# Competing Localized-Itinerant Magnetism Evidenced by Critical Behavior in the FexTi2S4 Heideite Sulfides

Romualdo S. Silva, João E. Rodrigues, Federico Serrano-Sánchez, Javier Gainza, Norbert M. Nemes, José Luis Martínez, José Antonio Alonso

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Romualdo S. Silva, João E. Rodrigues, Federico Serrano-Sánchez, Javier Gainza, Norbert M. Nemes, et al.. Competing Localized-Itinerant Magnetism Evidenced by Critical Behavior in the FexTi2S4 Heideite Sulfides. ACS Applied Electronic Materials, 2024, 6 (10), pp.7611-7616. 10.1021/acsaelm.4c01441. hal-05118238

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# Competing Localized-Itinerant Magnetism Evidenced by Critical Behavior in the FeₓTi₂S₄ Heideite Sulfides

Romualdo S. Silva,* João E. Rodrigues, Federico Serrano-Sánchez, Javier Gainza, Norbert M. Nemes, José Luis Martínez, and José Antonio Alonso*

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Cite This: ACS Appl. Electron. Mater. 2024, 6, 7611–7616

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**ABSTRACT:** We report the critical behavior of the FeₓTi₂S₄ (x = 0.24, 0.42) intercalated Heideite sulfides in the vicinity of their second-order magnetic phase transition. Several methods including the modified Arrott plot, Widom scaling law, and the critical isotherm analysis reliably yield critical exponents β = 1.105/0.442, γ = 0.913/1.042, and δ = 1.826/3.357, in agreement with the scaling hypothesis, although slightly deviating from the conventional theoretical values. Using the renormalization group theory analysis, we conclude that the exchange distance J(r) and the correlation length critical exponent ν indicate that increasing Fe content induces a transition from localized spin interactions, described by the mean-field model, to an itinerant-electron 3D Heisenberg-like

model near T<sub>C</sub>. These features reveal a coupling between short- and long-range magnetic interactions, which are responsible for the unconventional critical behavior in Fe<sub>x</sub>Ti<sub>2</sub>S<sub>4</sub>. Our results provide valuable insights into the magnetic nature and offer tuning mechanisms in Fe<sub>x</sub>Ti<sub>2</sub>S<sub>4</sub> intercalated sulfides.

**KEYWORDS:** intercalated sulfides, Fe<sub>x</sub>Ti<sub>2</sub>S<sub>4</sub>, magnetic interactions, exchange distance, scaling hypothesis, unconventional critical behavior, localized-itinerant magnetism

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## INTRODUCTION

The critical exponents related to the magnetic order transition, such as the susceptibility (γ) and the correlation length (ν) exponents, provide valuable insights into the nature of magnetic interactions and the emergence of short- and long-range magnetic orders.<sup>1</sup> Several studies through different theoretical models, such as mean-field theory and renormalization group theory, are employed to describe the critical behavior of various materials, such as CrI<sub>3</sub>, Co<sub>2</sub>TiSn, PrMn<sub>2</sub>Ge<sub>2</sub>, and Sn<sub>0.6</sub>NFe<sub>3.4</sub>.<sup>2–5</sup> The origin of the critical magnetic behavior is typically triggered by a combination of long- and short-range magnetic coupling, hybridization between localized electrons and delocalized holes, and structural frustration.<sup>5</sup> These models are useful to elucidate the underlying mechanisms driving the magnetic phase transitions and provide important predictions that can be tested experimentally.

