Observation of cluster spin glass behavior in thermally decomposed nanocrystalline Sn_0.5Fe_0.5O_2−δ

Abstract

We report the structural and magnetic properties of nanocrystalline Sn_0.5Fe_0.5O_2−δ prepared by thermal decomposition of hexameric organotin ferrocenecarboxylate. The X-ray diffraction study revealed that Fe doping retains the tetragonal rutile structure of SnO₂. FTIR shows the presence of O–Sn–O stretching vibration. Microstructural investigation by FESEM and HRTEM indicated nanoparticle agglomeration and different orientations of lattice fringes with an interplanar spacing of 0.332 nm. The XPS analysis unveiled the incorporation of Fe³⁺ ions into the SnO₂ matrix. Mössbauer spectroscopy suggested the presence of Fe³⁺ ions in a distorted octahedral environment. Bulk magnetization and ac susceptibility studies assert the presence of competing ferromagnetic and antiferromagnetic interactions and a cluster spin glass state (T_g = 72 K) at low temperatures.

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Introduction

Dilute magnetic semiconductors (DMS) possessing good semiconducting and magnetic properties at room temperature have attracted intense interest due to their potential practical applications.^1–3 However, the origin of magnetic interactions in DMS is ambiguous.^4–8 Most models are based on the interactions among magnetic impurities mediated via free carriers or oxygen ions. Defects as well as non-magnetic dopant induced ferromagnetism have also been reported.^7,8 DMS are created by partially incorporating transition metal atoms such as V, Cr, Mn, Fe, Co, Ni and so on into the semiconductors. Among oxide semiconductors, tin oxide (SnO₂), a wide band gap semiconductor owing to its high transparency, chemical stability and electrical conductivity with interesting applications in solar cells, catalysis and gas sensing, is widely explored as a promising candidate in DMS research. Therefore, room temperature ferromagnetism in transition metal-doped SnO₂ was investigated by many groups.^9–26 In particular, partially Fe doped Fe–SnO₂ has displayed large magnetic moments²⁴ resulting in magnetic properties suitable for spintronic applications. Both p- and n-type behaviour has been observed in Fe–SnO₂ which depends on the Fe content and operating temperature.²⁷ More specifically, in Fe-doped SnO₂ systems, the addition of iron induces changes in SnO₂ properties, such as the band gap value, optical transmittance, grain size, grain boundary properties, electrical and magnetic behaviors, etc. Furthermore, apart from the interesting magnetic properties, Fe-doped SnO₂ was used to detect ethanol,²⁷ carbon monoxide,^28,29 hydrogen sulphide,³⁰ methane,³¹ acetone³² and humidity³³ and degrade rhodamine B in aqueous solutions.³⁴

The physical properties of Fe–SnO₂ can be tailored by altering its structure, composition and particle/grain size and it is sensitive to growth conditions. Various synthesis methods were employed to prepare Fe–SnO₂ samples in bulk, nanocrystalline and thin film forms.^{13,15,19,24,27–50} First principles calculations suggested that the ferromagnetic state is energetically favourable compared to the antiferromagnetic state in Fe doped SnO₂.¹⁰ Bulk Fe–SnO₂ exhibited room temperature ferromagnetism.¹⁶ Nanocrystalline Sn_1−xFe_xO₂ prepared by a cost-effective sol–gel route^35–38 also exhibited room temperature ferromagnetism. The maximum iron doping accomplished is 20% but the magnetic nature is unknown.³⁸ A polymeric modified Pechini process³⁹ with Sn(II)/Fe(II) and Sn(IV)/Fe(III) as starting reactants showed that Sn(IV)/Fe(III) was effective to get pure nanocrystalline Sn_1−xFe_xO₂ (x = 0.1). A one-step co-precipitation method^40–42 was successfully employed to get an x = 0.15 sample wherein the system displayed a combination of paramagnetism and weak ferromagnetism. A similar inference was obtained in the nanocrystalline Sn_1−xFe_xO_2−δ (x = 0.1) sample prepared using the high-energy ball milling method.⁴³ Nanocrystalline samples prepared using the hydrothermal method^34,44,45 also exhibited ferromagnetic behaviour. Room temperature ferromagnetism (T_c ∼ 610 K) in Sn_0.95Fe_0.05O₂ thin films⁴⁷ prepared using the pulsed laser deposition (PLD) method was explained using the ferromagnetic coupling of ferric ions via an electron trapped in oxygen vacancy (F-center exchange mechanism).⁵ The magnetic moment reduces drastically as x approaches a percolation threshold of 0.25.⁵ Other studies on Fe–SnO₂ thin films prepared by PLD also reported the role of oxygen vacancies near Fe atoms⁴⁸ or the importance of the double exchange mechanism²⁶ in Sn_1−xFe_xO₂ (x ≤ 0.4) in establishing the ferromagnetism in the system. In contrast, nanocrystalline Sn_0.8Fe_0.2O₂ films had a Fe₂O₃ impurity phase that displayed excitonic features due to 2p–3d hybridization.⁴⁹ The changes in electronic structure and magnetism of Fe–SnO₂ thin films grown by radio frequency magnetron sputtering^50,51 were attributed to bound magnetic polarons. Sn_1−xFe_xO₂ thin films deposited by the spray pyrolysis method⁵² exhibited secondary phases like β-Fe₂O₃ and β-Fe₃Sn as x changes from 0.078 to 0.396.

