# Exploring Fe-V-Ta-Al Heusler thin films: Thermoelectric Properties and Anomalous Hall Effect for Spintronics Applications

N Claus, Sébastien Pairis, O Leynaud, D Bourgault

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N Claus, Sébastien Pairis, O Leynaud, D Bourgault. Exploring Fe-V-Ta-Al Heusler thin films: Thermoelectric Properties and Anomalous Hall Effect for Spintronics Applications. Journal of Magnetism and Magnetic Materials, 2025, 633, pp.173554. 10.1016/j.jmmm.2025.173554. hal-05344137

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# Exploring Fe-V-Ta-Al Heusler thin films: Thermoelectric Properties and Anomalous Hall Effect for Spintronics Applications

N. Claus<sup>(1,2)</sup>, S. Pairis<sup>(1,2)</sup>, O. Leynaud<sup>(1,2)</sup>, D. Bourgault<sup>(1,2)</sup>

<sup>(1)</sup> Univ. Grenoble Alpes, Institut Néel, F-38042 Grenoble, France.

<sup>(2)</sup> Centre National de la Recherche Scientifique / Institut Néel, 25 Avenue des Martyrs,
BP 166, 38042 Grenoble Cedex 9, France

* Corresponding author : E-mail : daniel.bourgault@neel.cnrs.fr

## Abstract :

The electronic transport and magnetic properties of Fe-V-Ta-Al thin films synthesized via co-sputtering were investigated, demonstrating the technique's effectiveness for precise compositional tuning. Thermoelectric measurements revealed Seebeck coefficients ranging from -37 to +44 µV/K for n-type and p-type films, respectively, in correlation with the valence electron concentration (VEC). Despite this, the power factors remained lower than those of bulk counterparts (~0.35 mW·K⁻²·m⁻¹), primarily due to high electrical resistivity (0.4 – 1 mΩ·cm), porous microstructures, and the incomplete formation of the fully ordered L2₁ phase. Magnetic studies revealed ferromagnetic behavior with saturation magnetization dependent on Fe content. Magnetoresistance (MR) was observed, showing dependence on Fe doping and reaching -2.5% near 200 K for Fe-overdoped films, with stronger effects at lower temperatures for Fe-underdoped films (8% at 5K). Anomalous Hall Effect (AHE) was observed, with resistivity ρ<sub>xy</sub> correlating strongly with magnetization. Although AHE values were lower than Co-based Heusler alloys, they were comparable to disordered Fe₂VAl-based compounds. The intrinsic contribution was predominant over any extrinsic scattering effects in these Fe-V-Ta-Al thin films.

## Keywords :

Heusler, Thermoelectric thin film, Anomalous Hall effect, Magnetoresistance
# 1. Introduction

Heusler compounds, such as Fe₂VAl, are increasingly investigated for their potential in thermoelectric applications, including generators that convert waste heat into electricity and cooling devices. Research has demonstrated that tailoring the composition, particularly through tantalum (Ta) substitution, can significantly enhance thermoelectric performance in bulk materials [1, 2]. Specifically, recent studies indicate that incorporating Ta into Fe₂VAl improves the figure of merit (ZT) by simultaneously increasing the Seebeck coefficient and reducing thermal conductivity [3]. The figure of merit (ZT) measures thermoelectric efficiency and is given by $ZT=S^2\sigma T/\kappa$, where S is the Seebeck coefficient, $\sigma$ is electrical conductivity, T is the absolute temperature, and $\kappa$ is thermal conductivity.

In addition to thermoelectric properties, Heusler material can exhibit interesting Anomalous Hall Effect (AHE) properties. The AHE is characterized by a transverse voltage generated in response to an applied current in the presence of a magnetic field, which is significantly larger than the ordinary Hall effect in ferromagnetic materials. The magnitude of the AHE can be influenced by the specific composition and thickness of the thin films, making these materials attractive for spintronic applications where control of spin currents and magnetic properties are essential.

Many studies have investigated AHE in Co-based Heusler alloys [4, 5]. However, research on the more cost-effective Fe-based Heusler alloys, which exhibit significantly higher Curie temperatures (up to 1000 K), remains scarce [6-8]. Notably, Noky et al. [9] conducted a study on the intrinsic anomalous transport properties of ferromagnetic Heusler compounds and predicted several new Fe-based Heusler candidates with potentially large AHE. These predictions, however, have yet to be experimentally confirmed.

The magnetoresistance (MR) and anomalous electronic properties in Heusler alloys Fe₂+xV₁-xAl with an L2₁ structure have been investigated intensively [10-13]. Nishino et al. [11] found that Fe₂VAl possesses a nonmagnetic ground-state with a nonmetallic temperature dependence throughout a wide temperature range of the electrical resistivity. A negative MR of about 40% is also observed for the ferromagnet Fe₂₁V₀.₉Al composition at 4.2K in 13 T explained on the basis of the concept of magnetic clusters [12]. Garmroudi et al. reported observing AHE in highly disordered A₂-Fe₂VAl₀.₉Si₀.₁ samples [14]. Similarly, Tsujii et al. also detected AHE in weakly ferromagnetic Fe₂V₀.₉Cr₀.₁Al₀.₉Si₀.₁ Heusler compounds [15].
In this work, the thermoeletric and magnetic properties have been investigated in Fe-V-Ta-Al thin films prepared by a co-sputtering process. We show that some Fe-V-Ta-Al thin films exhibited ferromagnetic behavior, with composition-dependent magnetization and AHE for spintronics applications.