An example of possible complexities in Fe-containing materials is layered Fe<sub>3</sub>GaTe<sub>2</sub>. In fact, Chen et al.<sup>6</sup> reported that the Fe<sub>3</sub>GaTe<sub>2</sub> layered ferromagnetic (FM) insulator can be described by a 3D Ising model with long-range interactions by the critical exponents β = 0.405, γ = 1.085, and δ = 3.679 at a Curie temperature (T<sub>C</sub>) of 342 K. In contrast, Algaidi et al.<sup>7</sup> revealed that the magnetic interactions in van der Waals

Fe<sub>3</sub>GaTe<sub>2</sub> single-crystal correspond to 3D Heisenberg model by long-range magnetic coupling with β = 0.35, γ = 1.388, and δ = 4.97 at T<sub>C</sub> = 358 K. In the same material, evidence for a 2D Heisenberg ferromagnetism was observed, presenting β = 0.401, γ = 1.075, and δ = 3.717 at T<sub>C</sub> = 223 K.<sup>8</sup> Interestingly, the presence of both itinerant and local-moment magnetism in Fe<sub>3</sub>GeTe<sub>2</sub> through the multiorbital path with different spin–spin interactions was evidenced by the variable critical exponents. This phenomenon is potentially extensible to other materials containing Fe.<sup>5</sup>

Recently, we have reported on the Fe<sub>x</sub>Ti<sub>2</sub>S<sub>4</sub> intercalated sulfide system prepared under high-pressure conditions. Depending on the synthesis temperature, different Fe contents are incorporated into the Fe<sub>x</sub>Ti<sub>2</sub>S<sub>4</sub> structure, where Fe atoms occupy interstitial positions between TiS<sub>2</sub> layers, both in octahedral coordination.<sup>9</sup> This system presents a complex scenario of magnetic properties with both antiferromagnetic

Received: August 17, 2024

Revised: September 19, 2024

Accepted: September 23, 2024

Published: October 1, 2024

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(AFM) and FM-like ordering, correlating with competitive magnetic interactions that are Fe-content-dependent. These ingredients lead to spin-glass/cluster-glass behavior and magnetocaloric effect around $T_C$.⁹ Besides, the local atomic structure fluctuations in the vicinity of $T_C$ reveal a magnetoelastic coupling, being at the origin of the magnetoresistance and anomalous Hall effect in these compounds.¹⁰ In light of these findings, the metamagnetic transitions and the second-order phase transition AFM/FM → paramagnetic (PM) state call for critical exponent analysis around $T_C$. In this work, we study in detail the critical behavior of Fe$_x$Ti$_2$S$_4$ ($x = 0.24, 0.42$) sulfides characterized by the critical exponents to gain further insights into the nature of their magnetic interactions.

## EXPERIMENTAL SECTION

The Fe$_x$Ti$_2$S$_4$ ($x = 0.24, 0.42$) intercalated sulfides were synthesized by high-pressure synthesis. Stoichiometric amounts of xFe + 2TiS$_2$ were inserted into a Nb capsule (5 mm in diameter and 15 mm in length), sealed, and placed in a cylindrical graphite heater. The reaction was carried out in a piston-cylinder press (Rockland Research Co.) under a hydrostatic pressure of 3.5 GPa for 1 h at temperatures between 800 and 900 °C, involving the oxidation of Fe metal to Fe$^{2+}$ and the reduction of Ti$^{4+}$ to Ti$^{3+}$ within the sealed capsule, avoiding the volatilization or oxidation of sulfur. Then, the materials were quenched, and the pressure was released down to ambient conditions. The temperature plays a pivotal role to stabilize different amounts of Fe into Fe$_x$Ti$_2$S$_4$, herein, $x = 0.24$ at 900 °C and $x = 0.42$ at 800 °C. These sulfides were previously characterized by analysis of neutron and synchrotron X-ray diffraction, X-ray absorption and photoelectron spectroscopy, magnetization, specific heat, magnetoresistance, Hall effect, and magnetocaloric effect. More details can be found in previous studies.⁹,¹⁰ Herein, the critical behavior of the Fe$_x$Ti$_2$S$_4$ ($x = 0.24, 0.42$) sulfides was investigated through several isothermal magnetization $M(H)$ curves obtained with applied fields $H$ up to 70 kOe in the vicinity of $T_C = 82$ K for $x = 0.24$ and $T_C = 114$ K for $x = 0.42$ in a Magnetic Properties Measurement System with a 7 T magnet equipped with a vibrating sample magnetometer (VSM) option (MPMS3, Quantum Design, USA). The $T_C$ values were assumed from ref.⁹.

