Synthesis, Structural, and Magnetic Properties of High-Entropy (Fe_0.2Co_0.2Cu_0.2Ni_0.2Mn_0.2)Nb₂O₆

Abstract

In this work, we present the first report on the synthesis via the sol–gel method of a high-entropy (Fe_0.2Co_0.2Cu_0.2Ni_0.2Mn_0.2)Nb₂O₆ with columbite–orthorhombic structure. Polyvinylpyrrolidone (PVP), ammonium niobium oxalate, and equimolar amounts of Fe, Co, Cu, Ni, and Mn ions were used. The refinement of the XRD pattern showed the presence of niobate crystallites with an average size of 48.4 nm and a fraction of 7.6 wt% of a spinel-like phase. At temperatures below 5 K, the DC and AC magnetometry results revealed the presence of a ferromagnetic-like phase due to the niobate phase. The Mössbauer spectrum at 300 K showed a paramagnetic and two magnetically ordered components corresponding to the niobate and the spinel-like phases, respectively. The spectral components were typical of Fe³⁺, indicating the presence of cation vacancies. The elemental mapping obtained from EDS measurements showed compositional homogeneity. The XRF measurements confirmed a composition consistent with nominal values. These results confirm the feasibility of synthesizing entropy-stabilized columbite oxides via the sol–gel route, opening new opportunities for the design of multifunctional ceramics with tunable structural and magnetic properties for high-performance thermal barrier coatings and energy conversion applications.

1. Introduction

The development of emerging technologies, ranging from renewable energy conversion to advanced electronics, requires materials that combine low cost, high efficiency, and structural stability, along with specific features such as homogeneity, morphology, and well-defined physicochemical properties. These materials generally consist of five or more metal cations in approximately equimolar proportions, providing high thermal and crystalline stability and interesting magnetic properties [1,2].

High-entropy oxides (HEO) with enhanced properties have been extensively studied, for instance the high-entropy oxide Li(Gd_0.2Ho_0.2Er_0.2Yb_0.2Lu_0.2)GeO₄ was explored as a microwave dielectric ceramic for low-temperature cofired ceramic technologies [3]. Due to their increased stability driven by high configurational entropy, high-entropy perovskites show great potential in energy devices, such as (electro)catalysts, solid oxide fuel cell electrodes, and anodes for lithium-ion batteries [4]. Excellent microwave dielectric properties were found in high-entropy spinel-type (Mg_0.2Co_0.2Ni_0.2Li_0.4Zn_0.2)Al₂O₄ ceramics, making them an ideal candidate for applications in millimeter-wave communication [5]. High-entropy rare-earth niobates and tantalates were synthesized, the entropy-stabilization effect and the lattice distortions caused by multi-cation substitution were the primary factors contributing to their beneficial properties for high-performance thermal barrier coatings (TBC) for the next generation of TBCs designed for high-temperature applications [6]. High-entropy fluorite oxides can be used in a variety of applications including solid ionic conductors, high temperature coatings, and catalysts [7].

In HEO, the entropy is a thermodynamic property that quantifies the degree of cation disorder or randomness in the crystalline structure. A high entropy contains at least five different elements. The stability of the HEO is discussed in terms of the Gibbs free energy of mixing given by ΔG_mixing = ΔH_mixing − TΔS_config, where ΔH_mixing is the enthalpy of mixing, T is the absolute temperature, and ΔS_config is the configurational entropy. The configurational entropy for a HEO containing five different elements can be calculated by equation: ${\Delta S}_{config}=-R{\sum }_{i=1}^5{x}_{i}Ln\left(x_i\right)$, where R is the universal gas constant, and x_i is the mole fraction of elements present in the cation sites [8]. For a HEO sample with five elements in equimolar amounts, x_i = 0.2, the entropy will be ${\Delta S}_{config}=1.61R$.