## 2. Experimental details

DC magnetron sputtering deposition was performed using a primary target composed of $Fe_2V_{0.98}Ta_{0.07}Al_{0.95}$, with a diameter of 50 mm and a thickness of 3 mm. Additionally, a secondary target of either V or Al was utilized during deposition to fine-tune the film composition. A (001) oriented MgO single crystal served as the substrate due to its lattice parameter compatibility with $Fe_2VAl$, resulting in a lattice mismatch close to 3%. This substrate also facilitates quantitative composition analysis via Energy Dispersive X-ray Spectroscopy (EDX) and provides electrical insulation for transport measurements. The DC (Direct Current) power supplied to the primary ternary target was set at 130 W. The power for the secondary targets varied from 0 to 30 W for the V target and from 0 to 40 W for the Al target. Deposition was performed at 673 K over a duration of 60 minutes, yielding Fe-V-Al films with thicknesses ranging from 460 to 600 nm. The sputtering process was conducted under an argon pressure of $10^{-2}$ mbar, with a gas flow rate of 40 standard cubic centimeters per minute (sccm). The target-to-substrate distance was maintained at 13 cm, and the substrate holder rotated at 4 rpm to ensure uniform chemical composition and temperature, thereby achieving consistent film thickness.

Table 1 summarizes the deposition conditions, including the power applied to the secondary target, along with the thickness and composition obtained from EDX and profilometer analyses.

<table><thead><tr><th rowspan="2">Sample</th><th colspan="3">Target power (W)</th><th rowspan="2">Composition (At%)</th><th rowspan="2">Thickness (nm)</th></tr><tr><th>Fe<sub>2</sub>V<sub>0.98</sub>Ta<sub>0.07</sub>Al<sub>0.95</sub></th><th>V</th><th>Al</th></tr></thead><tbody><tr><td>SE101</td><td>130</td><td>0</td><td>0</td><td>Fe<sub>2.07</sub>V<sub>0.88</sub>Ta<sub>0.09</sub>Al<sub>0.96</sub></td><td>470</td></tr><tr><td>SE102</td><td>130</td><td>12</td><td>0</td><td>Fe<sub>1.98</sub>V<sub>1.01</sub>Ta<sub>0.08</sub>Al<sub>0.93</sub></td><td>580</td></tr><tr><td>SE103</td><td>130</td><td>21</td><td>0</td><td>Fe<sub>1.93</sub>V<sub>1.11</sub>Ta<sub>0.08</sub>Al<sub>0.88</sub></td><td>570</td></tr><tr><td>SE104</td><td>130</td><td>30</td><td>0</td><td>Fe<sub>1.90</sub>V<sub>1.19</sub>Ta<sub>0.08</sub>Al<sub>0.83</sub></td><td>590</td></tr></tbody></table>
<table><caption>Table 1: Deposition conditions, including the power applied to Fe₂V₀.₉₈Ta₀.₀₇Al₀.₉₅, V and Al targets, the atomic compositions determined by EDX and the film thickness obtained by profilometer analyses.</caption><tr><td>SE105</td><td>130</td><td>0</td><td>11</td><td>Fe<sub>1.95</sub>V<sub>0.88</sub>Ta<sub>0.08</sub>Al<sub>1.09</sub></td><td>585</td></tr><tr><td>SE106</td><td>130</td><td>0</td><td>20</td><td>Fe<sub>1.94</sub>V<sub>0.85</sub>Ta<sub>0.08</sub>Al<sub>1.13</sub></td><td>520</td></tr><tr><td>SE107</td><td>130</td><td>0</td><td>29</td><td>Fe<sub>1.84</sub>V<sub>0.86</sub>Ta<sub>0.08</sub>Al<sub>1.22</sub></td><td>580</td></tr><tr><td>SE108</td><td>130</td><td>0</td><td>40</td><td>Fe<sub>1.79</sub>V<sub>0.80</sub>Ta<sub>0.07</sub>Al<sub>1.34</sub></td><td>600</td></tr><tr><td>SE110</td><td>130</td><td>9</td><td>0</td><td>Fe<sub>2.07</sub>V<sub>0.93</sub>Ta<sub>0.10</sub>Al<sub>0.90</sub></td><td>480</td></tr><tr><td>SE111</td><td>130</td><td>5</td><td>0</td><td>Fe<sub>2.10</sub>V<sub>0.90</sub>Ta<sub>0.09</sub>Al<sub>0.91</sub></td><td>510</td></tr></table>

The crystalline structure was examined using an X-Ray Diffraction (XRD) system (D5000 Brucker) in the conventional Θ-2Θ mode with a Cu Kα radiation source and x-ray pole figure measurements. Film composition and microstructure were analyzed using EDX and a Zeiss Ultra + Field Emission Scanning Electron Microscope (FESEM). To verify film homogeneity, multiple spots along the film were analyzed.