## RESULTS AND DISCUSSION

Figure 1a,b displays the $M(H)$ curves in the critical region around $T_C$ (60–135 K) for $x = 0.24$ and $x = 0.42$, respectively. As expected, these isotherms exhibit a gradual transition from AFM/FM-like order to the PM state, where $T_C$ is denoted by the red line. In the second-order phase transition, the criticality is characterized by interdependent critical exponents.¹¹ Near this transition, the correlation length diverges as $\xi = \xi_0|(|T - T_C|/T_C|)^{-\nu}$, and there are universal scaling laws for the spontaneous magnetization $M_S$ and the inverse initial magnetic susceptibility $\chi_0^{-1}$. The $M_S$ below $T_C$, the $\chi_0^{-1}$ above $T_C$, and the $M(H)$ at $T_C$ are described by critical exponents $\beta, \gamma$, and $\delta$ that give insight into the magnetic interactions, correlation length, spin-dimensionality, and decaying distance of magnetic coupling,² defined as follows:

$$M_S(0, \epsilon) \sim (-\epsilon)^\beta, \epsilon < 0, T < T_C \quad (1)$$

<figure><img src="image_10.png" /><figcaption>Figure 1. Isothermal magnetization $M(H)$ curves at different temperatures around $T_C$ (red line) for (a) $x = 0.24$ and (b) $x = 0.42$.</figcaption></figure>

$$\chi_0^{-1}(0, \epsilon) \sim (\epsilon)^\gamma, \epsilon > 0, T > T_C \quad (2)$$

$$M(H, 0) \sim (H)^{1/\delta}, \epsilon = 0, T = T_C \quad (3)$$

where $\epsilon = (T - T_C)/T_C$ is the reduced temperature.¹² The critical exponents are interdependent, and the Widom scaling relation predicts that $\delta = 1 + \gamma/\beta$.¹

In this way, according to the Arrott-Noakes equation of state:

$$(H/M)^{1/\gamma} = a\epsilon + b(M)^{1/\beta} \quad (4)$$

where $a$ and $b$ are adjustable constants, the modified Arrott plot (MAP) of $(M)^{1/\beta}$ vs $(H/M)^{1/\gamma}$ (based on eq 4) is a widely used straightforward method to analyze critical behavior from the direct magnetization measurements.⁵ Thus, with proper $\beta$ and $\gamma$ values, a set of parallel straight lines are expected to show up in the high-field range, with the isotherm at $T_C$ passing through the origin of coordinates.¹³ Herein, we tested a few conventional theoretical models such as mean field ($\beta = 0.5, \gamma = 1.0$), tricritical mean field ($\beta = 0.25, \gamma = 1.0$), 3D Ising ($\beta = 0.325, \gamma = 1.24$), 3D Heisenberg ($\beta = 0.365, \gamma = 1.386$), and 3D XY ($\beta = 0.345, \gamma = 1.316$), as shown in Figure 2a–e for $x = 0.24$ and Figure 2f–j for $x = 0.42$, respectively. Clearly, the behavior of the MAP curves for $x = 0.24$ is distinct from that for $x = 0.42$, and these universality class models cannot precisely express the critical behavior of the entire Fe$_x$Ti$_2$S$_4$ for different $x$ values.