High-entropy ceramics with spinel, pyrochlore, fluorite, and perovskite structures have been extensively studied [8,9,10,11,12,13]; however, only two studies reported the production of high-entropy ceramics with columbite-type structure. The (Fe_0.2Co_0.2Cu_0.2Zn_0.2Mn_0.2)Nb₂O₆ is synthesized by the solid-state reaction method [14] and the (Mg_0.2Cu_0.2Ni_0.2Co_0.2Zn_0.2)Nb₂O₆ is obtained by a modified solution combustion method [15]. Compounds with columbite structure are described by the general formula ANb₂O₆ (space group Pbcn), where A is a divalent cation that could be Ca, Cd, Zn, Mg, Ni, Mn, Co, Fe, or Cu.

Niobium oxides with orthorhombic crystalline structure with chemical formula ANb₂O₆ were produced, aiming their use in solar cells, microwave devices, photo-catalysis, and energy storage devices among others [16,17,18,19].

High-entropy niobates-based materials also showed enhanced thermophysical properties. For instance, Zhu et al. prepared (Sr_0.2Ba_0.2La_0.2Eu_0.2Pb_0.2)Nb₂O₆ and found ultralow thermal conductivity combined with high thermopower [20]. Furthermore, Su et al. synthesized and studied the thermoelectric properties of the high-entropy (Fe_0.2Co_0.2Cu_0.2Zn_0.2Mn_0.2)Nb₂O₆ with columbite-type structure; their sample exhibited poor thermal conductivity and was used in thermal insulation applications [14].

Several methods have been reported for the synthesis of HEOs, namely high-energy ball milling [21,22], co-precipitation [23], combustion [17], and sol–gel [24]. In these cases, the synthesis process significantly affects the particle morphology and chemical characteristics of the samples [25].

PVP is a biocompatible polymer and a steric stabilizer widely used from the food to pharmaceutical industries [26]. PVP can be used in the synthesis of nanostructured powder via the sol–gel method. The role of PVP in the solution of metal salts is to afford a polymeric network to prevent cation mobility, ensuring homogeneous stoichiometry, homogeneous morphology, and preventing the formation of undesirable crystalline phases [27,28]. PVP has pyrrolidone rings attached to the carbon skeleton. In the resonance stage of the pyrrolidone rings, it contains (C-O) groups and nitrogen heteroatoms. Interactions between PVP molecules and metal nitrates/sulfates occur through strong ionic interactions between metal cations and the negatively charged (C-O)⁻ group, whereas the highly polar amide group interacts with the (NO₃)⁻ and (SO₄)²⁻ anions, and these functional groups facilitate in the nucleation and growth of nanoparticles [29].

The aim of this work was to synthesize the high-entropy (Fe_0.2Co_0.2Cu_0.2Ni_0.2Mn_0.2)Nb₂O₆ (HE-Nb₂O₆) by the sol–gel method, using PVP as a gel matrix, and study its crystalline, composition homogeneity, morphological characteristics and magnetic properties. As far as the authors are aware, it is the first report demonstrating the synthesis of HE-Nb₂O₆ and therefore the first report on the study on the crystallographic, morphological, and magnetic properties.

2. Experimental

2.1. Materials

Cobalt nitrate (Co(N₂O₆·6(H₂O), 98%, (Sigma Aldrich, São Paulo, SP, Brazil), copper nitrate (Cu(NO₃)₂·3(H₂O), 98%, (Êxodo Científica, Sumaré, SP, Brazil), iron nitrate (Fe(NO₃)₃·9(H₂O), 98%, (Dinâmica, Indaiatuba, SP, Brazil), manganese sulfate (MnSO₄)·H₂O 98%, (Científica ACS, Rio de Janeiro, RJ, Brazil), nickel nitrate (Ni(NO₃)₂·6H₂O), 98%,( Científica ACS, Rio de Janeiro, RJ, Brazil), polyvinylpyrrolidone (PVP, MW = 1.300.000 g·mol⁻¹, Companhia das Essencias, São Paulo, SP, Brazil), ethanol (99.8%, ASC), Nb₂O₅ (94.55%, Sigma Aldrich, São Paulo, SP, Brazil), potassium hydrogen sulfate KHSO₄, 96.55%, (Dinâmica, Indaiatuba, SP, Brazil).