The power factor $P_F = S^2/ρ$ at room temperature was determined by measuring the Seebeck coefficient S (μV/K) and the electrical resistivity ρ (mΩ cm). This factor reflects the electronic transport properties, while the figure of merit ZT = (S²/ρλ)T = $P_F T/κ$ (κ being the thermal conductivity) indicates its thermoelectric efficiency. A custom-built device, detailed in reference 16 [16], was used to measure the Seebeck coefficient by applying a thermal gradient across the film plane. Electrical resistivity of the films was determined using a Jandel 4-probe (Jandel Engineering, Ltd., Bedfordshire, U.K.). Film thickness was measured with a mechanical profilometer).

Charge carrier density (n/p), Hall effect and MR are obtained using a van der Pauw method using a Physical Property Measurement System (PPMS) from Quantum Design by sweeping the direction of the field from positive to negative values and by varying the temperature from 400 K to 5K.

Magnetization data are taken using a commercial SQUID magnetometer from Quantum Design.

### 3. Results
EDX analysis reveals a film composition of Fe<sub>51.75</sub>V<sub>22</sub>Ta<sub>2.25</sub>Al<sub>24</sub> (or Fe<sub>2.07</sub>V<sub>0.88</sub>Ta<sub>0.09</sub>Al<sub>0.96</sub>) when no secondary target is used. Table 1 shows the composition variation with respect to the power applied to the secondary Al and V targets for films deposited at 673 K. These compositions are plotted against the power of V (Fig. 1a) and Al (Fig. 1b) applied to the secondary target, showing a linear variation of atomic composition corresponding to the nature and power of the secondary target. The co-sputtering process allows for precise tuning of the film composition from near-stoichiometric Fe<sub>51.75</sub>V<sub>22</sub>Ta<sub>2.25</sub>Al<sub>24</sub> (or Fe<sub>2.07</sub>V<sub>0.88</sub>Ta<sub>0.09</sub>Al<sub>0.96</sub>) to Al-rich Fe<sub>44.75</sub>V<sub>20</sub>Ta<sub>1.75</sub>Al<sub>33.5</sub> (Fe<sub>1.79</sub>V<sub>0.80</sub>Ta<sub>0.07</sub>Al<sub>1.34</sub>) and to V-rich Fe<sub>47.5</sub>V<sub>29.75</sub>Ta<sub>2.0</sub>Al<sub>20.75</sub> (Fe<sub>1.90</sub>V<sub>1.19</sub>Ta<sub>0.08</sub>Al<sub>0.83</sub>).

<figure><img src="image_2.png" /><figcaption>Fig. 1: Atomic concentrations determined by EDX analysis for plasma power applied to the V (a) and Al (b) target. Temperature deposition is 673 K.</figcaption></figure>

Fig. 2a shows the powder X-ray diffraction patterns for the SE101-Fe<sub>2.07</sub>V<sub>0.88</sub>Ta<sub>0.09</sub>Al<sub>0.96</sub> thin film deposited under the conditions described in Table 1. No impurity peak or secondary phase has been observed. The (111) peak at around 27.1 in 2θ characteristic of the fully ordered L<sub>2</sub><sub>1</sub> structure is not visible due to the high degree of film orientation. The lattice parameter was obtained by Rietveld analysis for all samples. Fig. 2b exhibits the lattice parameter as a function of the V/Al ratio. In the presence of Ta doping, the lattice parameter shift follows the Vegard's law. The observed behavior differs from the lattice parameter variation reported for bulk and thin-film Fe<sub>2</sub>V<sub>1+x</sub>Al<sub>1-x</sub> samples [17-19]. In these studies, a minimum or "V-shape" behavior was observed, which was interpreted as being characteristic of Fe<sub>2</sub>VAl compound
that can be viewed as involving "charge transfer" with the nominal configuration
($Fe_2^{1.3-V}V^{0.8+}Al^{1.8+}$) [18].

<figure><img src="image_3.png" /><figcaption>Fig. 2 : X ray diffraction patterns of the SE101-Fe<sub>2.07</sub>V<sub>0.88</sub>Ta<sub>0.09</sub>Al<sub>0.96</sub> thin film deposited at 673 K on MgO substrates (a). Lattice parameter for various vanadium-aluminum ratio V/Al (b).</figcaption></figure>

In addition to the peak corresponding to the MgO substrate, the films exhibit only the (200) and (400) peaks. The presence of the (002) reflection suggests that the films adopt a B2 structure. A perfectly ordered L2₁ structure, however, is characterized by the presence of superlattice reflections such as (111) or (311). To determine the presence or absence of these superlattice peaks, we performed pole figure scan measurements.