Then, the critical exponents $\beta$ and $\gamma$ were precisely determined by the iteration method, converging in the MAP fitting $(M)^{1/\beta}$ vs $(H/M)^{1/\gamma}$ on values of $\beta = 1.012$ and $\gamma = 0.926$ for $x = 0.24$, whereas $\beta = 0.428$ and $\gamma = 1.112$ for $x = 0.42$ (see Figure 3a,b). With these critical exponents, the linear
<figure><img src="image_11.png" /><figcaption>Figure 2. Modified Arrott plot $M^{1/β}$ vs $(H/M)^{1/γ}$ with the mean-field model, tricritical mean-field model, 3D Ising model, 3D Heisenberg model, and 3D XY model, respectively, for: (a–e) $x = 0.24$ and (f–j) $x = 0.42$.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>Figure 3. Modified Arrott plot ($M^{1/β}$ vs $(H/M)^{1/γ}$ curves converged with precise critical exponents $β$ and $γ$ for $Fe_xTi_2S_4$ with (a) $x = 0.24$ and (b) $x = 0.42$. (c,d) Temperature dependence of spontaneous magnetization ($M_s$) and initial inverse susceptibility ($χ_0^{-1}$). The gray dashed lines represent the best-fit curve according to eqs 1 and 2. The insets show log-log plots of the $M(H)$ isotherm nearest to $T_C$. Scaling plots from eq 5 below ($T < T_C$) and above ($T > T_C$) $T_C$ for (e) $x = 0.24$ and (f) $x = 0.42$ using $β$ and $γ$ determined by the MAP method. The same plot in the log-log scale is shown in the inset plot.</figcaption></figure>

extrapolation from the high-field region of the $T_C$ curves passes through the origin of the coordinates (green lines). Curiously, the change of Fe content inverts the order of the exponents, with $β > γ$ for $x = 0.24$, whereas $β < γ$ for $x = 0.42$. This can be related to the presence of the magnetic anisotropy at low field originating from the competition between FM and AFM exchange interactions. The final $M_s$ and $χ_0^{-1}$ values as a function of temperature from extrapolated curves at $T < T_C$ and $T > T_C$ are presented in Figure 3c,d, respectively. The

converged $M_s(T)$ and $χ^{-1}(T)$ curves fitting (based on eqs 1 and 2, respectively) yielded $β = 1.105$ with $T_C = 78.56$ K and $γ = 0.913$ with $T_C = 80.32$ K for $x = 0.24$, whereas $β = 0.442$ with $T_C = 115.9$ K and $γ = 1.042$ with $T_C = 116.5$ K for $x = 0.42$. As expected, these critical temperatures from the MAP fitting are close to that previously reported for $T_C = 82$ K ($x = 0.24$) and $T_C = 114$ K ($x = 0.42$).⁹ A linear fitting of the $M(H)$ curve at $T_C$ (according to eq 3) for both samples in the log-log scale provided $δ = 1.878$ and 3.285 (inset of Figure 3c,d),
respectively. These values also agree with those obtained using the Widom scaling relation $\delta = 1 + \gamma/\beta$,¹,¹⁴ found to be $\delta = 1.826$ and 3.357, respectively. Thus, the critical exponents obtained from converged MAP curves and the final fitted curves of $M_S$ and $\chi_0^{-1}$ values are very close and self-consistent.

To certify the reliability of the obtained critical exponents, the scaling hypothesis was analyzed by the magnetic equation of state in the asymptotic critical region, expressed as

$$M(H, \epsilon) = |\epsilon|^{\beta} f_{\pm} \left( \frac{H}{|\epsilon|^{\beta\delta}} \right) \quad (5)$$

where $f_{\pm}$ are regular functions with $f_{\pm}$ for temperatures above $T_C$ and $f_{\mp}$ for temperatures below $T_C$.¹⁴,¹⁵ Figure 3e,f displays the result of $M|\epsilon|^{-\beta}$ vs $H|\epsilon|^{-\beta\delta}$ curves (from eq 5) with $\beta$, $\delta$, and $T_C$ values obtained from the MAP analyses for $x = 0.24$ and 0.42, respectively. Clearly, the collapse into two branches of well-defined universal curves for $T < T_C$ and $T > T_C$ are observed for $x = 0.24$, best noticed in the inset on a logarithmic scale (see Figure 3e). However, for $x = 0.42$, the curves do not collapse at all in the low-field region below $T_C$, as highlighted in the inset of Figure 3f. These results suggest that $Fe_{0.42}Ti_2S_4$ at low fields and $T < T_C$ is not a simple ferromagnet, similarly to $Fe_3GaTe_2$,⁶ which we believe is due to the competition between FM and AFM exchange interactions present on the $Fe_xTi_2S_4$ sulfides, as previously reported.⁹ Moreover, this scenario should be associated with the spin-glass-like behavior near the magnetic transition temperature in these sulfides.⁹