2.2. Synthesis

2.2.1. Synthesis of Ammonium Niobium Oxalate

The niobium oxalate was prepared as follows: the Nb₂O₅ was melted in a platinum crucible containing KHSO₄ in a mass proportion Nb₂O₅/KHSO₄ of 1/7. Then, the precursor was grinded and washed several times. Afterwards, the solid was treated with oxalic acid (H₂C₂O₄) and ammonium oxalate (C₂H₈N₂O₄) in a mass proportion of 1:3. The dispersion was thoroughly mixed at 60 °C in a magnetic stirrer (Solidsteel, Piracicaba, SP, Brazil) and then dried in the furnace (Q318M-Quimis, Diadema, SP, Brazil) at 100 °C for 12 h. This procedure was similar to the one developed by Souto et al. [30]. The resultant product was ammonium niobium oxalate, (NH₄)₃NbO(C₂O₄)₃·H₂O.

2.2.2. Synthesis of HE-Nb₂O₆

For the synthesis of HE-Nb₂O₆, 2 g of PVP was dissolved in 20 mL of ethanol. Then, equimolar amounts of transition metals (Co, Cu, Mn, Fe, and Ni) together with (NH₄)₃NbO(C₂O₄)₃. H₂O salts were then dissolved in 20 mL of ethanol for 2 h at 25 °C. The PVP and the metal salt solutions were mixed at 25 °C for 15 h. The final solution was warmed up in a furnace (Q318M-Quimis, Diadema, SP, Brazil) to 100 °C at a rate of 10 °C/min and remained for 2 h. The dried precursor was calcined in air at 1000 °C for 2 h, with a heating rate of 10 °C/min. Finally, the sample was grinded and characterized. We considered a lower calcination temperature (<1000 °C) but the sample presented a higher contribution of a spinel phase. At calcination temperatures higher than 1000 °C, the spinel contribution remained nearly constant. Therefore, the calcination temperature was set to 1000 °C.

2.3. Characterization

The chemical composition of the sample was determined using an X-ray fluorescence (XRF) spectrometer (Shimadzu XRF-1800, Kyoto, Japan). The crystalline structure of the sample was investigated by X-ray diffraction (XRD). XRD data was collected in a Miniflex II (Rigaku, Tokio, Japan) diffractometer within the angular range of 10–90° (2θ) at a step size of 0.02°, scan of 3°/min. Rietveld refinement was performed using Maud software (version 2.99993) to obtain a quantitative phase analysis and determine lattice parameters. The crystalline phase was identified using crystallographic data from the Inorganic Crystal Structure Database (ICSD). The morphological characterization of HE-Nb₂O₆ was conducted using a scanning electron microscope (SEM) from Carl Zeiss (Supra 35-VP, Carl Zeiss AG, Oberkochen, Germany), equipped with a Bruker energy-dispersive X-ray spectrometer (EDS) detector (Bruker Corporation, Billerica, MA, USA) and Shimadzu (SSX-550, Kyoto, Japan). The EDS was used to identify the chemical elements present in the sample. The magnetic measurements were conducted in a Physical Properties Measurement System model Dynacool from Quantum Design (San Diego, CA, USA) equipped with a vibrating sample magnetometer. The Mössbauer spectrum was recorded at 300 K using a Wissel spectrometer (Starnberg, Germany). The spectrum was fitted using the Normos95 software (version 2.0), and the isomer shift was reported in relation to α-Fe at 300 K.

3. Results and Discussion

3.1. Structural and Morphological Characterization

To confirm the presence of the elements in the prepared sample, elemental analysis was performed using X-ray fluorescence spectroscopy (XRF). The XRF results summarized in

Table 1. Elemental analysis by XRF.

