Study of the electronic, magnetic, and thermoelectric aspects of spinel chalcogenides SrCe₂Z₄ (Z = Te, Se, S) for spintronic and energy applications

Abstract

Spinel chalcogenides are promising candidates for the advancement of spintronic and thermoelectric devices. Therefore, this article presents the structural, electronic, and magnetic characteristics of SrCe₂Z₄ (Z = S, Se, Te) spinels employing WIEN2k in the context of density functional theory. The expansion of the unit cell is witnessed with the incorporation of larger anions and lattice parameters, including 12.01 Å for SrCe₂S₄, 12.52 Å for SrCe₂Se₄, and 13.42 Å for SrCe₂Te₄. The maximum release of energy in the FM states (rather than AFM states) and the negative enthalpy of formation (−2.20 eV, −2.05 eV, and −1.94 eV) confirm their dominant ferromagnetic nature and the thermodynamic stability of the system. The spin-polarized band structure exhibits the ferromagnetic semiconducting nature of SrCe₂S₄ and SrCe₂Te₄, as well as the half-metallic ferromagnetic behavior of SrCe₂Se₄. The analysis of the total density of states also endorses the exact nature predicted during the band structure investigation. The magnetic properties are explored by calculating the direct exchange energy Δ_x(f), indirect exchange energy Δ_x(pf), along with the exchange constants N_oα and N_oβ to analyze the magnetic behavior. The significant hybridization of chalcogenide's 2p states and the f states from the Ce atom located at the Fermi level results in the total magnetic moments. All these compositions reveal that the Curie temperature is near or above room temperature. The thermoelectric characteristics of the spinels are examined utilizing the BoltzTrap code to inspect the parameters including power factors and the figure of merit as a function of temperature. The ZT value of 0.90 for SrCe₂Te₄ indicates its higher thermoelectric efficiency and potential for future thermoelectric devices.

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1. Introduction

The high energy consumption, low processing speed, and large size of traditional electronic devices make them outdated, emphasizing the need for novel nanoscale chips that are more effective, faster, and more appropriate for cutting-edge technologies.¹ Nowadays, spintronics is one of the emerging fields that uses both the spin and charge of electrons, offering significant potential for next-generation electronic devices.² Electrons exist in two spin channels, i.e., spin-up (S↑) and spin-down (S↓).³ Understanding spintronics is essential to harness the full potential of electron spin to revolutionize the electronics industry, as it enables a wide range of innovative applications in data processing and storage.² The identification of giant magnetoresistance (GMR) in 1988 illustrated that under an applied magnetic field, the resistance of a thin magnetic layer significantly changes and can improve the performance of data storage devices. This internal response of electron spin has led to the development of memory devices that offer both rapid access and non-volatility.⁴ High spin-polarization is a key to improving the quality, faster data processing, and data storage aptitude of spintronics devices.^5,6 Ferromagnetic (FM) semiconductor materials have the highest spin polarization because of the different semiconducting and insulation properties in the spin majority (S↑) and spin minority (S↓) orientations.⁷ For potential spintronic devices, the Curie temperature (T_c) must be higher than RT.^8,9 GMR applications mostly involve spin filtering,¹⁰ including spin valves and magnetic field sensors used to form hard disks.¹¹ Double perovskites, Heusler alloys, and spinels have potential applications in spintronics, but the FM spinels, which have anions from chalcogens, have gained special interest for the newly discovered spintronic applications.¹²

In spintronics, spinel chalcogenides are recognized for their unique structural, electrical, magnetic, and transport characteristics. The empirical formula of spinel is AB₂X₄, in which A and B are cations, and X represents the anions Se, S, Te, and O.¹³ The cubic closed-packed arrangements of anions generate the octahedral and tetrahedral sites, which are filled by the cations.¹⁴ In the crystal structure of spinels, the A^II resides in 1/8th of the tetrahedral void, and the B^III resides in 1/2nd of the octahedral voids.¹⁵ To check whether the spinel structure is normal or inverse, we follow the specific rule that cations are transitional or non-transitional metals.¹⁶ Spinel chalcogenides have exceptional magnetic characteristics, including high magnetoresistance, which changes the electrical resistance in response to applied magnetic fields, making them suitable for magnetic sensing, data storage, and magnetic field modulation applications. In addition, the attractive thermoelectric (TE) properties enhance their utility for energy conversion and processing.² Spinels have high thermal and chemical stability.¹⁷ In light of existing literature, it has been observed that no research has been done on spinel composition SrCe₂Z₄, which has a wide spectrum of tunable properties, making it promising for advanced applications.¹⁸