For the SE101-Fe<sub>2.07</sub>V<sub>0.88</sub>Ta<sub>0.09</sub>Al<sub>0.96</sub> thin film, (022) peaks were observed with fourfold symmetry at ψ = 45° (Fig. 3a), while (111) peaks were not detected. These results, along with the observation of the (002) peak in the X-ray scan described above, confirm that the SE101 film has also grown epitaxially. However, the film exhibit a B2 structure, characterized by total disorder between V (Y) and Al (Z), while Fe (X) atoms occupy regular sites. For the SE107-Fe<sub>1.84</sub>V<sub>0.86</sub>Ta<sub>0.08</sub>Al<sub>1.22</sub> thin film, which has an excess of Al, Fig. 3b shows the fourfold symmetry of the (111) peaks at ψ = 54.7°, providing direct evidence that the film is epitaxial and at least partially crystallized in the L2<sub>1</sub> structure.

The degree of B₂ and L2₁ ordering, S<sub>B2</sub> and S<sub>L21</sub> were calculated based on S<sub>B2</sub> = √(I<sub>002</sub><sup>obs</sup>/I<sub>004</sub><sup>obs</sup>) and (S<sub>L21</sub> (3 - S<sub>B2</sub>)/2) = √(I<sub>111</sub><sup>obs</sup>/I<sub>220</sub><sup>obs</sup>) where I<sub>hkl</sub><sup>obs</sup> and I<sub>hkl</sub><sup>sim</sup> are the observed diffraction
intensity for the (hkl) plane and the simulated intensity for fully ordered alloys [20]. In SE107 thin film, S<sub>L21</sub> is equal to 42% which indicates the fully ordered structure is not perfectly formed.

<figure><img src="image_4.png" /><figcaption>**Fig. 3:** X-ray pole figures of 022 and 111 of SE101-Fe<sub>2.07</sub>V<sub>0.88</sub>Ta<sub>0.09</sub>Al<sub>0.96</sub> (a) SE107-Fe<sub>1.84</sub>V<sub>0.86</sub>Ta<sub>0.08</sub>Al<sub>1.22</sub> (b) thin films.</figcaption></figure>

Fig. 4 illustrates the typical microstructures of films deposited with a V/Al ratio greater than 1 (SE102-Fe<sub>1.98</sub>V<sub>1.01</sub>Ta<sub>0.08</sub>Al<sub>0.93</sub> for Fig. 4a) and less than 1 (SE106-Fe<sub>1.94</sub>V<sub>0.85</sub>Ta<sub>0.08</sub>Al<sub>1.13</sub> for Fig. 4b). The microstructures exhibit slight porosity, which appears marginally more pronounced in films with an excess of V doping. Furthermore, these observations corroborate the X-ray analysis, confirming the absence of any secondary phases on the film surfaces.
<figure><img src="image_5.png" /><figcaption>Fig. 4: Microstructure of the Fe-V-Ta-Al films deposited with an V/Al ratio greater than 1 (a) and less than 1 (b).</figcaption></figure>

<table><thead><tr><th>Sample</th><th>S (μV/K)</th><th>VEC</th><th>Electrical resistivity (Ω cm)</th><th>Carrier concentration (cm<sup>-3</sup>)</th><th>Thickness (nm)</th><th>Power factor (mW.K<sup>-2</sup>m<sup>-1</sup>)</th></tr></thead><tbody><tr><td>SE101<br>Fe<sub>2.07</sub>V<sub>0.88</sub>Ta<sub>0.09</sub>Al<sub>0.96</sub></td><td>-14</td><td>6.05</td><td>7.2 x 10<sup>-4</sup></td><td>- 4.87 x 10<sup>21</sup></td><td>470</td><td>0.03</td></tr><tr><td>SE102<br>Fe<sub>1.98</sub>V<sub>1.01</sub>Ta<sub>0.08</sub>Al<sub>0.93</sub></td><td>-26</td><td>6.02</td><td>8.3 x 10<sup>-4</sup></td><td>- 8.94 x 10<sup>21</sup></td><td>580</td><td>0.08</td></tr><tr><td>SE103<br>Fe<sub>1.93</sub>V<sub>1.11</sub>Ta<sub>0.08</sub>Al<sub>0.88</sub></td><td>-32</td><td>6.00</td><td>5.9 x 10<sup>-4</sup></td><td></td><td>570</td><td>0.17</td></tr><tr><td>SE104<br>Fe<sub>1.90</sub>V<sub>1.19</sub>Ta<sub>0.08</sub>Al<sub>0.83</sub></td><td>-37</td><td>6.01</td><td>3.8 x 10<sup>-4</sup></td><td>- 2.64 x 10<sup>22</sup></td><td>590</td><td>0.35</td></tr><tr><td>SE105<br>Fe<sub>1.95</sub>V<sub>0.87</sub>Ta<sub>0.082</sub>Al<sub>1.09</sub></td><td>-11</td><td>5.92</td><td>1.3 x 10<sup>-3</sup></td><td>- 3.56 x 10<sup>21</sup></td><td>580</td><td>0.01</td></tr><tr><td>SE106<br>Fe<sub>1.94</sub>V<sub>0.85</sub>Ta<sub>0.08</sub>Al<sub>1.13</sub></td><td>13</td><td>5.89</td><td>1.1 x 10<sup>-3</sup></td><td>+ 4.3 x 10<sup>21</sup></td><td>520</td><td>0.02</td></tr><tr><td>SE107<br>Fe<sub>1.84</sub>V<sub>0.86</sub>Ta<sub>0.08</sub>Al<sub>1.22</sub></td><td>44</td><td>5.77</td><td>6.2 x 10<sup>-4</sup></td><td></td><td>580</td><td>0.3</td></tr><tr><td>SE108<br>Fe<sub>1.79</sub>V<sub>0.80</sub>Ta<sub>0.07</sub>Al<sub>1.34</sub></td><td>27</td><td>5.67</td><td>3.9 x 10<sup>-4</sup></td><td></td><td>600</td><td>0.18</td></tr><tr><td>SE110<br>Fe<sub>2.07</sub>V<sub>0.93</sub>Ta<sub>0.10</sub>Al<sub>0.90</sub></td><td>-23</td><td>6.10</td><td>6.8 x 10<sup>-4</sup></td><td>- 1.01 x 10<sup>22</sup></td><td>480</td><td>0.08</td></tr><tr><td>SE111<br>Fe<sub>2.10</sub>V<sub>0.90</sub>Ta<sub>0.09</sub>Al<sub>0.91</sub></td><td>-20</td><td>6.12</td><td>7.4 x 10<sup>-4</sup></td><td>- 4.98 x 10<sup>21</sup></td><td>510</td><td>0.05</td></tr></tbody></table>
<figure><img src="image_6.png" /><figcaption>**Fig. 5 :** Seebeck coefficient vs Valence Electron Concentration (VEC) calculated from atomic concentration analysis.</figcaption></figure>