The obtained critical exponents for the $Fe_xTi_2S_4$ ($x = 0.24$, 0.42) sulfides are listed in Table 1, which exhibit substantial

<table><caption>**Table 1.** Comparison of the Critical Exponents of $Fe_xTi_2S_4$ ($x = 0.24$, 0.42) with Different Conventional Theoretical Models.¹⁵</caption><thead><tr><th></th><th>Method</th><th>T<sub>C</sub> (K)</th><th>β</th><th>γ</th><th>δ</th></tr></thead><tbody><tr><td rowspan="2">Fe<sub>0.24</sub>Ti<sub>2</sub>S<sub>4</sub></td><td>Modified Arrott plot</td><td>79.44</td><td>1.105</td><td>0.913</td><td>1.826</td></tr><tr><td>Critical isotherm</td><td>81</td><td></td><td></td><td>1.878</td></tr><tr><td rowspan="2">Fe<sub>0.42</sub>Ti<sub>2</sub>S<sub>4</sub></td><td>Modified Arrott plot</td><td>116.2</td><td>0.442</td><td>1.042</td><td>3.357</td></tr><tr><td>Critical isotherm</td><td>114</td><td></td><td></td><td>3.285</td></tr><tr><td>mean field</td><td>Theory</td><td></td><td>0.5</td><td>1.0</td><td>3.0</td></tr><tr><td>tricritical mean field</td><td>Theory</td><td></td><td>0.25</td><td>1.0</td><td>5.0</td></tr><tr><td>3D Ising</td><td>Theory</td><td></td><td>0.325</td><td>1.24</td><td>4.82</td></tr><tr><td>3D xy</td><td>Theory</td><td></td><td>0.345</td><td>1.316</td><td>4.81</td></tr><tr><td>3D Heisenberg</td><td>Theory</td><td></td><td>0.365</td><td>1.386</td><td>4.8</td></tr></tbody></table>

differences among themselves and are compared to several conventional theoretical models.¹⁵ Although the $\gamma$ critical exponents are found to be similar for both samples, $\beta$ and $\delta$ deviate significantly from any theoretical model. However, we noticed that $\beta$ tends to decrease; meanwhile, $\delta$ increases with highest Fe content. According to the estimated critical exponents, $Fe_xTi_2S_4$ cannot be exactly categorized into any single universality class. On the other hand, these values exhibit the tendency to be between the mean-field and 3D Heisenberg-like models, with short- and long-range interactions. This hypothesis is plausible due to the competing magnetic interactions in these sulfides. Thus, we demonstrate that the critical exponents obtained here are reliable and in agreement with the scaling hypothesis.

According to renormalization group analysis,¹⁶ the interactions between spins with long-range interactions decay with spin-spin distance $r$ as

$$J(r) \approx r^{-(d+\sigma)} \quad (6)$$

where $d$ is the spatial dimensionality and $\sigma$ is a constant ($\sigma > 0$). The long-range and short-range magnetic interactions correspond to $\sigma < 2$ and $\sigma > 2$, respectively. Furthermore, $\sigma$ has the following relation with the exponent $\gamma$:

$$\gamma = 1 + \frac{4(n + 2)}{d(n + 8)}\Delta\sigma + \frac{8(n + 2)(n - 4)}{d^2(n + 8)^2} \left[ 1 + \frac{2G(d/2)(7n + 20)}{(n - 4)(n + 8)} \right] \Delta\sigma^2 \quad (7)$$