The increase in iron doping creates more oxygen vacancies in the SnO₂ structure. It stimulates the possibility of displaying an interesting magnetic behavior. To date, most of the studies on the Sn_1−xFe_xO₂ system were concentrated around x ≤ 0.2 in the bulk wherein the occurrence of ferromagnetic behaviour was ascribed to impurity band exchange or competing double and super exchange interactions or secondary phase or isolated magnetic impurity (ferric ion) interactions. A large x (∼0.4) was attempted in thin films and ferromagnetic behaviour was retained²⁶ unlike the spin glass nature predicted by the donor-impurity model at such high doping. More so, neither higher Fe doping in nanocrystalline Fe–SnO₂ was attempted nor the nature of magnetism and underlying magnetic interactions were investigated. To the best of our knowledge, no report on x ≈ 0.5 exists for this compound. To this end, using the thermal decomposition of the hexameric organotin drum [nBuSn(O)O₂CFc]₆ (Fc = ferrocenyl), we prepared nanocrystalline Fe doped SnO₂ wherein Fe and Sn are in equal proportions. In the present work, we report the structural, microstructural, X-ray photoelectron spectroscopy, Mössbauer spectroscopy, bulk magnetization and ac susceptibility studies on the nanocrystalline Sn_0.5Fe_0.5O_2−δ system.

Experimental details

Synthesis of the Sn_0.5Fe_0.5O_2−δmaterial

We chose the already reported, organostannoxane-supported hexaferrocene carboxylate, [nBuSn(O)O₂CFc]₆ (Fc = C₅H₅FeC₅H₄, ferrocenyl), 1 as the starting precursor for this work.⁵³ Because the Sn : Fe ratio is 1 : 1, achieving 50% Fe-doped SnO₂ is possible. Recently, we have successfully prepared tin(IV) oxide from the thermal decomposition of the hexameric organotin drum [nBuSn(O)O₂CR]₆ (R = 9-xanthenyl) by heating it to a temperature range of 600–900 °C.⁵⁴ This method has been adopted to prepare 50% Fe-doped SnO₂. Another reason for choosing 1 is that the presence of this molecule can be simply confirmed by the NMR (¹H and ¹¹⁹Sn) technique, and also the molecular structure is already established. The interesting aspect of 1 is that it comprises six ferrocenecarboxylate moieties attached to a central stannoxane Sn₆O₆ core that appears to be a drum-like structure. Thermogravimetric analysis (TGA) performed provides information about the thermal stability of the obtained compound. The thermogram shows that the drum compound is stable up to 300 °C (Fig. S1, ESI†). Above this temperature, 50% decomposition occurs and after ∼600 °C, the compound shows stable behavior. Based on these results, the drum compound was heated at 600 °C for 2 h using a muffle furnace (Scheme 1). An orange solid obtained after thermal decomposition was crushed and powdered for further analysis.

Scheme 1 Synthesis of 50% Fe doped SnO₂.