Elements	Nominal (at.%)	XRF (at.%)
Niobium	66.65	67.80
Nickel	6.67	6.82
Iron	6.67	6.92
Cobalt	6.67	6.65
Copper	6.67	5.16
Manganese	6.67	6.65
Total	100	100

confirmed the presence of Ni, Cu, Fe, Co, Mn, and Nb elements with concentrations in close agreement with the nominal values. The analysis revealed no impurities were detected in the sample.

Figure 1a shows the Rietveld refinement and corresponding XRD pattern of the sample. The diffraction pattern revealed the presence of two crystalline phases. The analysis revealed the predominant presence of a columbite-type HE-Nb₂O₆ phase, accounting for 92.4 wt.% of the total amount, along with 7.6 wt.% of a spinel-like phase. The refinement was carried out using the ICSD-9712 card for the columbite-type structure and the ICSD-127433 for the spinel phase. The simulated curves showed excellent agreement with the experimental data.

All peaks corresponding to the main phase were indexed to an orthorhombic crystal structure with the Pbcn space group. The average crystallite size was estimated to be 48.4 nm using the Scherrer equation. In contrast, the spinel phase exhibited a crystallite size of 32.5 nm, indexed to a cubic crystal structure with the Fd-3m space group. It is acknowledged that peak broadening may also arise from additional contributions, such as microstructural strain, internal stress, possible phase overlap, and instrumental effects. Nevertheless, despite these inherent limitations, the Scherrer equation is a widely accepted and reliable method, providing values that are close to the actual dimensions of the coherent crystalline domains. Therefore, the estimated crystallite sizes reported here can be regarded as representative and meaningful for structural comparison between different phases and samples.

A magnified view of the main diffraction peaks, (311) and (020), of the niobate phase, showed in Figure 1a, did not exhibit any shoulders, suggesting the absence of a secondary niobate phase with a different lattice parameter and same orthorhombic structure with the Pbcn space group. At the angular range 30.0–30.4°, there was an overlapping of peaks from the niobate and spinel phases, where the peak of the spinel phase was very small and did not contribute significantly to the overall intensity, whereas the (311) peak of the niobate is the highest of this phase and dominated the diffractogram. The refined theoretical curve matched the experimental data well. The crystallographic results were in close agreement with the (Fe_0.2Co_0.2Cu_0.2Zn_0.2Mn_0.2)Nb₂O₆ sample with columbite structure reported by Su et al. [14]. Figure 1b presents a schematic representation of the crystal structure composed of two octahedral units, namely (Fe_0.2Ni_0.2Co_0.2Mn_0.2Cu_0.2)O₆ and NbO₆. The oxygen anions form corner-sharing octahedra around the TM²⁺ (TM is a transition metal) and Nb⁵⁺ ions, creating isolated zig-zag chains of the TM ions.

Table 2. Parameters obtained from Rietveld refinement.

Phase	Crystal Structure Parameters					Quality of Fit
ICSD 9712	Lattice parameter a (Å)	Lattice parameter b (Å)	Lattice parameter c (Å)	Phase (wt.%)	Cryst. Size (nm)	Rwp Rexp χ2 3.35 1.19 2.79
	14.18	5.72	5.05	92.4	48.4
ICSD 127433	8.45	8.45	8.45	7.6	32.5

summarizes the refinement results and quality indicators. The refinement produced β values of 90°, confirming orthorhombic symmetry. The Rietveld refinement indicators (χ² = (Rwp/Rexp)², Rwp, and Rexp) were within the acceptable range for complex oxide systems. High-entropy oxides with five or more elements can increase the χ² in Rietveld refinements due to the complexity of fitting a disordered structure with multiple cations of different radii. The varied ionic radii create local distortions, microstrain, and potential site disorder, that can be difficult to model with a single crystallographic structure, leading to a relatively high χ² value.