The previous studies reveal that spinels with rare earth metals are considered emerging breakthroughs for spintronics devices.¹⁹ Researchers are particularly interested in spinels having rare earth metals because of their intense spin polarization, which leads to higher magnetoresistance.²⁰ High magnetoresistance is primarily used in spintronic devices like spin valves, biosensors, magnetic field sensors, and other electronic devices. Hassan et al. (2024) reported on the presence of half-metallic ferromagnetism (HMF) with complete spin polarization in Heusler alloys, before moving on to other materials like chalcogenides and spinels.²¹ Similarly, Alburaih et al. (2024) found that RE-based MgSm₂Y₄ (Y = S, Se) spinels exhibited HM ferromagnetism, high SP, and promising TE characteristics, with MgSm₂S₄ showing the highest value of ZT.²² Manjunatha et al. (2020) investigated the magnetic and electronic characteristics of Co_1−xSc_xCr₂O₄ (x = 0.0 and 0.05) nanoparticles by DFT and experimental methods. To better understand the magnetic behavior, field-dependent magnetization and temperature-dependent susceptibility were measured in two magnetic transitions, paramagnetic, collinear ferrimagnetic, and non-collinear spiral states.²³ Maqsood et al. (2024) investigated Cd-based spinels CdSm₂(S/Se)₄ chalcogenide, and found them suitable for spintronic applications due to their promising magnetic and electrical properties. The total magnetic moment was 10.0 μ_B for both compositions.²⁴ Noor et al. (2024) carried out DFT-based research to inspect the mechanical, electronic, and magnetic properties of HgSm₂S₄ and HgSm₂Se₄ chalcogenides for spintronic applications. Both compounds exhibited a total magnetic moment of 10.0 μ_B.²⁵ Kattan et al. (2024) investigated the HMF and transport properties of MgCo₂ (S/Se)₄ chalcogenides for energy harvesting and spintronic implementations. Their study confirmed the half-metallic nature and robust ferromagnetic behavior of these materials, highlighting their potential for high-performance thermoelectric and spintronic devices.²⁶ In another study, Albalawi et al. (2023) inspected MgEr₂(S/Se)₄ spinels, revealing stable ferromagnetism, full SP, and showing potential in TE characteristics for energy harvesting.²⁷ The SrCe₂Z₄ spinels, especially SrCe₂Te₄, show exceptional thermoelectric efficiency and magnetic nature, positioning them as superior candidates for future thermoelectric and spintronic devices. Khushi et al. (2023) performed first-principles simulations on CdHo₂Y₄ (Y = S, Se) spinels, demonstrating their ferromagnetic behavior and suitability for energy storage.²⁸

Ramzan et al. (2022) confirmed HMF and favorable transport characteristics in MgV₂S/Se₄ chalcogenides, indicating their promise in thermoelectric and spintronic applications.²⁹ Bilal et al. (2022) explored the half-metallic ferromagnetism of spinel MgFe₂Z₄ (Z = S, Se) chalcogenides for spintronic implementations. Their results verified these material's half-metallic behavior and robust ferromagnetic ordering, highlighting their suitability for advanced spintronic device applications.³⁰ Alburaih (2021) examined the RE-doped spinels CdEr₂X₄ (X = S, Se), reporting strong ferromagnetism and efficient electronic transport for spintronic and energy harvesting applications. The study found that both materials exhibit a total magnetic moment of 5.0 μ_B.³¹ Based on the available data, no theoretical analysis has been carried out on the transport and ferromagnetism features of SrCe₂Z₄ (Z = Se, S, and Te) spinels. Thus, we theoretically investigated the electrical, magnetic, and transport properties of SrCe₂Z₄, where Z corresponds to Se, S, and Te, to realize their suitability for spintronic and energy harvesting device applications.