Material characterization

FT-IR spectra were recorded on a PerkinElmer instrument in the range 4000–400 cm⁻¹ using KBr pellets. The FT-IR technique was used to get information about metal–oxygen stretch. The FT-IR spectrum band at 593 cm⁻¹ can be related to the stretching mode vibration⁵⁵ of O–Sn–O/Sn–O–Sn/Sn–O (Fig. S2, ESI†). Thermal studies for compound 1 were carried out using an STA 6000 (PerkinElmer) instrument under a nitrogen atmosphere (20 mL min⁻¹) for 5.982 mg of sample in the temperature range of 30–700 °C. Furthermore, structural analysis with X-ray diffraction measurements was conducted in the reflection mode on an Empyrean PANalytical diffractometer (45 kV, 30 mA with Cu-K_α radiation with λ = 0.15406 nm). X-ray diffraction data were collected at a scanning rate of 0.0313° per second in the 2θ range from 10° to 80°. To record the X-ray diffraction (XRD) pattern, 10 mg of crushed sample was taken on zero-background silicon. The morphology of the material was examined by FE-SEM, and EDX analysis was performed using a Carl Zeiss (Ultra 55) instrument. The sample was carbon coated for FE-SEM analysis. HRTEM studies were carried out using a Tecnai G2 20 S-TWIN [FEI] instrument operated at an accelerating voltage of 200 keV. The sample was drop cast on a Cu grid for HR-TEM analysis. Oxidation states and chemical environment of elements were determined by XPS studies performed on a Kratos Axis Ultra instrument using monochromatic Mg K_α radiation. The Mössbauer spectrum of the material was recorded using a Mössbauer spectrometer operated in constant acceleration mode (triangular wave) in transmission geometry at room temperature. The source employed was ⁵⁷Co in the Rh matrix of strength 2 mCi. Calibration of the velocity scale was done by using an enriched α-⁵⁷Fe metal foil. The line width (inner) of calibration spectra was 0.26 mm s⁻¹. The isomer shift (δ) values are relative to the Fe metal foil (δ = 0.0 mm s⁻¹). Temperature and field dependent dc magnetic measurements were performed using a physical property measurement system (PPMS) (Dynacool, Quantum Design) with a vibrating sample magnetometer option (VSM). AC susceptibility measurements as a function of temperature at different frequencies were carried out using an ACMS (AC measurement system) option attached to the same PPMS setup.

Results and discussion

Fig. 1(a) shows the Rietveld refinement of room temperature powder XRD pattern of Sn_0.5Fe_0.5O_2−δ in the 2θ range 10°–80°. From the Rietveld refinement, it is confirmed that the sample crystallizes in a tetragonal structure (space group P42/mnm) with the lattice constants a = b = 4.734 Å and c = 3.173 Å and has a minor secondary phase of Fe_3−xSn_xO₄. A quantitative phase analysis through the Rietveld refinement estimated the amount of the impurity phase (Fe_3−xSn_xO₄) to be less than 2% and the impurity peak is marked with (*) in Fig. 1(a).

Fig. 1 (a) Rietveld refinement of room temperature XRD pattern for the Sn_0.5Fe_0.5O_2−δ. (220) plane of Fe_3−xSn_xO₄ is indicated by (*). (b) Williamson–Hall plot.

The average crystallite size (d) and lattice strain (ε) were estimated by employing the Williamson–Hall (WH) plot based on the equation β_FWHM Cos θ = kλ/d + 4ε Sin θ, where θ is Bragg's angle, β_FWHM is the full width at half-maximum corresponding to Bragg's peak, k is a constant equal to 0.89 and λ is the wavelength of Cu-K_α X-ray radiation (λ = 0.154 nm). The W–H plot for Sn_0.5Fe_0.5O_2−δ is shown in Fig. 1(b) which gives an average crystallite size (d) of 4.30 nm and a compressive micro-strain (lattice strain ε) of 3 × 10⁻³.

The crystal structure (Fig. 2) was constructed using the crystallographic information file (.cif) obtained by Rietveld refinement in 3D view with the help of VESTA software. It reveals that Sn/Fe atoms occupy the body center and corner positions of the unit cell. Every Sn/Fe atom is bonded with six oxygen atoms at octahedral positions and forms an octahedron as shown in Fig. 2b. Every unit cell consists of nine Sn/FeO₆ octahedra, out of which one is inside, and the remaining eight are at the corners of the unit cell.