Figure 2a–d show the scanning electron microscopy (SEM) images of the sample, revealing polycrystalline particles with sizes of a few micrometers, agglomerated and with rod-like morphology. In the sol–gel synthesis, the polymer PVP may influence the shape and size of particles when the calcination temperature is below 600 °C. At 600 °C, the PVP begins to transform into carbon. At higher temperatures, the grains aggregate and coalesce, forming bigger particles and leading to micron-sized rods. These rods had an average size of 3.62 μm, as shown in the inset of Figure 2c. The elemental distribution was analyzed using energy-dispersive X-ray spectroscopy (EDS). The picture in Figure 2e shows the area that was analyzed to obtain the elemental mapping. A general view of all elements is shown in Figure 2f. The mapping of elements Mn, Nb, Cu, Ni, Co, Fe, and O is shown in pictures g, h, i, j, k, l, and m, respectively. These images show, in an approximate manner, the homogenous dispersion of elements in the particles, indicating a chemical homogeneity of elements in the HE-Nb₂O₆ sample.

3.2. Magnetic Properties

Mossbauer spectroscopy is a highly sensitive technique used to study the occupancy, magnetic ordering, and oxidation state of Fe ions among the available sites in the niobate and spinel phases. Figure 3 shows the Mossbauer spectrum recorded at 300 K.

The Mössbauer spectrum was fitted to three components, namely sextets S1 and S2 and, a doublet D. The hyperfine parameters obtained from the fit are shown in

Table 3. Hyperfine parameters from the Mössbauer spectrum. ΔQ and QS are quadrupole shift (related to the sextets) and quadrupole splitting (related to the doublet), respectively.

	S1	S2	D
IS (mm/s)	0.28	0.40	0.42
ΔQ or QS (mm/s)	0.01	0.03	0.64
Width (mm/s)	0.56	0.38	0.50
Bhf (T)	47.9	51.1	-
Area (%)	48	15	37O

. It is important to mention that a single sextet did not adequately fit correctly the spectrum, because the magnetic spectral component is asymmetric, i.e., the first and second peaks have a higher intensity when compared with the fifth and sixth peaks. Moreover, the rightmost peak exhibited a shoulder that confirmed the presence of the second sextet. The two sextets were ascribed to Fe in the spinel crystal structure and reflected two different chemical environments. In fact, cations in the spinel structure occupy tetrahedral and octahedral oxygen coordinated sites and the sextet with the lowest isomer shift (IS) is usually ascribed to Fe at tetrahedral sites [31]. In the present case, the sextets S1 and S2 were related to Fe at tetrahedral and octahedral sites, respectively. It is known that paramagnetic Fe²⁺ has IS and quadrupole splitting (QS) larger than 1.0 mm/s [32]. In the present work, the sextets and the doublet had IS smaller than 0.5 mm/s. These results clearly indicated that the Fe oxidation state in the sample was Fe³⁺. In the niobate structure, all their cations occupy octahedral sites. Taking into account that pure phases of MNb₂O₆, where M = {Fe, Co, Ni}, have magnetic ordering temperatures below 10 K [33], and at 300 K, these phases are paramagnetic. Therefore, the doublet may be associated with the HE-Nb₂O₆ phase.

The general chemical formula for niobates is ANb₂O₆, which contains cations with Nb⁵⁺ and A²⁺ oxidation states. In the present work, the Fe²⁺ was substituted by Fe³⁺, which resulted in a charge imbalance in the HE-Nb₂O₆ phase. To restore charge neutrality of the crystal, the niobate may form cation vacancies at A or Nb sites. For instance, it is clear that every two Fe³⁺ ions will induce a single A²⁺ vacancy, or every five Fe³⁺ will induce a single Nb⁵⁺ vacancy. Regarding the magnetic behavior of the HE-Nb₂O₆ phase, the interaction between magnetic A ions, A = {Fe, Co, Cu, Ni, Mn}, are through a superexchange of the type A₁-O-A₂. Assuming that A ions have valences of Fe³⁺, Co²⁺, Cu²⁺, Ni²⁺, and Mn²⁺, it will provide a high-spin magnetic moment of 5.92, 3.87, 1.73, 2.83, and 5.92 μ_B. The wide range of magnetic moments and the presence of cationic vacancies can alter the superexchange interactions leading to changes in magnetic properties such as spin disorder and an overall reduction in magnetic moment. These vacancies disrupt the ideal A₁-O-A₂ path leading to a reduction in the coupling strength and potentially creating sites where magnetic interactions are absent.