2. Computational study

The computations on SrCe₂Z₄ (Z = S, Se, Te) were performed utilizing the DFT-based FP-LAPW method within WIEN2k,³² which is highly recommended for computing the structural, electronic, and magnetic characteristics. The structural characteristics were calculated using the PBE-GGA approximation.³³ This approximation calculates the structural findings exactly, but underestimates the electronic band gaps and electronic state calculations on which magnetic and thermoelectric characteristics depend. Therefore, the TB-mBJ potential³⁴ was used to compute these compositions' band structure and density of states. This versatile and accurate potential consumes less computational cost and is easier to handle than the hybrid functionals HSE06 and GGA + U potentials. The basis set comprises non-overlapping atomic spheres with muffin tin radii R_MT and an interstitial region having a plane wave expansion with wave vector k. The R_MT and K_max products are set to be 8. The plane wave cutoff value related to the Gaussian factor (G_max) was set to 16 during initialization. For the expansion of the wave function, the maximum value of the angular momentum L_max was set as 10, as it is a dimensionless quantity. For a non-shifted 14 × 14 × 14 grid, a denser k-mesh is utilized for all physical properties. The default energy convergence criteria were set at 10⁻⁵ Ry. The BoltzTrap code³⁵ was used to compute the transport parameters of the studied compounds. The calculation of the electrical conductivity σ_αβ(T) and Seebeck coefficient S_αβ(T) as a function of temperature was performed using the following equations:where Ω is the unit cell volume, f(T) is the Fermi–Dirac distribution, e is the charge of the electron, and σ_αβ(ε) is the transport distribution function as a function of energy, given by:

3. Results and discussions

3.1. Structural properties

For spinel SrCe₂Z₄ (where Z is equal to S, Se, or Te), the face-centered cubic unit cell, having 8 formula units per unit cell, is depicted by a ball-stick model in Fig. 1(a). Sr, Ce, and Z have been represented with blue, brown, and yellow balls in this model, respectively. Sr is divalent (Sr²⁺) and Ce is trivalent (Ce³⁺), making them both non-transition cations, thereby classifying the structure as a normal spinel. The configurations have a space group of Fd3̄m (#227). In this unit cell, the atoms Sr, Ce, and Z have coordinates (0.125, 0.125, 0.125), (0.5, 0.5, 0.5), and (0.25, 0.25, 0.25), respectively. Each individual atom, Sr, Ce, and Z, has unique Wyckoff positions, such as 8a, 16d, and 32e,³⁶ respectively. Fig. 2(b) represents the polyhedral structure, where the anions form an FCC lattice. It can also be observed that the Sr atom occupies the tetrahedral void in SrZ₄, whereas Ce occupies the octahedral void in CeZ₆ in the FCC lattice.^37,38 So, from the above information, the coordination numbers of Sr, Ce, and Z in SrCe₂Z₄ are 4, 6, and 4, correspondingly.

Fig. 1 (a) Illustration of the ball-stick model of the SrCe₂Z₄ crystal structure (with Z = S, Se, and Te), while (b) depicts the structure of the polyhedron.

Fig. 2 Energy optimization trends for (a) SrCe₂S₄, (b) SrCe₂Se₄, and (c) SrCe₂Te₄.

The ground state energy (Ryd) and the volume (a.u.³) in AFM and FM states were calculated and plotted using the Murnaghan equation of state.³⁹ Fig. 2 shows the two parabolic curves, with the red one representing the AFM state and the black curve representing the FM state. Fig. 2(a–c) demonstrates the volume optimization graphs of SrCe₂S₄, SrCe₂Se₄, and SrCe₂Te₄. In the AFM state, all compositions release less energy than in the FM state. Therefore, the FM state is energetically more favorable for all compositions. Among all these compositions, SrCe₂Te₄ has the highest lattice parameters and lowest ground state energy. Therefore, it is the most stable.⁴⁰

The lattice constant a₀ (Å) can be calculated from Fig. 2. SrCe₂Te₄ has a higher lattice constant value (13.42 Å) [Table 1] because of the larger ionic radii of Te. The lattice constants for SrCe₂S₄ and SrCe₂Se₄ were 12.01 and 12.52 Å, respectively. As the bulk modulus B₀ (GPa) of the material is inversely proportional to the lattice constant, the bulk moduli decrease with the rise of the lattice constant. The value of B₀ was reported as 53.42 GPa for SrCe₂S₄, which declined to 42.76 and 33.42 GPa for SrCe₂Se₄ and SrCe₂Te₄, respectively.⁴¹ The B₀ quantifies the hardness of a material by evaluating its resistance to uniform volumetric compression under applied pressure.⁴² The FM states have higher thermodynamic stability due to their higher enthalpy (H_f) of formation, as the material releases more energy in this state.⁴³ From Table 1, the H_f value of SrCe₂S₄ is −2.20 eV, indicating its higher thermodynamic stability. The values of H_f for the Se and Te-based compositions are noted as −2.05 and −1.94 eV, respectively. The Curie temperatures of all compositions are above room temperature, but SrCe₂Te₄ has a higher Curie temperature (310 K). The Curie temperature being near room temperature positions these materials as promising aspirants for energy-efficient data erasing and writing under manageable thermal conditions.³⁶