Table 2 shows transport electronic properties (S, ρ, n/p, P<sub>F</sub>), Valence Electron Concentration (VEC) calculated from atomic concentration analysis. The maximum Seebeck coefficient values are -37 µV/K and +44 µV/K respectively for n-type and p-type. Electrical resistivities vary from 0.4 to 1 mohm cm. These high values for some thin films can be explained by the fairly porous microstructures, as can be seen in Fig. 4. The power factors calculated are 0.35 and 0.2 mW K<sup>-2</sup> m<sup>-1</sup> which are about an order of magnitude lower than those obtained in FeV<sub>1+x</sub>Al<sub>1-x</sub> bulk [2, 18, 21] or thin films [19, 22] because the Seebeck coefficient is much too low and the electrical resistivity too high. The sub-50% Fe content observed in many films, along with the incomplete formation of the fully ordered L<sub>2</sub><sub>1</sub> structure as indicated by XRD analysis, may further contribute to the reduced P<sub>F</sub> values. In the future, we plan to start from a primary target with a composition close to Fe<sub>2</sub>Val and to deposit in the presence of a secondary target of pure Ta type to obtain Fe<sub>2</sub>V<sub>1-x</sub>Ta<sub>x</sub>Al compositions. Post-annealing treatments aimed at achieving the complete formation of the fully ordered structure will also be investigated.

Fig. 5 shows the variation of the Seebeck coefficient as a function of the valence electron concentration (VEC) which can be calculated from the measured film composition (VEC=(8*Fe<sub>%at</sub> + 5*V<sub>%at</sub> + 3*Al<sub>%at</sub> + 5*Ta<sub>%at</sub>) / 100).
The law is in agreement with that found in ref [19] with negative Seebeck coefficients for VEC>6 and positive for VEC<6.

It should be noted that in Fe-V-Ta-Al compounds, the coexistence of high carrier concentration and a large Seebeck coefficient can arise from the band structure complexity: narrow and degenerate bands, strong density of State asymmetry, and possible disorder/correlation effects [3, 23, 24]. These break the conventional Sα1/n trend seen in simpler semiconductors. This behavior is observed in our study for sample SE104, where both a high carrier concentration and a large Seebeck coefficient are obtained.

The films obtained show relatively high electrical resistivities despite significant carrier concentrations. This is mainly due to low carrier mobility caused by structural disorder, alloy scattering, grain boundary effects, and, in magnetic samples, spin-disorder scattering. Flat or pseudo-gapped bands near the Fermi level further can also suppress carrier transport.

<figure><img src="image_7.png" /><figcaption>Magnetic properties</figcaption></figure>

Fig. 6: Magnetization as a function of temperature in field cooled for H = 1000 Oe in n-type films (a) and magnetization as a function of magnetic field measured at 5 K (b) and 300 K (c) for different compositions (SE101-Fe<sub>2.07</sub>V<sub>0.88</sub>Ta<sub>0.09</sub>Al<sub>0.96</sub>, SE102-Fe<sub>1.98</sub>V<sub>1.01</sub>Ta<sub>0.08</sub>Al<sub>0.93</sub>, SE104-Fe<sub>1.90</sub>V<sub>1.19</sub>Ta<sub>0.08</sub>Al<sub>0.83</sub>, SE105-Fe<sub>1.95</sub>V<sub>0.87</sub>Ta<sub>0.082</sub>Al<sub>1.09</sub>, SE110-Fe<sub>2.07</sub>V<sub>0.93</sub>Ta<sub>0.10</sub>Al<sub>0.90</sub>, SE111-Fe<sub>2.10</sub>V<sub>0.90</sub>Ta<sub>0.09</sub>Al<sub>0.91</sub>). The inset in Fig. 6b shows the saturation magnetization as a function of the atomic Fe composition.