Magnetic measurements were performed to better understand the overall magnetic behavior of the sample. The zero-field-cooled (Mzfc) and field-cooled (Mfc) magnetizations were recorded under a magnetic field of 200 Oe and are shown in Figure 4. The measurements were conducted in the warming mode, i.e., they initiated at 3 K and continued up to 300 K.

Starting at 3 K, the Mzfc values decreased rapidly up to T ≈ 25 K and then increased gradually up to 140 K, where shoulder feature was observed before continuing to increase until reaching 300 K. These facts suggest that at 300 K, there is a magnetically ordered phase in the sample and its blocking temperature lies at higher temperatures. The Mfc values started at 3 K and decreased quickly until 25 K, continued decreasing slowly up to 200 K, and then slightly increased up to 300 K. At temperatures below 25 K, both Mzfc and Mfc curves seem to follow a T⁻¹ trend that can be ascribed to paramagnetic regime. These curves merged at 300 K, indicating that the irreversibility temperature was at T > 300 K, and this reinforces the idea that at room temperature, the sample has a magnetically ordered component. It is known that spinels contain cations bearing magnetic moments and usually exhibit a ferromagnetic to paramagnetic Néel transition (T_N) at temperatures well above room temperature. It confirms the conclusions of the Mössbauer study, that the spinel is related to the sextets and the doublet is related to the niobate phase.

The literature has several reports on the magnetic properties of niobates of the type ANb₂O₆, where A = {Co, Ni, Cu, Fe, Mn}. The comparison of earlier reports with the present results will help us to understand the magnetic behavior for the HE-Nb₂O₆ phase. For instance, Lei et al. studied the magnetic properties of MNb₂O₆ where M = {Fe, Co, Ni}, their samples had an antiferromagnetic (AFM) ordering with Tn at 1.8, 3.0, and 6.0 K, respectively, and above these temperatures the samples were paramagnetic [33]. In other work, Sarvezuk et al. studied the magnetic behavior of the Ni_xFe_1−xNb₂O₆ and in spite of the fact that FeNb₂O₆ and NiNb₂O₆ were magnetically ordered at low temperature, chemical disorder induces a loss of long-range magnetic order in the Ni_xFe_1−xNb₂O₆ series for x = {0.2, 0.4, 0.6, 0.8 }. Nevertheless, the dominant exchange interactions in the system were ferromagnetic-like, occurring inside the zig-zag chains along the c axis [34]. Ghosh et al. studied the magnetic ground state of MnNb₂O₆ polycrystals, and they obtained T_N = 4.33 K [35].

Similarly, Liu et al. studied the magnetic properties of a Co_0.1Zn_0.9Nb₂O₆ sample. In their susceptibility data in the range of 3–300 K, they did not observe any peak related to the AFM transition, whereas the analysis of the inverse of the susceptibility χ⁻¹ and the Curie–Weiss model χ⁻¹ = (T − θ)/C resulted in θ = −0.165 K, indicating an AFM coupling of Co moments. Therefore, they postulated a T_N smaller than 3 K [36]. Liu et al. concluded that their results agreed well with those reported by Nakajima et al., in which the commensurate AFM ground state disappeared by substituting Co by nonmagnetic Mg ions in CoNb₂O₆ [37]. Nakajima et al. studied the magnetic properties, by means of neutron diffraction measurements, of single crystals of Co_1−xMg_xNb₂O₆ with x = {0, 0.004, 0.008}. They found that the commensurate AFM ground state disappeared by substituting only 0.8% of magnetic Co²⁺ for nonmagnetic Mg²⁺. They concluded that the disappearance of the AFM phase was because the phase transition from the incommensurate phase to the AFM phase was strongly suppressed by pinning effects due to the impurities [37]. In light of the above references for structures of the type ANb₂O₆, Nakajima et al. concluded that their samples had AFM transitions at temperatures smaller than 5 K, and none of them showed ferromagnetic/ferrimagnetic behavior at room temperature. In the present work, the M-T measurements also suggested that the HE-Nb₂O₆ phase had a magnetic transition at temperatures below 7 K.