Fig. 2 Structural model of Sn_0.5Fe_0.5O_2−δ. (a) Octahedra present in the tetragonal lattice and (b) octahedron formed by coordination of one Sn/Fe atom and six oxygen atoms.

Table 1 reports the structural parameters obtained from the Rietveld analysis of X-ray diffraction data collected at room temperature. In the refinement, cation occupancies were determined to be the same as the nominal values. The negligible iron oxide impurity phase in the XRD pattern implies that the magnetism and the underlying magnetic interactions are related to the properties of the host system and its oxygen off-stoichiometry, if any.

Table 1 Structural parameters and agreement indices obtained by Rietveld refinement of the room temperature X-ray powder diffraction pattern for Sn_0.5Fe_0.5O_2−δ

Parameter	Result
Space group	P42/mnm
Space group number	136
Crystal system	Tetragonal
No. formula units per unit cell	2
Cell parameters
a = b (Å)	4.734
c (Å)	3.173
Volume (Å^3)	71.10
Density (g cm^−3)	5.570
Atom coordinates
Sn/Fe (x, y, z)	0.0000, 0.0000, 0.0000
O (x, y, z)	0.2721, 0.2721, 0.0000
Occupancy
Sn	0.50
Fe	0.49
O	1.78
Bond distance (Fig. 2b)
Sn–O(1) (Å)	2.20
Sn–O(2) (Å)	2.20
Sn–O(3) (Å)	1.82
Sn–O(4) (Å)	2.20
Sn–O(5) (Å)	2.20
Sn–O(6) (Å)	1.82
Bond angles
O(1)–Sn–O(2) (°)	92.24
O(1)–Sn–O(3) (°)	90.00
O(1)–Sn–O(4) (°)	180.00
O(1)–Sn–O(5) (°)	87.76
O(1)–Sn–O(6) (°)	90.00
χ ^2	1.7
R p	19.7
R wp	19.0
R e	14.2

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FE-SEM image was recorded to gain knowledge about the surface morphology of the material (Fig. 3a). Film-like morphology of the prepared material can be observed from the FE-SEM images. The TEM image shows the presence of agglomerated circular particles having an average diameter of ∼8.5 nm (Fig. 3b). A concentric ring pattern in the selected area electron diffraction (SAED) image indicates the polycrystalline nature of the material (Fig. 3c). Lattice fringes present in the HR-TEM image (Fig. 3d) show an interplanar spacing of 0.332 nm which corresponds to the (110) plane⁵⁷ of SnO₂. Lattice fringes are rotated in different directions to show the random orientation of particles. The chemical composition revealed by EDX spectra yields Fe/(Fe + Sn) ≅ 0.5.

Fig. 3 (a) FE-SEM image, (b) TEM image, (c) SAED pattern, and (d) HR-TEM image of the synthesized material (the inset shows the calculated interplanar spacing).

X-ray photoelectron spectroscopy (XPS)