The magnetic properties of films with various compositions were investigated (Fig. 6). Films with n-type compositions exhibit ferromagnetic behavior, whereas p-type compounds are non-magnetic. The variation of magnetization in field cooled as a function of temperature for H=1000 Oe in n-type films, as well as the M(H) curves measured at 5 K and 300 K for
different compositions, are shown in Fig. 6a, 6b and 6c. These films exhibit ferromagnetic properties, with spontaneous magnetization depending on the composition. The inset in Fig. 6b illustrates this dependence as a function of the atomic Fe composition. It is observed that the films become magnetic when the Fe content exceeds approximately 1.9. This behavior aligns with the magnetic measurements reported by Endo et al [13]. In Fe<sub>2+x</sub>V<sub>1-x</sub>Al alloys, the spontaneous magnetization increases linearly with the Fe excess, reaching approximately 20 emu/g for an Fe content of 2.2. Although VEC = 6 usually favors nonmagnetic behavior, all p-type samples in this study are nonmagnetic despite VEC ≠ 6. This can be attributed to Fe deficiency on the Fe sublattice, which reduces the number of magnetic centers and suppresses long-range ordering, as well as chemical disorder and atomic substitutions that further destabilize magnetism.

Fig. 7 shows the field-dependent magnetization measured at different temperatures between 5K and 300 K for the ferromagnetic film SE101-Fe<sub>2.07</sub>V<sub>0.88</sub>Ta<sub>0.09</sub>Al<sub>0.96</sub>. In agreement with Fig. 6a, the curves show that ferromagnetic behavior develops at low temperatures. It is to be noticed that the spontaneous magnetization is only 16 emu/g (0.55 µ<sub>B</sub>/f.u.) at 5 K indicating weak itinerant ferromagnetic state. This behavior is consistent with observations reported in [15] for Fe<sub>2</sub>V<sub>0.9</sub>Cr<sub>0.1</sub>Al<sub>0.9</sub>Si<sub>0.1</sub> and in [25] for Fe<sub>2+x</sub>V<sub>1-x</sub> Al alloys.

<figure><img src="image_8.png" /><figcaption>Fig. 7: Field-dependent magnetization measured at different temperatures between 5K and 300 K for the film SE101-Fe<sub>2.07</sub>V<sub>0.88</sub>Ta<sub>0.09</sub>Al<sub>0.96</sub>.</figcaption></figure>
Fig. 8a shows the variation of electrical resistivity as a function of temperature in zero magnetic field and under a magnetic field of 9T for different thin films. For thin film SE101-Fe<sub>2.07</sub>V<sub>0.88</sub>Ta<sub>0.09</sub>Al<sub>0.96</sub>, SE110-Fe<sub>2.07</sub>V<sub>0.93</sub>Ta<sub>0.10</sub>Al<sub>0.90</sub> and SE111-Fe<sub>2.10</sub>V<sub>0.90</sub>Ta<sub>0.09</sub>Al<sub>0.91</sub> rich in V and overdoped in Fe, the curve shows a plateau for T between 70 and 150K (Fig. 8b). ρ(T) shows a semiconductor-like increase for temperatures below this plateau. For films (SE105-Fe<sub>1.95</sub>V<sub>0.87</sub>Ta<sub>0.082</sub>Al<sub>1.09</sub>) becoming less rich in V but richer in Al (underdoped in Fe), the plateau shifts toward a temperature of 100K. For films (SE106-Fe<sub>1.94</sub>V<sub>0.85</sub>Ta<sub>0.08</sub>Al<sub>1.13</sub>) even richer in Al (further underdoped in Fe), the behavior is semiconducting across the entire temperature range without showing a plateau.

A similar change in the ρ(T) slope at T<sub>c</sub> has been reported for Fe<sub>2+x</sub>V<sub>1-x</sub>Al (for x=0.2) as well [11, 13]. When magnetic field of 9T is applied, the plateau observed in thin films overdoped in Fe becomes slightly less pronounced. This leads to a MR that varies depending on the Fe doping.

Fig. 8c illustrates the percentage of MR (MR = Δρ/ρ(0)) for magnetic fields varying between -9 and +9T at different temperatures, where Δρ represents the difference between the electrical resistivities ρ(H) and ρ(0), with ρ(H) being the resistivity in the presence of a magnetic field and ρ(0) the resistivity without a magnetic field. For Fe overdoped thin films, MR is most significant at temperature close to 200 K. As shown in Fig. 8c, MR is -2.5% for temperature close to 200K. In contrast MR is close to 8% at 5K for Fe underdoped thin films.