where $d$ and $n$ are the spatial and spin dimensions of the magnetic system, respectively, whereas $\Delta\sigma = \sigma - d/2$ and $G(d/2) = 3 - 1/4(d/2)^2$. For a three-dimensional material ($d = 3$), we have $J(r) \approx r^{-(3+\sigma)}$ with $3/2 \le \sigma \le 2$. When $\sigma = 2$, the 3D Heisenberg model ($\beta = 0.365$, $\gamma = 1.386$, and $\delta = 4.8$) is valid for the isotropic three-dimensional ferromagnet, with $J(r)$ decreasing precisely as $r^{-5}$. When $\sigma = 3/2$, conditions for the mean-field model ($\beta = 0.5$, $\gamma = 1.0$, and $\delta = 3.0$) are satisfied, with $J(r)$ decreasing slower than $r^{-4.5}$.¹⁷ Using our magnetic data, the parameters in eq 7 were adjusted for particular values of {$d:n$} to generate critical exponents consistent with those that are experimentally obtained in Table 1. We found that using {$3:3$} gives $\sigma = 1.35$ ($<3/2$) for $x = 0.24$, implying in magnetic exchange distance decreasing as $J(r) \approx r^{-4.4}$, whereas for $x = 0.42$, it yields $\sigma = 1.61$ ($>3/2$) with $J(r) \approx r^{-4.6}$. The $J(r)$ values suggest that the main spin interactions are long-range magnetic interactions. In the case of $x = 0.24$, the $\sigma < 3/2$ indicates slow decay of the magnetic coupling, expected for a mean-field model type. On the other hand, the Fe-content increase in $Fe_xTi_2S_4$ ($x = 0.42$) induces a tendency toward the 3D Heisenberg model type with both short- and long-range magnetic coupling, similar to the conclusions recently reported for $PrMn_2Ge_2$,⁴ and $Fe_3GaTe_2$.⁷ Moreover, the correlation length critical exponent $\nu = \gamma/\sigma$ is smaller for $x = 0.42$, being 0.647 compared to 0.676 obtained for $x = 0.24$, which further reinforces our arguments.

Based on our findings, we proposed a scheme of the possible exchange interactions into the $Fe_xTi_2S_4$ lattice depending on the Fe content (in Figure 4), considering the Hamiltonian model of spin as follows:

$$\vec{H}_{\text{spin}} = -J_{nn} \sum_{\langle i,j \rangle} (\vec{S}_i \cdot \vec{S}_j) - J_{nm} \sum_{\langle i,j \rangle} (\vec{S}_i \cdot \vec{S}_j) \quad (8)$$

where $J_{nn}$ and $J_{nm}$ represent the FM (↑↓) and AFM (↓↑) exchange couplings, respectively; $\vec{S}$ denotes the spin representation; and $i,j$ are the spin pairs. For the case of $Fe_xTi_2S_4$, when the Fe content is lower, the long-range magnetic interactions are more significant than the short-range ones, mostly favoring AFM coupling between nearest neighbors ($J_{nn} < J_{nm}$). However, with increasing Fe content, some ions may couple to each other antiferromagnetically, while others remain aligned to the external field. This situation yields a ferromagnetic coupling ($J_{nn} \approx J_{nm}$), favoring a competition between FM and AFM clusters, and therefore modulating the magnetic order in the system;⁹ see Figure 4. As a result, the Fe-content increase leads to the majority of
<figure><img src="image_13.png" /><figcaption>**Figure 4.** Scheme of the possible exchange interactions into the Fe<sub>x</sub>Ti<sub>2</sub>S<sub>4</sub> lattice, depending on the Fe-content. For x = 0.24, more Fe vacancies promote the stabilization of long-range AFM interactions with exchange distance decaying as r<sup>-4.4</sup>. For x = 0.42, less Fe vacancies promote the enhancement of J<sub>nn</sub> term (short-range FM interactions) which changes the nature of magnetic interactions, yielding an exchange distance of r<sup>-4.6</sup>.</figcaption></figure>

