplementary material, including the detailed synthesis of nanoparticles, the fabrication process of the electrical characterization chip, the experimental condition used during the magnetophoresis-
driven assembly, and additional microscopy images and RF characterization, is available in the online version of this article at http:

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