<figure><img src="image_9.png" /><figcaption>Fig. 8: a) Electrical resistivity versus temperature for different thin films without and under a magnetic field of 9T. b) Magnification for thin films SE101-Fe<sub>2.07</sub>V<sub>0.88</sub>Ta<sub>0.09</sub>Al<sub>0.96</sub>, SE102-Fe<sub>1.98</sub>V<sub>1.01</sub>Ta<sub>0.08</sub>Al<sub>0.93</sub>, SE110-Fe<sub>2.07</sub>V<sub>0.93</sub>Ta<sub>0.10</sub>Al<sub>0.90</sub> and SE111-Fe<sub>2.10</sub>V<sub>0.90</sub>Ta<sub>0.09</sub>Al<sub>0.91</sub>. c) Magnetoresistance versus temperature for different thin films.</figcaption></figure>

In Supplementary Materials (Fig. S1) is shown MR (H) for different temperatures for thin films with various compositions.
The MR values we obtained are lower than those reported in the literature by Matsuda et al. [12]. Matsuda observed a giant magnetoresistance (GMR) of approximately 35% in the weakly inhomogeneous ferromagnet Fe₂.₁V₀.₉Al at 4.2K under a magnetic field of 9T, interpreting this behavior as a result of Anderson localization [12]. Similarly, Endo et al. [13] reported an MR of 30% in Fe₂.₁V₀.₉Al at 4.2K under a 6T magnetic field, attributing the observed metal-insulator transition to magnetic ordering, such as a ferromagnetic state or magnetic clusters under high magnetic fields.

The experimentally measured Hall resistivity, $\rho_{xy}$, is shown in Fig. 9a for various temperatures ranging from 5 K to 300 K for SE101-Fe₂.₀₇V₀.₈₈Ta₀.₀₉Al₀.₉₆ thin film. The magnetic field was swept from H = -9T to +9T. The Hall resistivity initially increases sharply up to a field of approximately 0.5T, after which the slope of the curves changes significantly, marking two distinct regions in the $\rho_{xy}$ curves. This behavior in a ferromagnetic system can be described by the sum of the ordinary Hall resistivity, $\rho_{xy}^{OHE}$, and the anomalous Hall resistivity, $\rho_{xy}^{AHE}$, according to the following relationship (1) [26, 27]):

$$ (1) \quad \rho_{xy} = \rho_{xy}^{OHE} + \rho_{xy}^{AHE} = R_0 H + 4\pi R_s M $$

Here, $R_0$ and $R_s$ are the ordinary and anomalous Hall coefficients, respectively, corresponding to the applied magnetic field H and the spontaneous magnetization M of the material.

The ordinary Hall resistivity, $\rho_{xy}^{OHE}$, dominates in the high-field region (above 1T), where $\rho_{xy}$ exhibits a weak, linear dependence on the magnetic field up to 9T. The values of $\rho_{xy}^{AHE}$ and $R_0$ can be determined by applying a linear fit to the $\rho_{xy}$ versus H curves in the high-field region, as shown in inset in Fig. 8a for a representative sample at T = 5 K. The intercept of the fit on the y-axis and its slope provide the values of $\rho_{xy}^{AHE}$ and $R_0$, respectively, while the anomalous Hall coefficient $R_s$ can be derived using the relation $\rho_{xy}^{AHE} = 4\pi R_s M$.

Hall resistivity measurements at different temperatures were carried out on thin films of different compositions (Fig. S2). Fig. 9b and 9c show the $\rho_{xy}$ versus H curves recorded respectively at 5K and 300 K. A clear analogy between the two sets of curves $\rho_{xy}$ (H) and M(H) (see Fig. 6b and 6c) is evident, confirming that the anomalous Hall resistivity $\rho_{xy}^{AHE}$ is strongly correlated with the magnetisation M.
<figure><img src="image_10.png" /><figcaption>Fig. 9: Hall resistivity, $\rho_{xy}$, for various temperatures ranging from 5 K to 300 K for SE101-Fe$_{2.07}$V$_{0.88}$Ta$_{0.09}$Al$_{0.96}$ thin film (a) and for different thin films at T = 5K (b) and T=300K (c). Anomalous Hall conductivity $\sigma_{xy}^{AHE}$ versus temperature for different thin films (d). $|\rho|$ and $|\rho^2|$ contributions in $\rho_{xy}^{AHE}$ versus temperature for SE101 thin film (e). Variation of anomalous Hall scaling coefficient ($S_H$) versus temperature for different thin films (f).</figcaption></figure>

The magnetic field-dependent Hall conductivity, $\sigma_{xy}$ (H), is calculated using the relation (2). This value is obtained by fitting the high-field data with a linear curve and extrapolating it to the zero-field axis. Fig. 9d shows the linear variation of $\sigma_{xy}^{AHE}$ versus temperature for different thin films. At 5 K, the anomalous Hall conductivity is determined to be approximately, $\sigma_{xy}^{AHE} \sim 16$ S cm$^{-1}$ for SE101-Fe$_{2.07}$V$_{0.88}$Ta$_{0.09}$Al$_{0.96}$ thin film.

$$ (2) \quad \sigma_{xy}(H) = \frac{\rho_{xy}(H)}{\rho_{xx}^2(H=0) + \rho_{xy}^2(H)} $$