XPS spectra of the sample were recorded to know the oxidation states of elements. A survey scan of the sample shows the presence of mainly carbon C(1s), oxygen O(1s), tin Sn(3d) and iron Fe(2p) peaks (Fig. 4a). A C–C bond peak was observed at 284.6 eV which is considered a reference peak (Fig. S4, ESI†). The peak at 529.4 eV in O(1s) is due to the presence of the Fe–O bond⁵⁸ and the peak at 532.9 eV may occur due to H₂O adsorbed⁵⁹ on the Fe doped SnO₂ surface (Fig. 4b). In the Sn(3d) spectrum, a doublet with peaks at 489.1 and 497.6 eV for (3d_5/2) and (3d_3/2) with a peak separation (spin–orbit splitting) of ∼8.5 eV respectively suggests the presence⁶⁰ of the Sn⁴⁺ state of Fe/SnO₂. Another less intense deconvoluted doublet occurred at 485.8 eV and 494.1 eV assigned^56,61,62 to (3d_5/2) and (3d_3/2) respectively, indicating the presence of the Sn⁴⁺ oxidation state in different chemical environments (Fig. 4c). Other than these peaks, a single peak at 716.3 eV also occurred in the spectrum which belongs to Sn(3p_3/2)^63,64 of the Sn⁴⁺ state. In the Fe(2p) spectrum, the presence of Fe³⁺ was confirmed due to the presence of peaks⁶⁵ at 713.5 eV and 726.6 eV due to (2p_3/2) and (2p_1/2) lines respectively, with a separation (2p_1/2–2p_3/2) of 13.1 eV. A satellite peak⁶⁶ for Fe³⁺ was also observed at 719.5 eV which appears highly intense due to association with the Sn 3p_3/2 peak (Fig. 4d). A broad peak around 58.5–60 eV was assigned to the Fe³⁺ (3p) state (Fig. S5, ESI†). Additionally, a shoulder-type peak is also observed at about 53–56 eV. However, the absence of a doublet corresponding to Fe 2p in 709–710 eV⁶⁷ (Fig. 4) confirms no Fe²⁺ or Fe₃O₄ impurity. The oxygen deficiency content using the standard protocol turns out to be δ = 0.18 which is slightly less than δ = 0.25 expected from the charge neutrality of the nominal composition Sn_0.5Fe_0.5O_2−δ.

Fig. 4 XPS spectra: (a) survey scan, (b) O 1s, (c) Sn 3d and (d) Fe 2p.

Mössbauer spectroscopy

Knowledge of the local environment around the dopant atom is necessary to understand the underlying mechanism leading to magnetic order in the system. Therefore, a Mössbauer spectroscopy study was done to ascertain the oxidation state and local environment of Fe. The room temperature Mössbauer spectrum of Sn_0.5Fe_0.5O_2−δ shown in Fig. 5 exhibits a well-defined doublet indicating that the incorporated Fe-ions are paramagnetic and in the 3+ oxidation state in an octahedral environment. The presence of Fe²⁺ ions was not observed in the system. The Mössbauer spectrum measured even at a higher velocity (±11.5 mm s⁻¹) shows no sextet (six lines Zeeman splitting pattern) related to magnetically ordered Fe³⁺ ions but a doublet. The values of spectral parameters such as δ_IS – the isomer shift (relative to Fe metal foil), ΔE_Q – the quadrupole splitting, Γ – the full width at half maximum, R_A – the relative spectral area and the co-ordination number of the Fe ion are provided in Table 2. Larger electric quadrupole splitting suggests a different Fe environment and more distorted sites in the rutile structure. This is the case of the Fe³⁺ ions in the octahedral cage of oxygen ions with relatively large concentrations of oxygen vacancies leading to a distorted environment. The data quality of the Mössbauer spectrum is poor due to the very old (low strength) Mössbauer source used for the experiment and the nano-nature of the sample. Therefore, the impurity phase of Fe_3−xSn_xO₄ (∼2%) is not visible, which should show two sextets (tetrahedral and octahedral sites) with broader line widths in the Mössbauer spectrum.

Fig. 5 Mössbauer spectrum of Sn_0.5Fe_0.5O_2−δ showing a doublet due to Fe³⁺ ions present in the octahedral site. The inset shows the full-scale Mössbauer spectrum.

Table 2 Mössbauer spectral parameters of the Sn_0.5Fe_0.5O_2−δ sample at room temperature

Sample code	δ IS (mm s^−1)	ΔEQ (mm s^−1)	Γ (mm s^−1)	R A (%)	Fe-site (doublet)	Fitting quality (χ^2)
Sn0.5Fe0.5O2−δ	0.332 ± 0.006	0.938 ± 0.01	0.603 ± 0.016	100	Doublet-Fe^3+(VI)	1.16

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Magnetic properties

Fig. 6 shows the thermal evolution of magnetization in the temperature range of 2 K to 390 K measured in zero-field cooled (ZFC) and field-cooled (FC) modes. It can be seen that magnetization does not attain zero value even at 390 K suggesting the presence of magnetic order much above 390 K. It is interesting to see that FC magnetization at 2 K is 3 times the magnetization at 390 K. Magnetizations in ZFC and FC modes overlap with each other above a certain value of temperature, the so-called irreversibility temperature (T_ir ∼ 252 K) while deviating from each other below T_ir. This irreversibility suggests the presence of magnetic anisotropy in the system. Irreversibility in magnetization is observed in ferromagnets, spin-glass (SG), and superparamagnetic (SPM) systems. ZFC magnetization (M_ZFC) exhibits a peak at T_p = 72 K and decreases continuously with temperature. This type of feature in M_ZFC is generally seen in SG and SPM systems. On the other hand, FC magnetization (M_FC) increases continuously below T_p suggesting the presence of antiferromagnetic interactions at low temperatures.