Table 1 The computed structural parameters for SrCe₂Z₄ (Z = S, Se, Te)

Parameters	a0 (Å)	B0 (GPa)	Hf (eV)	Tc (K)	Eg (eV)	Ref.
SrCe2S4	12.01	53.42	−2.2	295	2.20	This work
HgY2S4	11.12	76.19	−8.64	—	1.20	44
MgLu2S4	10.82	78.03	—	—	2.60	45
MgY2S4	11.06	64.88	—	—	1.62	46
LiCr2S4	9.73	97.41	−1.18	—	1.40	47
ZnMn2S4	9.98	—	−2.86	—	1.55	48
SrCe2Se4	12.52	42.76	−2.05	302	1.71	This work
HgY2Se4	11.62	63.65	−6.88	—	0.60	44
MgLu2Se4	11.32	65.14	—	—	2.00	45
MgY2Se4	11.54	53.88	—	—	1.09	46
LiCr2Se4	10.24	78.86	—	—	1.10	47
ZnMn2Se4	10.57	—	−2.98	—	0.85	48
SrCe2Te4	13.42	33.42	−1.94	310	1.30	This work
ZnMn2Te4	11.34	—	−3.01	—	0.24	48

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3.2. Electronics properties

The electrical properties, such as the density of states (DOS) and the band structure (BS), are critical computations to evaluate the composite's potential for optical applications. Sr-based spinels exhibit exciting electronic properties that verify their FM nature. The TB-mBJ potential is used as the theoretical approach to achieve an accurate bandgap value because of its ability to accurately predict BS, as investigated in previous studies.⁴⁹ The BS properties of three compositions, SrCe₂S₄, SrCe₂Se₄, and SrCe₂Te₄, are demonstrated in Fig. 3(a–c). The dashed line separating the conduction (CB) and the valence bands (VB) represents the Fermi energy (E_f). In all compositions, the VB maxima and CB minima lie on the same symmetry point, showing the direct bandgap nature of these materials.⁵⁰ In Fig. 3(a) and (c), in the S↑ orientation, the energy states are close to the E_f, indicating semiconducting behavior. In contrast, the S↓ channel shows the insulating behavior due to a large bandgap separating the states of the VB and CBs. This suggests their FM nature with complete spin polarization. Overall, the BS of SrCe₂S₄ and SrCe₂Te₄ indicates that the material behaves as an FM semiconductor.⁵¹ The spin-polarized behavior of both examined compositions is calculated by utilizing this formula:where Do^↑(E_f) and Do^↑(E_f) signify the DOS at the E_f for the S↑ and S↓ channels, correspondingly.⁵² Due to the energy states being slightly above the E_f, the SrCe₂Se₄ in the S↑ channel exhibits a metallic nature, as illustrated in Fig. 3(b). The S↓ channel shows insulating behavior because the Fermi level lies within these bands.⁵³ So, the overall nature of SrCe₂Se₄ is half-metallic. In Fig. 3(c), the energy difference between the VB and CB indicates that the E_g of SrCe₂Te₄ is minimal. Due to the half-metallic nature, the E_g of SrCe₂Se₄ is not considered.

Fig. 3 The band structures in both the spin-up and spin-down channels: (a) SrCe₂S₄, (b) SrCe₂Se₄, and (c) SrCe₂Te₄.

The total DOS and the partial DOS for each atom are calculated to provide a detailed explanation of the mechanism of ferromagnetism.⁵⁴ Fig. 4 illustrates the TDOS and PDOS of the SrCe₂S₄ composition. The TDOS reflects the electronic BS, and the energy states are shown as peaks. In Fig. 4, the TDOS reflects the combined contributions of all atoms and their corresponding valence orbitals, with VB on the left side and CB on the other side of the Fermi level. According to the PDOS plot, the VB edge at the Fermi energy is composed of 4f—Ce states and 3p—S states together, while 5s—Sr and 3p—S states firmly hybridize in the VB in the energy range from −2.8 eV to −1 eV. In the CB, near the E_f, 4f—Ce has a significant contribution, ranging from 0.5 to 1.95 eV. So, Ce's overall PDOS has made a substantial contribution to TDOS.