This value is relatively low compared to Co-based Heusler thin films, where anomalous Hall conductivity values as high as 180 S cm$^{-1}$ have been reported [28]. Our results are comparable to those reported by Garmroudi et al. for highly disordered A2-Fe$_{2}$VAl$_{0.9}$Si$_{0.1}$ samples [14], but remain approximately 3–4 times lower than the values previously observed
in weakly ferromagnetic Fe₂V₀.₉Cr₀.₁Al₀.₉Si₀.₁ Heusler compounds [15]. However, the measured ρₓᵧ, is nearly twice as large as that reported for the AHE in ferromagnetic Fe₁₋ₓCoₓSi semiconductors [29].

One of the questions often raised in these Fe or Co-based Heusler materials is what mechanism governs these AHE? One method involves plotting the ratio) ρ<sub>xy</sub><sup>AHE</sup>/ρ<sub>xx</sub> as a function of ρ<sub>xx</sub>. This yields a linear curve following the equation (3):

$$ (3) \rho_{xy}^{AHE} / \rho_{xx} = a + b \rho_{xx} $$

The coefficients a and b provide key insights into the underlying extrinsic and intrinsic Berry curvature mechanisms. Once these coefficients are determined, we can plot |ap| and |bp²| as functions of temperature. As shown in Fig. 9e, the term |bp²| exceeds |ap|, indicating that intrinsic mechanisms dominate over extrinsic ones.

In addition it has been proposed that the intrinsic anomalous Hall conductivity σ<sub>xy</sub><sup>AHE</sup> is nearly proportional to the magnetization, meaning that the scaling coefficient S<sub>H</sub> = σ<sub>xy</sub><sup>AHE</sup>/M<sub>s</sub> should remain temperature-independent if the intrinsic contribution to the AHE is dominant [30]. Fig. 9f confirms this for our thin films, where S<sub>H</sub> is indeed invariant with temperature, indicating that the intrinsic contribution, due to the momentum space Berry curvature associated with the electronic band structure, is predominant compared to any extrinsic scattering effects in the AHE.

## 4. Conclusion

The co-sputtering synthesis of Fe-V-Ta-Al thin films highlights the versatility of this technique in achieving precise compositional control, thereby enabling the investigation of both thermoelectric and magnetic properties. Structural characterization revealed an incomplete formation of the fully ordered L2₁ phase. Thermoelectric measurements yielded Seebeck coefficients ranging from -37 µV/K to +44 µV/K for n-type and p-type films, respectively. However, the power factors remained relatively low (around 0.35 mW·K⁻²·m⁻¹), primarily due to high electrical resistivity (0.4–1 mΩ·cm), porous microstructures, and the incomplete development of the L2₁ ordered structure.

Beyond thermoelectric properties, the films exhibited ferromagnetic behavior, with composition-dependent magnetization and MR. The observation of the AHE and its intrinsic
dominance over extrinsic scattering effects further reinforces the material's potential in spintronic devices. By refining deposition techniques and optimizing composition, future research could unlock enhanced thermoelectric efficiency and novel functionalities in magnetic and electronic applications, paving the way for next-generation multifunctional materials.

**Supplementary Materials :**

The magnetoresistance MR (%) and Anomalous Hall Effect (AHE) as a function of magnetic field are presented for the following thin films: SE101-Fe<sub>2.07</sub>V<sub>0.88</sub>Ta<sub>0.09</sub>Al<sub>0.96</sub> (a), SE102-Fe<sub>1.98</sub>V<sub>1.01</sub>Ta<sub>0.08</sub>Al<sub>0.93</sub> (b), SE104-Fe<sub>1.90</sub>V<sub>1.19</sub>Ta<sub>0.08</sub>Al<sub>0.83</sub> (c), SE105-Fe<sub>1.95</sub>V<sub>0.87</sub>Ta<sub>0.082</sub>Al<sub>1.09</sub> (d), SE106-Fe<sub>1.94</sub>V<sub>0.85</sub>Ta<sub>0.08</sub>Al<sub>1.13</sub> (e), SE110-Fe<sub>2.07</sub>V<sub>0.93</sub>Ta<sub>0.10</sub>Al<sub>0.90</sub> (f) and SE111-Fe<sub>2.10</sub>V<sub>0.90</sub>Ta<sub>0.09</sub>Al<sub>0.91</sub> (g).

**Acknowledgments :** This work was supported by the Agence Nationale de la Recherche (ANR) under project "IOTEGH" (N° ANR-23-CE05-0013-03). The authors would like to express their gratitude to Stéphane Giraud from Schneider Electric for his assistance with thin film deposition. Stéphane Grenier from the Néel Institute is gratefully acknowledged for the insightful discussion and valuable assistance with the pole figure interpretation. The authors thank Paul Chometon from the same institute's for his support with sample cutting. Special thanks also go to Pierre Lachkar and Didier Dufeu from platform « Ingénierie expérimentale » at the Néel Institute for their support in PPMS and VSM-SQUID measurements.

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