It is worth mentioning that the blocking temperature (T_B) is relative to the measuring time (t_m) of the technique used to study a given system. For instance, t_m for Mössbauer spectroscopy and magnetometry techniques are 10⁻⁸ s and 1–10 s, respectively. It implies that the T_B obtained by Mössbauer spectroscopy will be higher than the one obtained by magnetometry. Thus, at 300 K, a given sample can appear as thermally blocked by Mossbauer spectroscopy and superparamagnetic by magnetometry.

Figure 5 presents the isothermal magnetization obtained at 3 and 300 K for the sample. At 300 K, the high field (~100 kOe) did not saturate the magnetizations of the sample, indicating the superposition of paramagnetic and ferromagnetic signals. The magnetization measured at 3 K and at a field of 100 kOe was of 38.3 emu/g, the remanence magnetization was Mr = 1.59 emu/g, the coercivity field Hc = 380 Oe. Whereas, the magnetization measured at 300 K and at a field of 100 kOe was of 5.6 emu/g, Mr = 0.47 emu/g, and Hc = 110 Oe. The lower inset presents the hysteresis in a low field range; this figure clearly shows the variations of Mr and Hc values for both measurements and suggests the presence of an overall ferromagnetic-like phase for the measurement recorded at 3 K. To further show the presence of the spinel phase, the upper inset presents a zoomed-in view of the derivative of the magnetizations obtained at 3 and 300 K. Both derivatives were conducted in the ascending magnetization curves. As one can notice, the derivatives showed symmetric curves, i.e., besides the central peak, there was not any shoulder that may indicate the presence of a second ferromagnetic phase. This provides evidence that at 3 K, both phases were interacting magnetically via superexchange forces leading to a collective magnetic behavior. For the measurement recorded at 300 K, the derivative curve was centralized at a field close to the Hc = 110 Oe and was sharper when compared with the derivative of the magnetization at 3 K.

Figure 6 shows the AC susceptibility measurements recorded under frequencies from 100 to 5000 Hz. Figure 6a shows the in-phase (χ′) AC susceptibility data recorded under an AC magnetic field of 10 Oe and frequency of 5 kHz. The trend observed in the χ′ graph is approximately similar to that observed in the DC Mzfc curve shown in Figure 4. However, the out-of-phase AC susceptibility signal (χ″), presented in Figure 6b, showed interesting features. Notably, there is a strong signal below 7 K; this behavior is typical of a ferromagnetic-like phase. In fact, the absence of a net magnetic moment, e.g., as in AFM material with perfectly matched antiparallel alignment of opposing moments, should show no signal in the χ″ measurements. Meanwhile, the signal observed at T < 7 K, in χ″ data, suggested that the HE-Nb₂O₆ may be a ferromagnetic-like phase, therefore exhibiting a net magnetic moment. As mentioned before, earlier reports on magnetic characterization on samples of the type ANb₂O₆, where A = {Fe, Co, Ni, Mn} [33,35] showed AFM behavior, samples of (Ni_xFe_1−x)Nb₂O₆ showed ferromagnetic like behavior with ordering temperatures below 10 K [34], and samples (Co_xZn_1−x)Nb₂O₆ showed AFM properties [36,37]. In the present case, a certain amount of vacancies (A_v) are expected at the A or Nb sites due to the presence of Fe³⁺ substituting Fe²⁺; thus, the linkage A_v-O-A will affect the overall superexchange interaction of neighbors A cations, therefore leading to a disordered magnetic structure and to a net magnetic signal.