Fig. 6 Field-cooled (FC) and zero-field-cooled (ZFC) temperature dependent magnetizations at 500 Oe for Sn_0.5Fe_0.5O_2−δ. Inset: M_FC–M_ZFC as a function of temperature.

In Fig. 7, M(H) hysteresis loops of the Sn_0.5Fe_0.5O_2−δ sample measured at 10 K, 50 K, and 100 K are shown. The inset shows the magnified view of MH data around the zero field. Finite coercivity (H_c) at these temperatures reflects the ferromagnetic (FM) character of the Sn_0.5Fe_0.5O_2−δ system. However, non-saturating MH loops at a magnetic field as high as 80 kOe suggest the presence of antiferromagnetic (AFM) correlations in the system. As the temperature increases from 10 K to 50 K, both remanent magnetization (M_r) and H_c values reduced drastically from 0.56 emu g⁻¹ to 0.1 emu g⁻¹ and 1500 Oe to 82 Oe, which eventually reach values of 0.02 emu g⁻¹ and 22 Oe, respectively at 100 K. This is in contrast to nanocrystalline Sn_0.95Fe_0.05O₂ whose H_c increased with temperature¹¹ which was attributed to freezing of superparamagnetic domains embedded in the antiferromagnetic matrix at low temperatures. Therefore, it can be inferred that both FM and AFM interactions are present in Sn_0.5Fe_0.5O_2−δ. The saturation magnetization at 10 K in H = 80 kOe reduces from 0.21 μ_B/Fe to 0.05 μ_B/Fe at 100 K.

Fig. 7 M–H loops of Sn_0.5Fe_0.5O_2−δ at different temperatures and the inset shows the magnified view of MH loops at low magnetic fields.

To gain more insights into the ground state of Sn_0.5Fe_0.5O_2−δ, ac susceptibility measurements were carried out. As shown in Fig. 8a, the real part of ac susceptibility shows a frequency dependent peak which is typical in spin glass (SG), cluster spin glass (CSG), and SPM systems. Generally, the Mydosh parameter, δ = ΔT_f/T_f[Δlog f], which quantifies relative peak temperature shift per decade of frequency is employed to distinguish canonical spin glass (CG) (0.005), SG (0–0.01), CSG (0.01–0.1) and SPM (0.1–1) systems.^69–72 The estimated Mydosh parameter for Sn_0.5Fe_0.5O_2−δ is 0.06(1) which suggests the system to be a cluster spin glass. This value is larger than 0.0189 found in nanocrystalline Sn_0.95Sn_0.05O₂¹¹ and 0.05(1) for Sn_0.9Fe_0.1O_2−δ¹² which reported SG behaviour. Furthermore, the frequency dependent peak temperature (T_P) is analyzed in terms of the critical slowing down (CSD) model,⁶⁹where τ₀ is the relaxation time, T_f is the glass temperature and zv is the critical exponent. As shown in Fig. 8b, the CSD model describes T_P(ω) data well yielding τ₀ = 4.7(3) × 10⁻⁹ s, T_f = 67.9(8) K, and zv = 9.2(5). For canonical SG: τ₀ = 10⁻¹²–10⁻¹³ s; for conventional spin glass: τ₀ = 10⁻¹⁰–10⁻¹³ s (zv = 4–12) while τ₀ = 10⁻⁷–10⁻¹⁰ s for cluster spin glass.^{70–73,75,76} Therefore, Sn_0.5Fe_0.5O_2−δ is a cluster spin glass at low temperatures.

Fig. 8 (a) Real part of the ac susceptibility as a function of temperature at a fixed driving field amplitude and different frequencies. Frequency-dependent peak temperature T_P fit using (b) the critical slowing down model and (c) the Vogel–Fulcher law for Sn_0.5Fe_0.5O_2−δ.