Fig. 4 The TDOS and PDOS of SrCe₂S₄ in the spin-up and spin-down channels.

In contrast to earlier compositions, SrCe₂Se₄ demonstrates a half-metallic ferromagnetic nature, as demonstrated by its band structure and DOS analysis. The TDOS and PDOS plots for this composition are highlighted in Fig. 5, which indicates that the 4f—Ce states play a significant role close to the Fermi level, crossing the E_f between −0.2 eV and 0.2 eV and causing the metallic behavior in the spin-up channel. On the other hand, the 4p—Se states exhibit insulating properties and contribute little at E_f, but are essential in the valence band (VB) between −2.9 eV and −1 eV. Furthermore, these states lie in the range of 2–6 eV in the conduction band. The unique half-metallic behavior is reinforced by the fact that Ce makes the most significant overall contribution to the TDOS. The interaction of energy states is responsible for this behavior, which aligns with observations in similar materials and highlights the importance of composition in controlling electronic properties.⁵⁵

Fig. 5 The TDOS and PDOS of SrCe₂Se₄ in the spin up and spin down channels.

Fig. 6 illustrates the TDOS and PDOS for SrCe₂Te₄. Like the other two compositions, the Ce element has the maximum involvement in the development of the TDOS. In this case, the energy states near the E_F, extending from −1 eV to the Fermi level, show that a greater number of peaks are present compared to the other two compositions, and there is a slight variance between the highest value of the VB and the minimum value of the CB, indicating the lowest E_g of SrCe₂Te₄.

Fig. 6 The TDOS and PDOS of SrCe₂Te₄ in the spin up and spin down channels.

3.3. Magnetic properties

The magnetic properties reflect how the material responds to an external magnetic force field. The magnetic nature of the substance can be conceptualized in terms of direct Δ_x(f) and indirect Δ_x(pf) exchange energies, crystal field stabilization energy Δ_CF, and exchange constants N_oα and N_oβ.⁵⁶ The geometry of f-orbitals is more complex than that of d orbitals, so the crystal field stabilization energy, ΔCF, cannot be calculated for compositions containing f-block metal cations. For a material to exhibit an FM nature, the value of the direct exchange energy Δ_x(f) must be higher than the stabilization energy.⁵⁷ The Δ_x(f) exhibits negative values of −0.32, −1.047, and −0.36 eV for SrCe₂Z₄ (Z = S, Se, Te), where SrCe₂S₄ and SrCe₂Te₄ show ferromagnetic semiconducting behavior and SrCe₂Se₄ exhibits a half-metallic nature. The negative sign usually indicates the material's ferromagnetic ordering, confirming its ferromagnetic nature.⁵⁸ This unexpected ferromagnetism is due to the dominance of indirect exchange interaction, such as double exchange or the super exchange mechanism.⁵⁹ The formula can calculate the value of Δ_x(f) as Δ_x(f) = Δ\(f)^↓ − Δ(f)^↑.⁶⁰ The indirect exchange of energy Δ_x(pf) is produced by the hybridization between p-block chalcogens (S, Se, Te) and f-block Ce. We can calculate the Δ_x(pf) from only the VB maximum S and the S channel's maximum peaks. The value of the indirect exchange is negative, indicating the FM behavior in the S↓ channel for SrCe₂S₄, SrCe₂Se₄, and SrCe₂Te₄, showing their intense spin polarization.⁶¹ All the calculated values are presented in Table 3.

The interaction in which electrons from CBs exchange with the localized MM is referred to as the exchange constant N_oα. The exchange interaction involving holes from the VB and the localized MM is categorized by the exchange constant N_oβ. The following formula can be used to calculate the N_oα and N_oβ:

From Table 2, we can observe the value of N_oα and N_oβ. Here, ΔE_c = E_c^↓ − E_c^↑ indicates the splitting at the CB edge, and ΔE_v = E_v^↓ − E_v^↑ represents the splitting at the VB edge.⁵⁷ Table 2 shows that the obtained results of N_oα and N_oβ for SrCe₂Z₄ (Z = S, Se, Te) are negative and induce intense spin polarization, leading to the FM order of SrCe₂S₄ and SrCe₂Te₄. With the influence of the spin-exchange interactions and electronic structure, SrCe₂Se₄ shows half-metallic ferromagnetism.⁶² From the exchange constant equations, the splitting of the CB edge depends on s-f hybridization among the s-Sr and f-Ce orbitals. In contrast, VB maxima splitting relies on the p–f coupling between p–Z (Z = S, Se, Te) and f-Ce orbitals.⁵⁹ The total amount of MM can be determined based on the number of unpaired electrons in the f-orbitals.⁵⁵ From Table 2, the value of total MM for all three compositions is 4 μ_B, which indicates that all magnetic spins are equally aligned and have significant magnetic order, leading to intense spin polarization. The small value of Sr and the considerable value of Ce indicate that Ce makes a greater contribution to the overall composition SrCe₂Z₄. The value of interstitial MM suggests that the regions between the atomic gaps also contribute to the overall magnetic response of these materials.

Table 2 List of the computed aspects (Δ_x(pf), Δ_x(f), N_oβ, N_oα, Sr, Ce, X, Int, and the total magnetic moments) for SrCe₂Z₄ (Z = S, Se, Te)

Compositions	Δx(f) (eV)	Δx(pf) (eV)	Noα	Noβ	Total (μB)	Int (μB)	Sr (μB)	X (μB)	Ce (μB)
SrCe2S4	−0.32	−0.945	−1.89	−0.732	4	0.151	0.007	0.005	0.952
SrCe2Se4	−1.047	−0.75	−1.056	−0.959	4	0.148	0.01	0.012	0.983
SrCe2Te4	−0.36	−0.45	−1.463	−0.403	4	0.154	0.008	0.04	0.97

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3.4. Transport properties

Thermoelectric materials can facilitate heat transformation into electrical power, and their efficiency is measured in the context of the power factor (PF) or Figure of Merit (ZT). These performance-determining parameters are calculated in terms of the thermal conductivity (κ), electrical conductivity (σ), Seebeck coefficient (S), power factor (S²σ), and the ZT.^61,62 The numerical values of these parameters are critical in deciding the applications of materials. Fig. 7 shows how different thermoelectric parameters change with T for SrCe₂S₄, SrCe₂Se₄, and SrCe₂Te₄. Fig. 7(a) demonstrates the graph between σ and T, indicating that σ rises with temperature, attributed to the increase in the thermally generated charge carrier concentration and their mobility.⁶³ Among the compositions studied, SrCe₂Te₄ showed the highest σ values because of its smaller E_g, leading to higher carrier concentration and mobility.

Fig. 7 Temperature-dependent variation of (a) σ, (b) k_e, (c) S, and (d) S²σ for SrCe₂Z₄.

Thermal conductivity (κ) measures how much heat can be transferred through a material. There are two parts of κ; electronic (κ_e) and lattice thermal conductivity (κ_L).⁶² Here, we can report the κ_e because the lattice part is beyond the computational capabilities of the BoltzTraP function. The variation of κ_e with T has been presented in Fig. 7(b), indicating that κ_e increases with T because more electrons can be thermally excited from the VB to the CB at the elevated temperature.⁴³ This leads to higher carrier concentration and higher mobility, which increases the κ_e.⁶³

Fig. 7(c) shows how the Seebeck coefficient changes with T. The Seebeck coefficient measures how much voltage is produced due to a 1 K temperature change in any material.⁶²

At lower temperatures, carrier concentrations are lower, leading to a higher S. So, as the T increases, the S decreases because of an increase in the carrier concentration and higher mobility. Higher mobility causes a reduction in voltage production, leading to a lower S at higher T.⁵⁶ The S value of SrCe₂S₄ is larger than that of other compositions because of its lower carrier concentration, leading to a higher S.⁶³ Fig. 7(b) shows the temperature-dependent electronic part of the thermal conductivity for SrCe₂Z₄. It is clear that SrCe₂Te₄ showed a higher value of thermal conductivity, which is attributed to a higher carrier concentration, higher mobility, and less phonon scattering as compared to other compositions. ZT and PF are key parameters that are employed to govern the thermoelectric efficiency of any material. The value of PF depends upon the value of σ and the S, and can be expressed as:⁶⁰

From Fig. 7(d), we can observe that the reported results of PF confirm the slight upsurges with the elevation of T. The value of PF will be higher when the product of σ and S square is the maximum value in semiconductors.⁶⁰ In Fig. 8(a), it has been observed that there is minimal phonon scattering at lower T, resulting in the usual scattering where the momentum and energy are conserved.⁶⁴ This leads to the elastic scattering of phonons, and there is thus a greater κ_L at the start. However, as T continues to rise, the scattering becomes more pronounced, due to which the energy and momentum are no longer conserved, causing a reduction in κ_L.⁵⁴ From Table 3, the value of PF for SrCe₂Te₄ is observed to be 4.90 W mK⁻² at RT. The value of ZT may be determined based on κ, S, and σ, employing the expression below.⁶⁰

Fig. 8 Temperature-dependent variation of (a) k_L and (b) ZT for SrCe₂Z₄.