The small signal observed at 31–35 K was from the holder sample and did not belong to the sample. There was also a peak at T_P = 285 K, and to study this signal, AC susceptibility measurements were conducted as a function of frequency for temperatures in the range 200–330 K. The AC susceptibility data is shown in Figure 6c, and as one can see, the χ″ susceptibility peak shifts to higher temperatures when the frequency increases, indicating the presence of a dynamic effect due to the magnetic moments in the presence of an AC magnetic field.

In order to study the variation of T_P as a function of frequency, the Néel–Brown model was considered [38,39]. This model is indicated to study an ensemble of non-interacting single domain magnetic nanoparticles with their super-moments relaxing with a period of τ = 1/f and in an absolute temperature T_P. The equation of the Néel–Brown model is given by

$$f=f_o{e}^{-{\displaystyle \frac{E_m}{K_B{T}_P}}}$$

(1)

where f_o is the attempt frequency that is of the order of 10⁹–10¹² s⁻¹, E_m is the activation anisotropy energy of each particle, K_B is the Boltzmann constant, and T_P is the peak temperature. Equation (1) can be presented as Ln(f) = Ln(f_o) − (E_m/K_B)·T_P⁻¹. Figure 6d shows the plot of Ln(f) versus T_P⁻¹ and its fitting to a straight line; the inset shows the equation obtained from the linear fit. The obtained fitting parameters were Ln(f_o) = 29 and E_m/K_B = 5822 K; therefore, the values of f_o and E_m were 3.9 10¹² s⁻¹ and 8.034 10⁻²⁰ J, respectively. As noted, the f_o value is within the expected for the attempt frequency, and this result suggests that the Néel–Brown model well describes the superparamagnetic regime of the spinel phase.

In order to further confirm the superparamagnetic behavior of the system, one can use the empirical φ parameter. It is known that for non-interacting superparamagnetic particles, φ takes the values of 0.1 < φ < 0.13. For systems under a spinglass regime, the φ values can be in the weak interaction regime for 0.03 < φ < 0.06, and for the strong interaction regime when 0.005 < φ < 0.02 [40]. The equation for the φ parameter is given by

$$\phi ={\displaystyle \frac{∆T_P}{T_P∆\left(Log\right(f\left)\right)}}$$

(2)

In the present work, the obtained value for φ was of 0.097; this value was very close to 0.1 and suggested that the AC signal at T > 230 K is related to non-interacting superparamagnetic particles. In general, spinels have ferrimagnetic (FIM) behavior with ordering temperature well above 300 K [39]. In the present work, at T > 5 K, the spinel nanoparticles are embedded in the paramagnetic HE-Nb₂O₆ phase and developed a superparamagnetic behavior.

4. Conclusions

The high-entropy compound (Fe_0.2Co_0.2Cu_0.2Ni_0.2Mn_0.2)Nb₂O₆ with an orthorhombic crystal structure was synthesized for the first time, and a secondary spinel phase was also formed. The synthesis method was adjusted to minimize the amount of the spinel phase; thus, the precursor sample was thermally treated at 1000 °C for 2 h. The Rietveld refinement results indicated the formation of a niobate with orthorhombic structure with an average crystallite size of 48.4 nm, while the spinel phase exhibited a crystallite size of 32.5 nm. The SEM images showed polycrystalline particles with an average size of 3.62 μm. The elemental mapping revealed a homogeneous distribution of elements within the sample. The XRF data confirmed the nominal concentration of elements in the sample. The AC and DC magnetic measurements suggested the presence of a ferromagnetic-like phase due to HE-Nb₂O₆ at temperatures below 7 K. A ferromagnetic response was also observed at 300 K, originating from the spinel phase. The spinel nanoparticles were dispersed within paramagnetic niobate phase at 300 K and exhibited a superparamagnetic behavior close to room temperature as shown by the AC susceptibility measurements. The method used to prepare the sample seems to be useful to synthesize high-entropy structures with disordered chemical occupancy. This material has potential applications for high-performance thermal barrier coatings.