localized spin magnetic interactions, described by the mean-field model, to an itinerant spin magnetic interactions nature of the 3D Heisenberg model type, as suggested by the *J*(r) exchange distance (from eq 6) values [J(r) ≈ r<sup>-4.4</sup> → J(r) ≈ r<sup>-4.6</sup>]. Therefore, the critical exponents further confirm the coexistence and complex magnetic exchange between short- and long-range interactions in the system, which should be responsible for the unconventional critical behavior in the Fe<sub>x</sub>Ti<sub>2</sub>S<sub>4</sub> sulfides.

## ■ CONCLUSION

In summary, we have performed a comprehensive study of the critical behavior of the Fe<sub>x</sub>Ti<sub>2</sub>S<sub>4</sub> (x = 0.24, 0.42) sulfides around the critical region of their FM/AFM-PM magnetic phase transition. The respective critical exponents β = 1.105/0.442, γ = 0.913/1.042, and δ = 1.826/3.357 extracted iteratively from the modified Arrott plots are self-consistent. However, the divergence in the scaling hypothesis for x = 0.42 indicates the competition between the FM and AFM exchange interactions. Using the renormalization group analysis, we concluded that the exchange distance for the spin-spin interaction decays as J(r) ≈ r<sup>-4.4</sup> for x = 0.24, whereas it does somewhat faster as J(r) ≈ r<sup>-4.6</sup> for x = 0.42. This result suggests a trend toward the presence of 3D Heisenberg-type interactions with short- and long-range magnetic coupling, with a slightly smaller correlation length critical exponent. Lastly, we provided insights into the nature of the magnetism of the Fe<sub>x</sub>Ti<sub>2</sub>S<sub>4</sub> sulfides and argued for the coexistence of the magnetic interactions being responsible for their unconventional critical behavior.

## ■ AUTHOR INFORMATION

### Corresponding Authors

Romualdo S. Silva - Instituto de Ciencia de Materiales de Madrid (ICMM), CSIC, Madrid E-28049, Spain;

● orcid.org/0000-0002-6749-5293; Email: romu.fisica@gmail.com

José Antonio Alonso - Instituto de Ciencia de Materiales de Madrid (ICMM), CSIC, Madrid E-28049, Spain;

● orcid.org/0000-0001-5329-1225; Email: ja.alonso@icmm.csic.es

### Authors

João E. Rodrigues - CELLS-ALBA Synchrotron Light Source, Barcelona E-08290, Spain; ● orcid.org/0000-0002-9220-5809

Federico Serrano-Sánchez - Instituto de Ciencia de Materiales de Madrid (ICMM), CSIC, Madrid E-28049, Spain

Javier Gainza - European Synchrotron Radiation Facility (ESRF), Grenoble 38000, France; ● orcid.org/0000-0002-1999-3116

Norbert M. Nemes - Instituto de Ciencia de Materiales de Madrid (ICMM), CSIC, Madrid E-28049, Spain; Departamento de Física de Materiales, Universidad Complutense de Madrid, Madrid E-28040, Spain

José Luis Martínez - Instituto de Ciencia de Materiales de Madrid (ICMM), CSIC, Madrid E-28049, Spain;

● orcid.org/0000-0001-9046-8237

Complete contact information is available at:
https://pubs.acs.org/10.1021/acsaelm.4c01441

### Notes

The authors declare no competing financial interest.

## ■ ACKNOWLEDGMENTS

We acknowledge the financial support of the Spanish Ministry for Science and Innovation (MCIN/AEI/10.13039/501100011033) for granting the projects: PID2021-122477OB-100, TED2021-129254B-C21, and TED2021-129254B-C22.

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