Table 3 Thermoelectric parameters of SrCe₂Z₄ (where Z = S, Se, Te) at room temperature

Compositions	σ/τ (1/Ωm × 10^4)	κe/τ (W mK^−1)	S (mV K^−1)	PF (W mK^−2)	ZT	Ref.
SrCe2S4	0.97	0.106	0.14	3.6	0.60	This work
HgY2S4	24.1	0.49	223.36	1.20	0.72	44
MgLu2S4	1.91	0.46	245.6	1.15	0.74	45
MgY2S4	1.381	0.334	242.567	—	0.731	46
LiCr2S4	0.88	0.90	−94.43	0.79 × 10^−3	—	47
ZnMn2S4	9.48	6.61	7.46	0.05 × 10^−3	—	48
SrCe2Se4	1.05	0.14	0.17	4.20	0.70	This work
HgY2Se4	17.6	0.40	239.48	1.01	0.75	44
MgLu2Se4	1.82	0.42	239.1	1.04	0.75	45
MgY2Se4	1.150	0.248	230.585	—	0.739	46
LiCr2Se4	1.58	1.67	−64.20	0.66	—	47
ZnMn2Se4	11.58	8.11	6.60	0.05 × 10^−3	—	48
SrCe2Te4	1.17	0.168	0.196	4.9	0.94	This work
ZnMn2Te4	12.10	8.65	10.07	0.12 × 10^−3	—	48

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From Fig. 8(b), we can observe that with an increase in T, the value of ZT decreases due to the combined effect of κ and S.^57,60 At low T, the ZT value is higher due to the larger value of S and σ. So, when the T rises, the value of ZT decreases because of the increase of κ.^64,65 At higher T, the S and σ also decrease, resulting in a lower value of ZT. The calculated values of all thermoelectric parameters for SrCe₂S₄, SrCe₂Se₄, and SrCe₂Te₄ at room temperature are listed in Table 3. These values provide a quick reference for the thermoelectric performance of the studied material at room temperature.⁶⁶ The large ZT at room temperature ensures their applications for thermoelectric generators, effectively transforming heat into electrical power.⁶⁷

4. Conclusion

In summary, the structural, electrical, magnetic, and thermoelectric aspects of SrCe₂Z₄ (Z = S, Se, Te) have been systematically explored to validate their applicability for energy harvesting and spintronic implementations. In optimization, the released energy upon transition to the FM state and negative formation energy collectively ensured their structural and thermodynamic stability in FM states. The analysis of the spin-polarized band structure demonstrated the half-metallic ferromagnetic behavior of SrCe₂Se₄ and the ferromagnetic semiconducting nature of SrCe₂S₄ and SrCe₂Te₄. The Heisenberg model analysis showed that the Curie temperature ranged from 295–310 K, which is above room temperature, indicating ferromagnetism in these spinels. The DOS confirmed that the strong coupling of p-orbitals of chalcogens and the 4f-states of Ce governed the exchange mechanism of electrons, resulting in ferromagnetism. The investigation of direct and indirect exchange energy, along with exchange constants, ascertained the dropping of energy of the FM state and stabilized ferromagnetism. Moreover, Ce's magnetic moment distribution to the Sr and S/Se/Te sites was attributed to the electron exchange interactions, rather than the formation of a magnetic cluster of Ce ions. Finally, the bigger electrical and ultra-low thermal conductivity improved the power factor and figure of merit performances. The ZT value of 0.90 at room temperature for SrCe₂Te₄ showcased its potential for thermoelectric devices.

Conflicts of interest

There is no conflict to declare.

Data availability

All data included in this study may be obtained from the corresponding author on reasonable request.

Acknowledgements

This research was funded by the Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2025R7), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia. The authors express their gratitude to the Deanship of Scientific Research at Northern Border University, Arar, KSA, for funding this research work through the project number “NBU-FFR-2025-2985-18”.

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