Moreover, fit based on the Vogel–Fulcher law,^69,70, where E_a/k_B is the activation energy per Boltzmann constant and T₀ is the coupling strength, yield E_a/k_B = 550.2(2) K and T₀ = 53.3(2) K reconfirming the glassiness of the system (Fig. 8c). is comparable to τ₀ = 3 × 10⁻¹⁰ s found for Sn_0.9Fe_0.1O_2−δ¹² wherein Fe exists in +2 and +3 oxidation states. For T₀ = 0, this law reduces to the Arrhenius law⁷³ often employed for SPM systems which clearly fails in the current context. Assuming the cluster's size to be related to their coupling strength, the ratio of E_a/k_B and T₀ is used as a measure of coupling/clustering strength among the dynamic entities that freeze at T_f. E_a/(k_BT₀) < 1 signifies the strong coupling between the magnetic entities while E_a/(k_BT₀) > 1 indicates the weak coupling^68,74 In our case, E_a/k_B ∼ 10T₀, suggests a weak coupling among the clusters and E_a/(k_BT₀) > 1 had been observed in cluster SG systems^75,76 which is consistent with our system. In view of the above observations, the cluster spin glass state of Sn_0.5Fe_0.5O_2−δ at low temperatures results due to the competing AFM and FM interactions. The FM character of the clusters is reflected in the finite values of H_c.

When a trivalent iron (Fe³⁺: 3d⁵, S = 5/2) replaces a tetravalent tin in the crystallographic structure, charge neutrality ensures the creation of one oxygen vacancy per two iron ions in the lattice. Furthermore, lower ionic radii Fe³⁺ (0.069 nm) substituting for Sn⁴⁺ (0.083 nm) retains the rutile structure of pristine SnO₂ but disturbs the arrangement of the oxygen octahedral cage wherever it replaces the Sn ion. This is reflected in the large electric quadrupole splitting. The chemical formula based on XPS analysis can be written as Sn⁴⁺_0.5Fe³⁺_0.5O²⁻_2−δ where δ is the oxygen off-stoichiometry associated with the presence of oxygen vacancies. In epitaxial thin films of Sn_1−xFe_xO₂ (x = 0–0.4),²⁶ it was argued that a substantial fraction of Fe led charge compensation results in oxygen vacancies and holes. Room temperature saturation moment (coercivity) increased from 0.12 μ_B/Fe (300 Oe) for x = 0.1 to 0.71 μ_B/Fe (800 Oe) for x = 0.4. The origin of ferromagnetism²⁶ was attributed to dominant FM double exchange (Fe²⁺−O²⁻−Fe³⁺ and Fe³⁺−O²⁻−Fe²⁺) interactions over AFM superexchange (Fe³⁺−O²⁻−Fe³⁺ and Fe²⁺−O²⁻−Fe²⁺) interactions. On the other hand, the donor impurity band exchange mechanism⁵ was proposed to explain the existence of large moments and ferromagnetism in dilute ferromagnetic oxides. In particular, in the case of the Fe–SnO₂ system, F-center exchange mechanism⁴⁷ was invoked wherein F-centers created due to oxygen vacancies (□) trap spin polarized electrons leading to ferromagnetic Fe³⁺−□−Fe³⁺ interactions that dominate over existing antiferromagnetic Fe³⁺−O²⁻−Fe³⁺ superexchange interactions. These shallow donor electrons form bound magnetic polarons coupling the adjacent magnetic cations within their hydrogenic radius (ν). For large enough ν, δ > δ_p (polaron percolation threshold) and x < x_p (cation percolation threshold), this model⁵ predicts the occurrence of room temperature ferromagnetism. For the Sn_1−xTM_xO₂ system, δ_p = 0.001 and x_p = 0.25 where TM is the magnetic transition metal. When x > x_p, antiferromagnetic or ferrimagnetic behavior is predicted as there are continuous paths throughout the lattice joining nearest-neighbor cations so much so that the net magnetic moment drastically vanishes. This impurity band model fails when δ increases, as the donor state merges with the bottom of the conduction band and the system behaves as a spin glass system whose description can be understood in terms of the Ruderman–Kittel–Kasuya–Yosida (RKKY) exchange interaction. In the present case of highly doped Sn_0.5Fe_0.5O_2−δ (x = 0.5 and δ = 0.25), the Fe³⁺−Fe³⁺ interaction pathways are nearest neighbour (AFM Fe³⁺−O²⁻−Fe³⁺ and FM Fe³⁺−□−Fe³⁺) and next-nearest neighbour (Fe³⁺−O²⁻−Sn⁴⁺−O²⁻−Fe³⁺, Fe³⁺−□−Sn⁴⁺−O²⁻−Fe³⁺, Fe³⁺−O²⁻−Sn⁴⁺−□−Fe³⁺ and Fe³⁺−□−Sn⁴⁺−□−Fe³⁺) interactions. Among them, the nearest neighbour interactions (antiferromagnetic Fe³⁺−O²⁻−Fe³⁺ and ferromagnetic Fe³⁺−□−Fe³⁺) play a pivotal role in governing the magnetic behavior of the dilute Fe-doped SnO₂ system (x < x_p). However, in the Sn_0.5Fe_0.5O_2−δ (x > x_p and δ > δ_p) system, neither the donor impurity band exchange nor RKKY exchange mechanisms could explain the observed cluster spin glass behavior at low temperatures. More so, the contributions from next-nearest neighbour interactions, however small, become significant in addition to the existing nearest-neighbour (AFM Fe³⁺−O²⁻−Fe³⁺ and FM Fe³⁺−□−Fe³⁺) interactions as the probability of finding an Sn⁴⁺ ion as the nearest neighbor to Fe³⁺ ion is 1/2. Eventually, these competing interactions lead to the cluster glass behavior at low temperatures. The finite coercivity at temperatures T < T_g corresponds to those of the FM clusters embedded in the AFM matrix. The dominant AFM correlations of the matrix are reflected in the upturn in magnetization at low temperatures. We believe that as temperature increases above T_g, the AFM state survives and may transform into a paramagnetic state above 390 K.

Conclusions

A thermally decomposed nanocrystalline Sn_0.5Fe_0.5O_2−δ sample was characterized by XRD, FTIR, FESEM, HRTEM, XPS, Mössbauer spectroscopy, bulk magnetization and ac susceptibility measurements. The Rietveld refined XRD data showed the single-phase compound (≈98%) exhibiting a tetragonal rutile structure and an average crystallite size of 4.3 nm. FTIR confirmed the presence of stretching vibration mode of the O–Sn–O group at ∼593 cm⁻¹. FESEM displayed a platelet-like surface while HRTEM showed nanoparticle agglomeration and reconfirmed polycrystallinity through the SAED pattern. EDX confirmed the presence of Fe and Sn in equal proportions. XPS and Mössbauer studies verified the trivalent nature of Fe and its distorted oxygen environment due to oxygen vacancies. The magnetic study (M–H, M–T and ACS) showed evidence for (i) competing ferromagnetic and antiferromagnetic interactions involving Fe³⁺ ions and (ii) cluster spin glass state at low temperatures and magnetic ordering temperature much above room temperature.

Author contributions

A. S.: investigation, formal analysis, validation, and visualization. K. D.: investigation. M. V.: investigation, visualization, and formal analysis. S. S. M.: investigation, formal analysis, and visualization. Y. B.: investigation, formal analysis, methodology, visualization, and validation. R. T.: conceptualization, methodology, resources, supervision, and funding acquisition. All the authors contributed to writing the manuscript.

Conflicts of interest

There are no conflicts of interest to declare.

Acknowledgements

AS is thankful to CURAJ for the University Fellowship. KD & MV gratefully acknowledge UGC for Senior Research Fellowships. RT thanks the Council of Scientific and Industrial Research, India (grant no. 01(2970)/19/EMR-II dated: 20th June 2019 to Ramalingam Thirumoorthi). We are thankful to IISc Bangalore for FE-SEM and XPS analysis, MNIT Jaipur for HR-TEM, BARC Mumbai for Mössbauer spectroscopy, and CURAJ for instrumental facilities (PXRD and PPMS).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4ma00077c

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